Session 1: Applied Harmonic Analysis and Operator Theory

Organizers:
Javed Mashreghi (Université Laval, Canada, contact organizer)
Akram Aldroubi (Vanderbilt University, USA)
Rocio Diaz Martin (Vanderbilt University, USA)

Brief Summary: The emergence of wavelet theory in the early 1990s has provided a powerful tool for signal processing, data compression, and image analysis, while compressed sensing has become a common method in various areas of mathematics, engineering, and life sciences. At the core of these developments lies the general theory of sampling in shift-invariant spaces, frame theory, and operator theory. Specifically, the wavelet transform can be seen as a type of sampling and representation in shift-invariant spaces, while frame theory provides a connection to operator theory. Compressed sensing, on the other hand, relies on both sampling theory and operator theoretical methods. Additionally, the scattering transform has emerged as a crucial tool for machine learning, offering a framework for deep learning and neural networks. The interaction between applied harmonic analysis, functional analysis, and operator theory has led to significant advances in these fields, with methods that have practical applications in communication theory, signal processing, learning theory, and biomedicine. For instance, this interaction has helped solve fundamental problems in mathematics, such as the Kadison-Singer/Feichtinger conjecture and the Kato conjecture. Despite the significant progress in these fields, many classical questions in the study of Hilbert spaces of analytic functions, such as the characterization of zero sets, uniqueness sets, boundary behavior, invariant subspaces, and cyclicity, remain largely open, with only partial answers available. To promote further interaction between functional analysis, operator theory, harmonic analysis, and their applications, in this session we will focus on topics such as learning theory, sampling, frames, compressed sensing, high-dimensional data geometry, control theory, and operator classes. The primary goal of the session is to provide a platform for experts in these areas to exchange ideas, identify common problems, and explore new trends.

Session 2: Coding Theory

Organizers:
Henry Chimal-Dzul (University of Notre Dame, USA, contact organizer)
Maria Chara (Universidad Nacional del Litoral, Argentina)
Hiram H. Lopez (Virginia Tech, USA)
Luciane Quoos (Universidade Federal Rio de Janeiro, Brazil)

Brief Summary: Coding theory, a field that emerged over 60 years ago to ensure reliable information transmission, has remained a vibrant area of research. Its significance lies in its profound connections to various branches of mathematics, such as algebra, number theory, algebraic geometry, and combinatorics. In recent years, coding theory has undergone significant advancements to meet the demands of increasingly challenging modern applications, including the 6G platform, quantum computations, secure protocols for post-quantum cryptography, and distributed storage systems. Notably, certain classes of codes have garnered considerable attention, including low-density and moderate-density parity-check codes, evaluation codes and their association with Grobner basis, self-orthogonal and self-dual codes, and locally repairable codes. Despite the huge advances in the field, fundamental questions like determining the length, minimum distance, dimension, and error floor of these classes of codes are still challenging and primary for modern applications of coding theory. The main goal of this session is to provide a space for people from the Americas at different stages of their careers, from students to senior researchers that investigate fundamental questions and applications in coding theory and related areas, to exchange ideas and explore new trends in the field.

Session 3: Geometric Variational Problems in Smooth and Nonsmooth Metric Spaces

Organizers:
Reinaldo Resende (Carnegie Mellon University, USA, contact organizer)
Stefano Nardulli (Federal University of ABC, Brazil)
Paolo Piccione (University of Sao Paulo, Brazil)
Christina Sormani (Lehman College CUNY and CUNYGC Graduate Center, USA)

Brief Summary: This session aims at offering an engaging exploration of research at the intersection of Geometric Analysis and Geometric Measure Theory (GMT), with an emphasis on variational problems. The program is designed to give space to the latest advancements in geometric analysis within both smooth and nonsmooth settings. Variational problems have long been attracting researchers from diverse mathematical backgrounds, and this session will provide a platform for specialists and young researchers in the field to share their insights.

This session will provide an opportunity to delve into the frontier of geometric analysis, where the elegance of mathematical theory meets the complexities of real-world phenomena. The thematic session will include but not be limited to: Curvature flows and their geometric applications; Geometric aspects of minimal surfaces and soap bubbles; Isoperimetric and partitioning problems; Nonsmooth analysis and variational principles in metric spaces.

The calculus of variations and GMT offer a venue to underlie principles governing various physical phenomena and optimize complex systems. It uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals. The study of geometric variational problems is one of the oldest and most fascinating topics in the Calculus of Variations and GMT. Solutions of geometric variational problems describe equilibrium configurations of physical systems. Their study is then of fundamental importance both in applications and in pure Mathematics. Some central problems in the theory include: solutions of boundary value problems for the Laplace equation satisfying Dirichlet's principle, and the Plateau problem in which it is required to find a surface of minimal area that spans a given contour in space: a solution can often be found by dipping a frame in soapy water. Although such experiments are relatively performable, their mathematical formulation is far from simple.

Session 4: Number Theory through the Americas

Organizers:
Matilde Lalın (Universite de Montreal, Canada, contact organizer)
Guillermo Mantilla-Soler (Universidad Nacional de Colombia, Colombia)
Amalia Pizarro-Madariaga (Universidad de Valparaıso, Chile)

Brief Summary: Number Theory in the Americas, and in particular in South and Central America has long been characterized by high quality work produced by a relatively small number of very strong researchers, with collaborations limited by geographical constraints and isolation. The level of communication among Number Theorists in the Americas was positively shaken by the COVID-19 pandemic and the popularization of online seminars and activities that arose as a result of the situation. As the world went back to more regular pre-pandemic activities, it became more difficult to attract speakers and participants to online activities. It is now clear that, while online activities have a central role to play in supporting and maintaining mathematical connections, in person activities are essential to catalyze collaborations. The goal of this special session is to gather Number Theorists from the whole continent in order to facilitate the exchange of ideas and foster new collaborations. The session will feature mathematicians working in diverse areas including analytic number theory, algebraic number theory, arithmetic geometry, arithmetic statistics, computational number theory, and other topics.

Session 5: Convexity, High-Dimensional Probability and Applications

Organizers:
Steven Hoehner (Longwood University, USA, contact organizer)
Umut Caglar (Florida International University, USA)
Julian Haddad (Universidad de Sevilla, Spain)
Galyna Livshyts (Georgia Institute of Technology, USA)

Brief Summary: High-dimensional convexity is a very active research area, which studies properties of objects in high dimensions, using the tools of probability and analysis (among others), and various phenomena often stem from convexity — be it convexity of sets, functions or functionals. The fields of convex geometry and probability have become increasingly connected in the past several decades, especially in view of their numerous applications to asymptotic geometric analysis, high-dimensional statistics and computer science. Recently, substantial progress has been made on some of the main problems in convexity, such as the KLS conjecture, the Thin Shell conjecture, and Bourgain’s slicing problem, and this progress has resulted in even faster development in these areas in recent years. Several recent ICM talks were dedicated to this subject, most notably the talks by Keith Ball and Ronen Eldan. Therefore, our session is timely and important, and will allow the researchers to share new ideas and developments, as well as discuss new results and emerging trends for future research activities. Connections between these areas, as well as their applications, will have a special highlighted focus in this session.

Session 6: Discrete Homotopy Theory

Organizers:
Chris Kapulkin (University of Western Ontario, Canada, contact organizer)
Anton Dochtermann (Texas State University, USA)
Antonio Rieser (Centro de Investigación en Matemáticas (CIMAT), Mexico)

Brief Summary: Discrete homotopy theory is an interdisciplinary area in which techniques from algebraic topology are adapted and extended to study combinatorial objects such as graphs. It has found numerous applications, including to hyperplane arrangements, geometric group theory, coarse geometry, graph colorings, digital imaging, as well as network and data analysis. By varying the choice of graphs and graph maps, the notion of product, etc., a variety of models of the theory have been proposed and studied for different applications.

In recent years, discrete homotopy theory has seen rapid growth, driven primarily by mathematicians from North American universities, and an increased interest from researchers working in other areas of mathematics. The goal of this special session is to present these recent developments to the broader mathematical community.

Session 7: Symbolic Dynamics and Combinatorial Algebras

Organizers:
Daniel Gonçalves (Universidade Federal de Santa Catarina, Brazil, contact organizer)
Maria Isabel Cortez (Pontificia Universidad Católica de Chile, Chile)
Charles Starling (Carleton University, Canada)
Ronnie Pavlov (University of Denver, USA)

Brief Summary: Symbolic dynamics is devoted to studying a particular family of group actions on the Cantor set called subshifts. Its origins go back to Hadamard’s work on coding geodesics of surfaces, but it is now a vibrant area of research in its own right. Many problems studied in symbolic dynamics involve viewing subshifts as topological dynamical systems or measure-theoretic objects, and so many open problems are stated in analytic terms.

As in many other areas, researchers were eventually able to recast some of these problems in algebraic terms, which allowed for the usage of new techniques. In symbolic dynamics, one of the most important examples of this phenomenon came from the foundational work of Giordano, Putnam, and Skau, who demonstrated a connection between various dynamical properties of Cantor systems and associated objects from algebraic K-theory. Another direction involves using C∗-algebras to encode the structure of dynamical systems. It took researchers some time to fully realize that partial dynamics can be profitably captured by certain generalizations of groups: groupoids and their cousins, inverse semigroups.

Two essential aspects of this intersection between dynamics and algebraic objects (including operator algebras and non-commutative algebras) are the rigidity and classification program of C∗-algebras and their algebraic parallels. Roughly speaking, rigidity treats the question: if the algebraic objects arising from two dynamical systems are the same, must the dynamical systems themselves be the same/similar in some appropriate sense?

Our goal is to gather together experts in symbolic dynamics, K-theory, C∗-algebras, graph algebras, and other related fields in a collaborative setting to meet and exchange ideas, as such interdisciplinary discussion is fundamental for providing new insights as well as identifying new research problems.

Session 8: Global Injectivity, Jacobian Conjecture and Related Topics

Organizers:
Francisco Braun (Universidade Federal de São Carlos, São Carlos, Brazil, contact organizer)
Luis Renato Gonçalves Dias (Universidade Federal de Uberlândia, Brazil)
Frederico Xavier (Texas Christian University, USA)

Brief Summary: The problem of finding conditions in order to guarantee that a local diffeomorphism F : M → M, M a smooth manifold, is global has long ago called the attention of researchers from different areas of mathematics. From the so called Hadamard global invertibility criterion, passing through conditions of Gale-Nikaedô in the Jacobian matrix of F, then to spectral conditions in R₂, there has been done a lot of work in order to understand the basics mechanisms insuring the global invertibility of F. Also, some related topics have been developed motivated by the invertibility problem, as for instance regular foliations and qualitative theory of dynamical systems. Anyway, the heart of this session is the celebrated Jacobian conjecture, that a polynomial local diffeomorphism of C_n is an automorphism. This conjecture, still open for all n ≥ 2, is included in Smale’s list of mathematical problems for this century.

Nowadays there is around the world a lot of activity on the subject of global invertibility, studying the Jacobian conjecture in particular. Our main motivation for this section is to gather together the most prominent and enthusiastic researchers in this subject for discussion about recent advances, ongoing works, aims of the subject for next years, and so on.

Session 9: Hopf Algebras and Tensor Categories

Organizers:
Iván Angiono (Universidad Nacional de Córdoba, Argentina, contact organizer)
César Galindo (Universidad de los Andes, Colombia)
Julia Plavnik (Indiana University, USA)

Brief Summary: Tensor categories and their realizations via Hopf algebras have appeared in many branches of mathematics, as well as in physics and computer science. Besides occurring in a diverse range of settings in the study of classical and quantum symmetry, these objects also provide an important link between algebra and topology via diagrammatic methods. Novel and innovative usage of diagrammatic methods has led to many recent advances in the classification programs for von Neumann algebras, knots and 3-manifolds, and models for topological quantum computers. Examples include the discovery of the Jones and HOMFLY polynomial knot invariants and the provision of the framework for quantum field theories. The study of tensor categories also plays a key role in the development of higher category theory.

In this Special Session, we aim to bring together researchers whose work involves the exploration of categorical structures in different contexts, and consequently, the proposed speakers study Hopf algebras, tensor categories, categorification, subfactors, and representation theory. We will ensure that a wide variety of researchers at different stages of their careers will attend and from different countries of the Americas, including several from underrepresented groups.

Session 10: Nonlinear Analysis on Banach Spaces

Organizers:
Javier Alejandro Chávez-Domínguez (University of Oklahoma, USA, contact organizer)
Bruno M. Braga (IMPA, Brazil)
Verónica Dimant (Universidad de San Andrés, Argentina)

Brief Summary: Banach spaces are complete normed spaces and, as such, the most natural approaches to understanding them are given by linear methods which take into account their vector space structures. However, nonlinear methods have been used since the early days of the area and this special session aims to bring together researchers throughout the Americas working in two rather different nonlinear aspects of Banach spaces with the aim of fostering interactions between them.

The first such approach is to look at Banach spaces simply as metric spaces, and look at the nonlinear maps that are relevant from this metric point of view. Surprisingly, metric information about Banach spaces may completely ordain their linear structure: the famous Mazur-Ulam theorem says that any surjective metric isometry between (real) Banach spaces preserving zero is automatically linear. For some spaces, even much weaker notions of equivalence are already strong enough to completely determine the linear structure. While the focus on linear methods had been prevalent for quite some time, for the last 2-3 decades this has been changing significantly motivated by several striking results which allow one to obtain linear outputs based on nonlinear inputs.

The second approach emphasizes certain maps which despite being nonlinear are intimately related to the linear structure, namely polynomials (which are restrictions of multilinear maps) and their natural companions: holomorphic mappings. The subject arose since the beginnings of functional analysis, and the next great leap in the area came in the 1960's/1970's in the Americas, with Nachbin's group in Brazil. Ever since, a number of particularly interesting areas in this field have blossomed. Some of these issues have also begun to be developed in the noncommutative context of operator spaces, with an impact on quantum information theory.

Session 11: Non-Standard Orthogonal Polynomials, Special Functions, and Harmonic Analysis: Recent Trends and Applications

Organizers:
Wilfredo Urbina Romero (Roosevelt University, USA, contact organizer)
Héctor Pijeira (Universidad Carlos III de Madrid, Spain)
Yamilet Quintana (Universidad Carlos III de Madrid, Spain)
Luis E. Garza (Universidad de Colima, Mexico)

Brief Summary: Non-standard orthogonal polynomials, special functions, and harmonic analysis are three well-established research areas in mathematical analysis. As is well-known, the last two subjects are considered classical, and there exist a large number of interesting developments in recent times. These developments are characterized by an original approach and an in-depth study of both theoretical and applied problems. Non-standard orthogonal polynomials refer to a class of orthogonal polynomials that deviate from conventional systems such as Legendre, Chebyshev, or Hermite polynomials. While these standard orthogonal polynomials have well-established properties and applications, non-standard orthogonal polynomials offer alternative mathematical frameworks for specific purposes. Specifically, Sobolev orthogonal polynomials, a subclass of non-standard orthogonal polynomials, arise in the theory of Sobolev spaces. They possess important properties related to orthogonality, differential operators, and approximation capabilities. The study of these polynomials contributes to understanding and solving problems in partial differential equations, approximation theory, and numerical methods. Since Sobolev orthogonal polynomials, special functions, and harmonic analysis are often driven by applications, these subjects have found numerous applications in various branches of mathematics. These applications include partial differential equations (PDEs), quantum mechanics, probability theory, number theory, signal processing, engineering, physics, astronomy, integrable systems, optics, quantum chemistry, computer science, and more. These examples highlight the broad impact of Sobolev orthogonal polynomials, special functions, and harmonic analysis across different areas of mathematics, as well as their significant contributions to problem-solving, which continue to grow.

The aim of this Special Session is to present recent trends and applications associated with these subjects and related topics.

Session 12: Harmonic Analysis in Geometric Tomography

Organizers:
Kateryna Tatarko (University of Waterloo, Canada, contact organizer)
Efrén Morales Amaya (Universidad Autónoma de Guerrero, Mexico)
Dmitry Ryabogin (Kent State University, USA)
Vladyslav Yaskin (University of Alberta, Canada)

Brief Summary: Geometric tomography deals with the retrieval of information about geometric objects based on the size of their sections, projections, or other tomographic data. Methods of harmonic analysis play a key role in geometric tomography. One of the earliest applications of harmonic analysis to sections of convex bodies goes back to Laplace and his formula for the area of a central section of the cube. A systematic use of spherical harmonics in the study of convex bodies began in the early 20th century: they were employed by Hurwitz in his proof of the isoperimetric inequality, and by Funk and Minkowski in the study of injectivity properties of the Radon transform, which yielded various uniqueness results for sections and projections of convex bodies. In recent times new methods based on the Fourier transform paved a way to various exciting developments in the field. They led to the solution of a number of long-standing problems including the Busemann-Petty problem, problems about extremal sections and projections of ℓp-balls, the Klee and Bonnesen problems, Ulam's problem, and many others.

The first goal of this special session is to use the momentum and foster interactions between harmonic analysis and geometric tomography. The second goal is to identify new potential applications. This area of research has connections with many other areas of mathematics (including discrete geometry, functional analysis, information theory), as well as other disciplines (including computer science, materials science, computerized tomography, to name a few). Finding new applications and bringing methods from other areas would be of paramount importance.

Session 13: Influences of Combinatorics and Topology in Commutative Algebra

Organizers:
Sara Faridi (Dalhousie University, Canada, contact organizer)
Susan Morey (Texas State University, USA)
Rafael Villarreal (CINVESTAV, Mexico)

Brief Summary: The influence of combinatorial and topological techniques in commutative algebra goes back many decades. Some of the best known such results are from works of Stanley and Hochster in the 1970's which led to Stanley's proof of the upper bound conjecture for simplicial spheres, and to Reisner's characterization of Cohen-Macaulay monomial ideals in terms of simplicial homology.

The development of edge ideals in the 1990's renewed interest in the subject, with the resulting publications expanding into various areas of mathematics: algebra, topology, discrete mathematics, representation theory and combinatorial optimization, among others.

The purpose of our session is to bring together people who have been studying the relations between combinatorics, topology, and algebra from these perspectives.

Session 14: Galois Representations and Automorphic Forms

Organizers:
Daniel Barrera Salazar (Universidad de Santiago de Chile, Chile, contact organizer)
Luis Alberto Lomelí (Pontificia Universidad Católica de Valparaíso, Chile)
Giovanni Rosso (Concordia University, Canada)
Claus Sorensen (UC San Diego, USA)
Jeanine Van Order (Pontifícia Universidade Católica do Rio de Janeiro, Brasil)

Brief Summary: A major quest in algebraic number theory today is to understand the absolute Galois group G_F of a number field F.

Since the 1960s, Robert Langlands has proposed a vast array of conjectural correspondences that would link finite dimensional representations of G_F with harmonic analysis via automorphic representations. This viewpoint has driven some of the most spectacular advances in the field over the past four decades, including the proof by Wiles et alia of the Taniyama-Shimura conjecture (which resolved Fermat’s Last Theorem) and the Sato-Tate conjecture.

This MCA Special Session seeks to highlight some recent contributions to the study of automorphic representations and their corresponding Galois representations – interpreted broadly – made by mathematicians based in the Americas.

We seek to highlight the contributions of emerging leaders, especially those from or connected to Latin America.

Session 15: Integrable Probability and KPZ Universality

Organizers:
Cesar Cuenca (The Ohio State University, USA, contact organizer)
Leonid Petrov (University of Virginia, USA)

Brief Summary: The field of Integrable Probability has recently seen explosive growth, powered by its connections to diverse areas such as algebraic combinatorics, representation theory, mathematical physics, and solvable lattice models in statistical mechanics. These developments are key in understanding the KPZ universality class, which describes various growth processes, random surfaces, and interacting particle systems, highlighting deep mathematical structures and unexpected connections between seemingly unrelated models. The session will bring experts in integrable and analytic aspects of growth models, random surfaces, interacting particle systems, and KPZ universality, who will present a state-of-the-art picture of the area.

Session 16: Special Session in Representation Theory of Algebras

Organizers:
Sonia Trepode (Universidad Nacional de Mar del Plata, Argentina, contact organizer)
Ibrahim Assem (Université de Sherbrooke, Canada)
Yadira Valdivieso Diaz (UDLAP, Mexico)
Flavio Ulhoa Coelho (Universidade de São Paulo, Brazil)
Ralf Schiffler (University of Connecticut, USA)

Brief Summary: The representation theory of algebras is one of the most active areas of mathematics. It grows in symbiosis with other branches, such as algebraic geometry, homological algebra, Lie theory, quantum groups and more recently the theory of cluster algebras. It has an important presence on the American Continent: representation theorists can be found in Canada, the U.S., Mexico, Colombia, Brazil, Argentina and Uruguay. All these groups are linked by several long-term collaborative projects.

Our Special Session in the Mathematical Congress of the Americas covers the following topics: structure of the category of modules, homological methods including Hochschild cohomology, conjectures and invariants in the representation theory of algebras, derived categories, triangulated categories and tilting, the Auslander-Reiten quiver, the combinatorial aspects of the representation theory of algebras, and its relations with cluster algebras, algebraic geometry and Lie algebras.

All of these topics are at the heart of the collaboration between representation theorists of this continent. We hope to stimulate discussions between participants on open problems and conjectures of the theory, in particular in those topics mentioned above. Our objective is to help creating new links between research groups operating in different countries and in different subdomains of the theory and to contribute to the education of those young students and post-doctoral fellows who will be present.

Session 17: Graph Theory and its Applications

Organizers:
Jonnathan Rodriguez (Universidad de Antofagasta, Chile, contact organizer)
M. Gabriela Araujo-Pardo (UNAM, Mexico)
Linda Lesniak (Western Michigan University, USA)
Luis Medina (Universidad de Antofagasta, Chile)

Brief Summary: In graph theory, we emphasize research aspects according to their structural, combinatorial and/or spectral properties, and their applications in mathematics and other disciplines. Related to spectral graph theory it is important to say that several types of matrices can be associated with every graph; the study of eigenvalues and eigenvectors of these matrices gives rise to Spectral Graph Theory. The foundations of spectral graph theory were laid in the 1950s and 1960s, because of the work of a considerable number of mathematicians. Most of the early results are concerned with the relation between spectral and structural properties of a graph.

The principal objective of this session is to offer a platform to disseminate the research of various experts in various countries in America, exchange ideas, identify common problems, and explore new techniques in Graph Theory. The principal objective of this session is to offer a platform to disseminate the research of various experts in various countries in America, exchange ideas, identify common problems, and explore new techniques in Graph Theory.

Session 18: Automorphisms, Derivations, and Identities of Algebras

Organizers:
Ualbai Umirbaev (Wayne State University, USA, contact organizer)
Ivan Shestakov (University of Sao Paulo, Brazil)
Faber Gomez Gonzalez (Universidad de Antioquia, Colombia)

Brief Summary: Over the past 40-50 years, many long-standing conjectures about the structure of automorphisms, derivations, and identities of commutative, associative, Lie, Jordan, alternative algebras, etc. have been resolved, often through the introduction of new methods that are quickly becoming central to the field. The well-known Burnside problem for groups was solved by E. Zelmanov, Specht's problem for associative algebras was solved by A. Kemer, the first examples of wild automorphisms of polynomial and free associative algebras were found, the equivalency of the Jacobian Conjecture and the Dixmier Conjecture was discovered by Y. Tsuchimoto and by A. Belov-Kanel and M. Kontsevich, and A. Giambruno and M. Zaitsev, etc proved the Amitsur Conjecture of PI exponent. All these results greatly affected and extended the area.

Despite the enormous progress in this field, many interesting problems, such as the Specht property of Lie algebras, the Jacobian conjecture, the Cancellation conjecture, the Linearization problem, the Belov-Kanel and Kontsevich conjecture on automorphism groups of Weyl and symplectic Poisson algebras, many questions on the structure of free algebras, their subalgebras, and numerical invariants in various varieties of algebras, and the identities of simple algebras and superalgebras remain open.

This session aims to bring together researchers from the Americas and the world, working in the field of combinatorial algebra, sharing the latest results and challenges in this field.

Session 19: Nonlinear Evolution Equations: Trends in Control Theory and Related Topics

Organizers:
Roberto Capistrano-Filho (Federal University of Pernambuco, Brazil, contact organizer)
Valeria Cavalcanti (State University of Maringá, Brazil)
Fernando Gallego (National University of Colombia - Manizales, Colombia)

Brief Summary: The area of Partial Differential Equations (PDEs) is an important research topic in both pure and applied mathematics. It is also an interdisciplinary area that involves Physics, Engineering, Biology, and many other fields. The topics, above mentioned, encompass various fascinating areas in the field of partial differential equations (PDEs) and their applications. The initial boundary value problem of dispersive systems focuses on describing wave-like phenomena, where different frequencies propagate at varying speeds, and methods such as Fourier analysis and numerical techniques are employed for resolution. Control theory and inverse problems for PDEs address influencing system behavior through external inputs and determining unknown parameters from observed data, finding applications in fluid dynamics and medical imaging. The study of solution behavior in dynamical systems covers stability, bifurcations, and chaos, utilizing linear stability analysis and numerical simulations. The theory of nonlinear evolution equations centers on systems where the rate of change depends nonlinearly on the variable, addressing issues like the existence and uniqueness of solutions. Furthermore, other topics related to PDEs find applications in fields such as mathematical biology, finance, and image processing, exploring a broad and exciting range of phenomena in various scientific and engineering disciplines.

This Special Session aims to bring together young and senior researchers working on different aspects of the field to discuss recent and new results in the field such as the initial boundary value problem of the dispersive system based on different methods, control theory, and inverse problems for PDEs, the behavior of the solution of dynamical systems, the theory of nonlinear evolution equations and other related topics involving PDEs. Another goal of the special session is to promote idea exchange as well as potential future collaborations.

Session 20: Advances in Nonlinear PDEs, Analysis and Geometry

Organizers:
Gabrielle Nornberg (University of Chile, Chile, contact organizer)
Boyan Sirakov (Pontifical Catholic University of Rio de Janeiro, Brazil)

Brief Summary: Analytical and geometrical methods combine beautifully in the theory of nonlinear elliptic and parabolic PDEs, for instance in the study of symmetry properties of solutions and overdetermined problems, or in regularity estimates and free boundary problems. On the other hand, many relevant problems in Geometric Analysis have been approached through techniques arising from the theory of nonlinear PDEs, for instance Yamabe type problems, isoperimetric inequalities, and the study of minimal surfaces.

The goal of this session is to gather leading experts in these fields, to present recent results and open questions, and to stimulate discussions that can be influential in these areas.

We anticipate an exchange of views on variational, topological and monotonicity methods in PDEs; qualitative properties of solutions such as symmetry, asymptotic behavior and spectral analysis; quantitative a priori and regularity estimates; critical exponents and Liouville properties; maximum and comparison principles; geometric measure theory; free boundary problems.

Session 21: Optimization and Control

Organizers:
Héctor Ramírez (Centro de Modelamiento Matematico, Chile, contact organizer)
María Soledad Aronna (Fundação Getúlio Vargas, Brazil)

Brief Summary: In this session we intend to present a variety of aspects of Optimization and Optimal Control, connections among some of the last results in each area, and give a general panorama of the ongoing research in different countries of the American continent. More precisely, we plan to cover, among others, the following topics:

- algorithms for solving Mean Field Games,
- constraints qualification condition for conic programming
- applications of optimal control problems to mathematical epidemiology, among other fields - theory of maximal monotone operators,
- algorithms for solving composite monotone inclusions,
- existence and stability results for sweeping problems,
- recent advances on stochastic optimization.

The accomplishment of the proposed session will be a great opportunity to create new connections and reinforce existing ones in the area.

Session 22: Partially Hyperbolic Dynamical Systems: Ergodic and Topological Aspects

Organizers:
Davi Obata (Brigham Young University, USA, contact organizer)
Pablo Carrasco (Universidade Federal de Minas Gerais, Brazil)

Brief Summary: Partial hyperbolicity was introduced in the 70s with the works of Brin and Pesin. Since then this has been a very active topic of research. It has become a powerful tool to understand higher dimensional dynamical systems and it has found applications in geometry, rigidity theory and number theory. Moreover, it has been studied by several research groups throughout the Americas.

The goal for this session is to bring several experts in partially hyperbolic theory throughout the Americas, working in ergodic and topological aspects of partially hyperbolic systems. These experts will cover a diverse list of topics within this theory.

Session 23: Special Geometries and Gauge Theory

Organizers:
Henrique Sá Earp (Universidade Estadual de Campinas, Brazil, contact organizer)
Romina M. Arroyo (Universidad Nacional de Córdoba, Argentina)
Da Rong Cheng (University of Miami, USA)
Spiro Karigiannis (University of Waterloo, Canada)

Brief Summary: Our proposed special session for MCA2025 aims to spotlight the exploration of geometric structures influenced by torsion or curvature. Organised by a collaborative team from Brazil, Argentina, the USA, and Canada, this session seeks to provide a dynamic and inclusive platform for the dissemination and discussion of recent developments in Differential Geometry.

The scope of the session is broad, encompassing symplectic geometry, Hermitian structures, G2-structures, calibrated submanifolds, higher-dimensional gauge theory, foliations, and various geometric flows. A particular emphasis will be placed on the role of symmetries that preserve certain geometric structures or flows, often formulated in terms of Lie group actions. This focus underpins the session's objective to delve into the complex interplay between these symmetries and geometric structures, addressing both current challenges and emerging opportunities within the field.

By assembling a diverse group of researchers, including both established experts and emerging scholars from across North and South America, the session aims to foster a rich exchange of ideas and methodologies. Our goal is to facilitate the integration of existing networks of collaboration and mentorship while also encouraging the formation of new connections among participants. Through this convergence of expertise and perspectives, the session aspires to contribute meaningfully to the ongoing advancement of Special Geometries and Gauge Theory, benefiting the wider mathematical community.

Scheduled over two days with 16 talks, this special session represents a unique opportunity to stimulate new developments and collaborations in the realm of Differential Geometry, offering participants a chance to engage deeply with the latest research and theoretical advancements in the field.

Session 24: Nonlinear Dispersive Equations

Organizers:
Felipe Linares (IMPA, Brazil, contact organizer)
Claudio Muñoz (University of Chile, Chile)
Svetlana Roudenko (Florida International University, USA)

Brief Summary: Over the past twenty years the theory of nonlinear dispersive, wave-type equations has experienced spectacular progress. This includes research concerning the dynamics of high or infinite dimensional systems at or below their natural critical threshold, which in its turn connects with the existence and dynamics of the coherent structures such as solitary waves. A delicate intertwining between nonlinear interactions and linear evolution affects a large-scale behavior of solutions. The development of analytical tools in nonlinear Fourier analysis to address multilinear estimates, related deep functional analytic methods, profile decompositions, and the use of geometric and spectral methods have fundamentally contributed to the study of the local and global-in-time well-posedness as well as singularity formation for many wave-type equations and systems. Many new ideas and techniques were introduced and developed, enabling researchers to work on problems which until not long ago seemed unapproachable. Important examples include semilinear wave (NLW) and Schrödinger (NLS) equations, the Korteweg-de Vries (KdV) family of equations, plasma models (Euler-Poisson, Euler-Maxwell), water waves, quasilinear equations arising in general relativity, the quasi-geostrophic (SQG) equation, and many others. While each of these equations has its own features, many aspects can be treated in a unified way while others require special further investigations.

This session will consist of talks presenting the most recent advances with the overarching goal to have participants draw integrated landscapes of those diverse phenomena, aiming towards a more complete description, classification and prediction of global dynamics as well as new phenomena and methods.

Session 26: Foliations and Singularities

Organizers:
Carolina Araujo (IMPA, Brazil, contact organizer)
Fernando Cukierman (UBA, Argentina)
Alexandre Fernandes (UFC, Brazil)
Arturo Fernández-Pérez (UFMG, Brazil)
Bruna Oréfice-Okamoto (UFSCAR, Brazil)
José Seade (UNAM, Mexico)

Brief Summary: Singularity theory is the branch of mathematics that studies properties of singular points of maps and manifolds. Holomorphic foliations are special geometric structures in complex manifolds. This theory has its origins in the study of differential equations in the complex plane, and is now a subject in its own right. These two theories have deep interconnections, being crossing points where several areas of mathematics converge. Progress on one side may resonate and bring deep insights and fertile ideas into the other. This session will present various aspects of singularity theory and the theory of holomorphic foliations.

Session 27: Pure and Applied Model Theory

Organizers:
Alf Onshuus (Universidad de los Andes, Colombia, contact organizer)
James Freitag (University of Illinois at Chicago, USA)
Isaac Goldbring (University of California, Irvine, USA)

Brief Summary: The goal of the Model Theory special session will be to highlight the research in model theory being done throughout the Americas, highlighting its applications across various branches of mathematics.

Model theory, with its foundational roots in logic and algebra, has evolved into a pivotal framework for analyzing mathematical structures using first order logic. Its applications span a remarkable array of domains, from algebraic geometry to number theory, and from differential equations to topology, showcasing its versatility and capacity to bridge diverse mathematical landscapes.

The session will feature a series of talks by leading experts who work in various countries exploring recent breakthroughs both in pure model theory and at the intersection of model theory and other branches of mathematics. Because of the particular directions that model theory has in our continent, highlights will probably include discussions on differentially closed fields and applications to differential algebra, continuous logic and applications to analysis, o-minimality and its ramifications for transcendental number theory, and how model theory serves as a very useful tool in extremal combinatorics and graph theory.

This session is designed to foster collaboration, encourage the exchange of ideas, and inspire further research.

Session 28: Recent Trends in Nonlinear Elliptic PDEs

Organizers:
Maya Chhetri (UNC Greensboro, USA, contact organizer)
Emer Lopera (Universidad Nacional de Colombia-Manizales, Colombia)

Brief Summary: Nonlinear Elliptic PDEs govern a wide spectrum of complex phenomena, encompassing population dynamics, combustion theory, fluid dynamics, stellar structure, and conservation laws. Understanding the qualitative aspects of nonlinear PDEs is paramount for gaining deeper insights into these multifaceted processes. This session aims to unite mathematicians with diverse interests, spanning both theoretical and applied focus. The presentations on theoretical findings will focus on qualitative analysis, exploring themes such as the regularity, the methods, existence, uniqueness, and multiplicity of solutions involving local and nonlocal diffusion operators. Meanwhile, speakers with applied interests will showcase the practical applications of PDEs in biological and physical phenomena.

The primary goal of this session is to feature presentations by senior researchers capable of delivering expository talks and shedding light on open problems within the field. Additionally, mid-career to early-career researchers, including graduate students, will showcase their recent advances.

Session 29: Interactions of Equivariant Bordism and Low Dimensional Topology

Organizers:
Carlos Segovia (UNAM, Oaxaca, Mexico, contact organizer)
Carmen Rovi (Loyola University Chicago, USA)

Brief Summary: Recently, there have been exciting breakthroughs in equivariant bordism that are revitalizing the field. To name a few, the unitary evenness conjecture, which established that unitary bordism is a free module over ordinary bordism with generators in even degrees, was disproved. Using techniques from low dimensional topology, Eric Samperton found a counterexample to the evenness conjecture with a group of order 243. This gave rise to the new question if the evenness conjecture was true at a homotopical level, but Sophie Kriz constructed a counterexample using a Sylow p-subgroup. Relationships emerged between equivariant bordism invariants and birational invariants associated with finite groups, namely rationality issues.

Our goal is to bring together specialists from diverse fields who are working on related topics, foster interactions, and promote new collaboration projects among participants.

Session 30: Birational Geometry and Singularities

Organizers:
Giancarlo Urzúa (Pontificia Universidad Católica de Chile, Chile, contact organizer)
Pedro Montero (Universidad Técnica Federico Santa María, Chile)
Joaquín Moraga (UCLA, USA)

Brief Summary: Birational geometry has its ancient roots in the resolution of singularities of plane curves, passing through the Italian school of minimal models of algebraic surfaces. A cornerstone of birational geometry was the resolution of singularities in characteristic 0 and Mori's developments on the Minimal Model Program (MMP). The MMP aims to classify higher-dimensional algebraic varieties up to birational transformations. In the last two decades, there have been several breakthroughs in birational geometry. For instance, the existence of minimal models for varieties of general type by Birkar, Cascini, Hacon, and McKernan, and the boundedness of mildly singular Fano varieties due to Birkar. These two developments had brought to us some important applications to the study of algebraic singularities, more precisely; log canonical and log terminal singularities. There has been substantial progress by mathematicians working in the Americas on the aforementioned topics with applications to areas beyond algebraic geometry. This session is about down-to-earth applications of birational geometry to singularities, algebraic dynamics, and topology of singularities and dual complexes.

Session 31: Structures of Submanifolds in Low Dimensional Topology

Organizers:
Kenneth L Baker (University of Miami, USA, contact organizer)
Mario Eudave-Muñoz (Universidad Nacional Autónoma de México, Mexico)
José Ayala Hoffmann (Universidad de Tarapacá, Chile)
Fabiola Manjarrez Gutiérrez (Universidad Nacional Autónoma de México, Mexico)
Puttipong Pongtanapaisan (Arizona State University, USA)
Jennifer Schultens (University of California at Davis, USA)

Brief Summary: Our understandings of manifolds of low dimensions are informed by theories of curves and surfaces in them. This manifests in many interconnected algebraic, geometric, and combinatorial ways: Curve complexes and Kakimizu complexes, knot theory of codimension 2 embeddings, decompositions via Heegaard splittings and trisections, fibrations and foliations, diagrammatic algebras and quantum invariants, cobordisms and concordances, symmetries and geometry. This session aims to bring together researchers with expertise in diverse areas such as these from countries across the Americas to share cutting edge developments and open problems to stimulate cross-pollination across these mathematical subfields and geographical regions.

Session 32: Vector Bundles on Varieties and Quantization

Organizers:
Laura P. Schaposnik (University of Illinois Chicago, USA, contact organizer)
Steven Rayan (University of Saskatchewan, Canada)
Ruxandra Moraru (University of Waterloo, Canada)

Brief Summary: Our session focuses on the intricate connections between moduli spaces of vector bundles over complex varieties and classical integrable systems, such as those related to the KdV hierarchy and Hitchin systems. These moduli spaces are pivotal in both mathematics and physics, serving as a fundamental framework for the exploration of various integrable systems through their algebraic and analytic structures. We will delve into the algebraic characteristics of moduli spaces of vector bundles, highlighting their importance in the existence of quantizations that can be understood both algebraically and combinatorially, featuring approaches like those of Beilinson-Drinfeld and topological recursion. Additionally, the session will cover the recent progress in the interaction between the algebraic and analytic/asymptotic structures of these spaces, particularly for Hitchin systems. Overall, the session aims to bridge the gap between geometry and high-energy physics by discussing new insights from string theory and various quantum field theories that interpret these moduli spaces and their quantizations. This gathering of experts from both geometry and physics is designed to foster discussions that could accelerate further developments in the field.

Session 33: Recent Progress in Mathematical Ecology and Epidemiology

Organizers:
King-Yeung Lam (The Ohio State University, USA, contact organizer)
Salomé Martínez (Universidad de Chile, Chile)
Zhisheng Shuai (University of Central Florida, USA)
Jorge Velasco-Hernández (Instituto de Matemáticas UNAM-Juriquilla, México)
Gail Wolkowicz (McMaster University, Canada)

Brief Summary: Mathematics at the intersection of ecology and epidemiology is a dynamic field of research that employs mathematical models and tools to understand the intricate relationships between living organisms and the environments which they inhabit. The multifaceted nature of biological processes continues to inspire novel modeling approaches, along with numerous challenging mathematical questions in their analysis. Furthermore, researchers in this field leverage a wide range of mathematical frameworks to address critical questions related to the spread of infectious diseases, the impact of climate change on ecosystems and disease vectors, and the design of feasible interventions in both ecological and epidemiological contexts. By consolidation of existing theory and the development of novel approaches, mathematicians contribute valuable insights that aid in the development of more effective strategies to tackle emerging ecological and epidemiological issues, ultimately promoting the health and resilience of both ecosystems and human populations.

This special session aims to showcase the research topics at the crossroads of mathematics, ecology, and epidemiology. Our objective is to facilitate discussions and encourage collaborations among experts and researchers from diverse backgrounds, emphasizing recent mathematical breakthroughs. Through these efforts, we aim to advance our understanding of the complex interactions arising in ecological systems and infectious diseases. Specifically, speakers and talks are carefully selected to make the session attractive to a diverse audience. We prioritize the inclusion of female and early career mathematicians while actively seeking to promote integration and collaborations among researchers from North/South America, and beyond, thereby emphasizing the continental synergistic character of the meeting.

Session 34: Randomness in Low-Dimensional Geometry

Organizers:
Lewis Bowen (University of Texas Austin, USA, contact organizer)
Kasra Rafi (University of Toronto, Canada)

Brief Summary: The last decade has seen tremendous advances in the the study of random geometric structures on surfaces, random planar maps, random simple closed curves, random walks on Teichmuller spaces, big mapping class groups, foliations of 3-manifolds, random finite covers of a fixed manifold, random matrix products, random 3-manifolds and so on. The purpose of this session is to shine a spotlight on the most recent of these developments especially in regards to research conducted in the Americas.

Session 35: Tropical Geometry, Twistor Spaces and Cluster Geometry

Organizers:
Helge Ruddat (University of Stavanger, Norway, contact organizer)
Lucia Lopez de Medrano (UNAM, Mexico)
Johannes Rau (Universidad de los Andes, Colombia)

Brief Summary: This session is designed to explore the interconnections among Tropical Geometry, Twistor Spaces, and Cluster Geometry. Cluster algebras are commutative rings introduced by Fomin and Zelevinsky to axiomatize positivity and canonical bases. The subject is combinatorial in nature with quiver mutations at its heart. A geometric perspective on cluster algebras has facilitated substantial recent advancements in the field, leading to the concept of toric models and cluster geometry. When a cluster variety is considered over the tropical semifield, it results in a tropical cluster variety. Tropical geometry can be seen as a combinatorial reflection of algebraic geometry, with tropical structures emerging from degenerations via logarithmic geometry by taking the Artin fan of a log space.

Cluster geometry has been applied to calculate scattering amplitudes in theoretical physics, which describe the probability amplitude associated with the transition from an incoming plane wave (representing a particle’s initial state) to an outgoing spherical wave (representing the final state post-scattering) in a stationary-state scattering process.

Twistor theory, introduced by Roger Penrose following mathematical developments in Einstein’s theory of general relativity towards a theory of quantum gravity, also originated in the realm of theoretical physics. The central idea is to transform physical fields in Minkowski space into complex analytic sections of the twistor space. It was recently discovered that the tropicalization process of a cluster variety can be interpreted as a twistor space.

Cluster structures are also found in many geometries relevant to representation theory. Twistor theory emerges in this context through the quantization of Poisson structures. A Poisson structure offers a framework for defining Hamiltonian systems in a coordinate-free manner. Generalized cluster structures appear in the context of the Strominger-Yau-Zaslow approach to mirror symmetry, providing yet another link to theoretical physics and forming a bridge to tropical, cluster, and twistor geometry.

Session 36: New Developments in Mathematical Fluid Dynamics

Organizers:
Cecilia Freire Mondaini (Drexel University, USA, contact organizer)
Anne Bronzi (Universidade Estadual de Campinas, Brazil)
Nathan Glatt-Holtz (Tulane University, USA)
Javier Gomez-Serrano (Brown University, USA)
Igor Kukavica (University of Southern California, USA)
Wojciech Ozanski (Florida State University, USA)

Brief Summary: Despite their venerable history, the fundamental equations of fluid dynamics represent one of the significant challenges in mathematical physics, as exemplified by the Clay Prize for the Navier-Stokes equations. There is a rich family of nonlinear partial differential equations arising in fluids modeling, for example, coming from aerospace engineering, geophysical and astrophysical systems, and biological applications. Beyond the fundamental questions of their well-posedness, these equations stimulate a wide variety of directions of contemporary research, including the stability, long-time behavior of solutions, the incorporation of uncertainties, ergodic properties, etc. This session will bring together a group of pure and applied mathematicians addressing cutting-edge problems in fluid dynamics. Topics will include: non-uniqueness of solutions; incorporation of data; development of singularities; stochastic approaches and models. Our session will provide early career researchers the opportunity to interact with established scholars in the field in a friendly and welcoming environment.

Session 37: Delay and Functional Differential Equations and Applications

Organizers:
Jaqueline Godoy Mesquita (Universidade de Brasília, Brazil, contact organizer)
Claudio Gallegos Castro (Universidad de Chile, Chile)
Guilherme Mazanti (INRIA, France)

Brief Summary: In several mathematical models, the evolution of a system may depend not only on its current state but also on some of its past values, which influence the state only after some delay. Such models arise from several applications, ranging, for instance, from biology, where delays may model maturing processes such as incubation periods or gestation times, to engineering, where delays are commonly used to model propagation or transmission phenomena that do not occur instantaneously.

Motivated by such applications, mathematicians from several backgrounds have considered systems with delays, or, more generally, functional differential equations, a theory that has flourished in the second half of the 20th century and is still the subject of much study, with many interesting problems yet to be explored.

This special session aims at bringing together mathematicians from different backgrounds working on systems with delays and functional differential equations, both from theoretical and applied perspectives, with the hope that, thanks to the high-quality talks of the session, existing research collaborations in the Americas will be reinforced and new ones will be created.

Session 38: Conservation Laws: Mathematical and Numerical Analysis with Applications

Organizers:
Eduardo Abreu (Universidade Estadual de Campinas, Brazil, contact organizer)
Fabio Ancona (University of Padua, Italy)
Maria Teresa Chiri (Queen’s University, Canada)
Xiaoqian Gong (Amherst College, USA)
Michael Herty (RWTH Aachen University, Germany)

Brief Summary: Hyperbolic conservation laws have been subject to extensive analytical and numerical studies over the last decades. It is widely known that their solutions can exhibit very complex behavior including the simultaneous presence of smooth waves, wave breaking, and shock waves. These equations describe the conservation of some basic physical quantities of a system, and they arise in all branches of science and engineering: from fluid dynamics to vehicular traffic modeling. The scope of this Special Session is to bring together researchers with interests in the theoretical, applied, and computational aspects of hyperbolic partial differential equations with real-life applications and discuss the state of the art of the field.

In the perspective of accomplishing the goals of the 2025 Mathematical Congress of the Americas (MCA2025), the invited speakers are of different ages, nationalities, and different scientific career stages and they are selected among the leaders in the field. This aspect makes the Special Session suitable for training young researchers and fostering interactions between several mathematical communities across the Americas (South, Central and North).

Session 39: Interplay between Asymptotic Geometric Analysis, Discrete Geometry, and Combinatorics

Organizers:
Alexander Litvak (University of Alberta, Canada, contact organizer)
Karoly Bezdek (University of Calgary, Canada)
Susanna Dann (Universidad de los Andes, Colombia)
Daniel E. Galicer (Universidad de Buenos Aires, Argentina)
Deborah Oliveros Braniff (Campus Juriquilla UNAM, Mexico)

Brief Summary: Asymptotic Geometric Analysis (AGA) is mainly concerned with geometric and linear properties of infinite dimensional objects, such as convex sets and normed spaces, especially with the characteristic behavior that emerges when the dimension, or a number of other relevant free parameters, is suitably large or tends to infinity. High-dimensional systems are very frequent in mathematics and applied sciences hence understanding of high-dimensional phenomena is becoming increasingly important. By virtue of AGA general framework, methods, and its impact on related fields, AGA can be situated at the crossroads of many branches of mathematics: functional analysis, convex and discrete geometry (described below), several areas of probability including random matrix theory, some aspects of graph theory, among others.

A closely related field of study, Discrete Geometry (DG), studies discrete arrangements of geometric objects in Euclidean, as well as in non-Euclidean spaces. This, as a classical core part, includes the theory of polytopes and tilings in addition to the theory of packing and covering. DG is driven by problems often featuring a very clear visual and applied character. It investigates combinatorial and analytic properties of configurations of geometric objects. It offers sophisticated results and techniques of great diversity, and it is a foundation for fields such as computational geometry and combinatorial optimization and also it includes some classical areas such as (analytic) convexity and geometry of numbers. Last but not least it continues to broaden its ties to analysis including AGA. This feature is a cornerstone for our session.

Session 40: Network Coding and Related Fields

Organizers:
Giuseppe Cotardo (Virginia Tech, USA, contact organizer)
Claudia Granados Pinzón (Universidad Industrial de Santander, Colombia)
Daniel Panario (Carleton University, Canada)

Brief Summary: The past decade witnessed the acceleration of industry digitalization driven by advancements in 5G, AI, and the Internet of Things. This trend is set to continue over the next decade and it is anticipated that 70% of the global population will be connected online by 2030. Robust communication networks are essential for global connectivity, trade facilitation, and emergency response. Despite their importance, digital communications face challenges such as data loss and corruption due to electromagnetic interference, leading to unreliable connections. Network coding emerges as a solution to these challenges, enabling nodes in a network to combine information packets and potentially offering significant throughput advantages over routing. This approach lays the theoretical groundwork for a more sustainable and efficient digital infrastructure. The field of network communication saw significant growth in the 1990s, particularly within engineering and computer science. Effective error-correction in network coding remained challenging until 2008 when rank-metric codes were proposed as a potential solution. These mathematical objects allow network receivers to repair or recover lost information. Since then, rank-metric codes have sparked significant interest among researchers in coding theory and beyond. This session focuses on network coding and related areas (such as graph theory, distributed storage, matrix algebra), aiming to gather together leading experts from the Americas whose research spans from theoretical underpinnings to practical applications. Our goal is to encompass all levels of seniority, from junior to very experienced researchers.

Session 41: Algebraic Geometry: the Numerical, the Random and the Tropical

Organizers:
Josué Tonelli-Cueto (Johns Hopkins Unversity, USA, contact organizer)
Gregorio Malajovich (Universidade Federal do Rio de Janeiro, Brasil)

Brief Summary: Many problems in computational algebraic geometry do not necessarily come from theoretical motivations, but from practical problems such as computer vision, chemical reaction networks, and statistics among many others. Because of this, a need for fast, efficient and reliable methods for solving these new problems of computational algebraic geometry has emerged.

As of today, numerical methods find themselves at the forefront of computational algebraic geometry in terms of speed and efficiency. However, despite their success, the so-called numerical algebraic geometry poses new challenges when having to justify the reliability of its algorithms. The need to develop and justify numerical methods in algebraic geometry requires the use of relatively young branches of algebraic geometry: the random and the tropical.

On the one hand, random algebraic geometry provides insight into the typical behavior of problems, which plays a fundamental role in understanding how hard a problem usually is. This knowledge, together with the probabilistic techniques that lead to it, leads them not only to justifications for the success of numerical methods but also to new algorithmic insights that can be used to improve the existing algorithms.

On the other hand, tropical algebraic geometry aims to simplify problems in algebraic geometry by taking them to the so-called tropical limit. Understanding what we can compute in this tropical limit and how we can take back what we can do in the tropical limit back to the original problem is a central issue in this branch. Moreover, we find this issue at the center of many directions in numerical algebraic geometry, where the objective is to make the tropical limit effective through numerical methods.

In this special session, we aim to join experts from the Americas and beyond to create a point of interaction and collaboration between these three recent branches of algebraic geometry.

Session 42: Combinatorial Number Theory in the Integer Lattice

Organizers:
Kevin O'Bryant (City University of New York, USA, contact organizer)
Sinai Robins (University of Sao Paolo, Brazil)

Brief Summary: This focused session is concerned with the utility and elegance at the intersection of point lattices and combinatorial number theory. Many classical results in Number theory and in Combinatorics are naturally concerned with either finite subsets of integers, or with various infinite subsets of integers. When confronted with a solved problem of this type, it is natural to extend it to the d-dimensional integer lattice, often revealing new aspects of the problem and leading to more general results. The additional flexibility of higher dimensions often offers a simpler path to the given problem. There are various applications to the geometry of numbers, crystallography, and coding theory.

Session 43: Harmonic Analysis and Partial Differential Equations

Organizers:
Jose Madrid (Virginia Tech, USA, contact organizer)
Guher Camliyurt (Virginia Tech, USA)
Dario Mena (Universidad de Costa Rica, Costa Rica)

Brief Summary: Harmonic analysis is the mathematical study of various types of natural oscillatory phenomena. It consistently contributes to many active research fields in pure and applied mathematics. In particular, methods from harmonic analysis have played fundamental roles in numerous classical results from PDEs. This session is dedicated to the recent advances in harmonic analysis and PDE, emphasizing the interaction between them. We hope this session serves as a platform for young and senior researchers working in different places in the Americas to exchange ideas and discuss recent progress and open problems in the area.

Session 44: Recent Advances in Harmonic Analysis, Partial Differential Equations, and Geometric Measure Theory

Organizers:
Tiago Picon (University of São Paulo, Brazil, contact organizer)
Galia Dafni (Concordia University, Canada)
Irina Mitrea (Temple University, USA)

Brief Summary: This special session is focused on the dissemination of recent developments in the area at the confluence between the fields of Harmonic Analysis, Partial Differential Equations, and Geometric Measure Theory. Themes of emphasis are: function spaces in non-smooth domains in the Euclidean or manifolds settings, well-posedeness and regularity theory for elliptic boundary value problems in non-smooth domains, Toeplitz type operators, optimal transport, metric measure spaces, and currents in Euclidean spaces and beyond. A thorough understanding of these themes is relevant to the theoretical and numerical treatment of boundary value problems arising in the modeling of physical phenomena such as elasticity, incompressible viscous fluid flow, electromagnetism, anisotropic plate bending, etc., in domains which may exhibit singularities at all boundary locations and all scales.

There are very active and successful working groups in these areas in the Americas, especially in Argentina, Brazil, Canada, and USA, and the goal of this session is to further support the collaborative efforts at the interface of these areas of mathematics, with a special attention paid to the involvement and training of junior mathematicians.

Session 45: Stochastic Partial Differential Equations

Organizers:
Hakima Bessaih (Florida International University, USA, contact organizer)
Raluca Balan (University of Ottawa, Canada)

Brief Summary: Stochastic partial differential equations (SPDEs) represent a dynamic and rapidly evolving field in probability theory. Over the past three decades, this field has experienced consistent growth, introducing novel methodologies for analyzing intricate systems influenced by random disturbances. SPDEs can be used for modeling various physical phenomena encountered in statistical mechanics, mathematical physics, theoretical neuroscience, fluid dynamics, and mathematical finance. This session aims to bring together distinguished researchers from diverse countries across the Americas and Europe, specializing in different aspects of SPDE theory and applications. The goal is to exchange the latest results and generate novel ideas for research directions and applications. The presentations will delve into cutting-edge SPDE theory advancements, covering topics such as solution existence and uniqueness, regularity characteristics, large deviation phenomena, numerical approximation techniques, and the exploration of SPDEs' applications in real-world contexts.

Session 46: Infinite Groups and Related Topics

Organizers:
Dmytro Savchuk (University of South Florida, USA, contact organizer)
Theo Zapata (University of Brasilia, Brazil)

Brief Summary: The aim of the session is to bring together researchers from the Americas working in the theory of infinite groups and related topics, such as topological dynamics, ergodic theory, logic, random walks, and others. These areas are often linked together by common objects of study that are viewed from different angles. In particular, the discussed topics will include latest achievements in the theory of profinite groups that serve as a bridge between the finite and the infinite group theories. Profinite groups appear naturally in topological dynamics, the area that witnessed a rapid development in the recent years with many links to geometric and asymptotic group theory and properties such as amenability, growth, random walks on groups, etc. The proposed session is designed to understand the connections among the aforementioned fields better and to foster new developments in this diverse and thriving area by reinforcing collaboration between researchers from North, Central, and South America.

Session 47: Mathematical Tools with Applications in Quantum and Genetic Coding

Organizers:
Cátia Regina de Oliveira Quilles Queiroz (Federal University of Alfenas, Brazil, contact organizer)
Juan Carlos Minango Negrete (Technological University Ruminahui, Ecuador)
Rafael Gregorio Lucas D'Oliveira (Clemson University, USA)

Brief Summary: In this special session, the aim is to work on the mathematical tools used to construct both quantum codes and genetic codes. Among the classes of quantum codes, the topological or surface codes stand out, due to their main advantage in quantum computing, which is naturally fault-tolerant due to the topological properties of the surface. Such codes associate qubits with the edges of euclidean or hyperbolic tessellations of a two-dimensional surface; the stabilizer operators are associated with the vertices and faces of the same tessellation. Other investigations present proposals for constructions of color codes and quantum hyperbolic asymmetric codes. The mathematical structures involved in these constructions, in addition to algebra, geometry, and surface topology, are Fuchsian groups, quotient rings, and quaternion orders. In addition to the mathematical tools used in the process of construction and analysis of quantum codes previously mentioned, it is important to highlight another area of great relevance and very promising: genetic coding, which arises from the establishment of connections between standard communication systems and genetic information transmission systems, where error correcting codes,-- especially BCH codes, are used in the genetic mutation analysis. In this process, algebraic structures of groups, rings, fields, and Galois field extensions stand out, as well as geometric tools such as Boolean lattices, Hasse diagrams, and Boolean hypercubes, fundamental in the analysis, understanding and interpretation of physicochemical properties related to the code genetic and that allow the analysis of genetic mutations.

Session 48: Free Boundary Problems and Nonlinear PDEs

Organizers:
Héctor Andrés Chang-Lara (Centro de Investigación en Matemáticas, Mexico, contact organizer)
Damião Júnio Araújo (Universidade Federal da Paraíba, Brazil)

Brief Summary: The study of partial differential equations and free boundary problems has driven progress in the analysis of nonlinear problems. This impulse has led to new techniques that advance classical problems, such as the obstacle problem, the Bernoulli one and two phase problem, the Hele-Shaw and Muskat equations, and various transmission problems. Current demands in applications, particularly from optimization, fluid and population dynamics, optimal control and differential games, continually introduce novel and challenging models.

This Special Session aims to showcase recent developments in these areas and promote the exchange of a diverse number of contemporary perspectives in the field such that: Blow-up analysis, monotonicity formulas, geometric measure theory, integro-differential operators, degenerate elliptic equations, optimal transport and homogenization.

We are dedicated to promoting interactions between established experts and emerging scholars, valuing the gender and locality balance.

Session 49: Bifurcations

Organizers:
Fernando Antoneli (Federal University of São Paulo, Brazil, contact organizer)
Martin Golubitsky (Ohio State, USA)
Miriam Manoel (University of São Paulo, Brazil)

Brief Summary: The application of dynamical systems to areas outside mathematics continues to be a vibrant, exciting, and fruitful endeavor. They are diverse and multidisciplinary, covering areas that include biology, chemistry, physics, climate science, social science, industrial mathematics, data science, and more, using ideas and concepts from singularity theory, bifurcation theory, equivariant dynamics, network dynamics, etc. The goal of this session is to bring several researchers in bifurcations of dynamical systems and foster a collaborative environment where participants can share their latest research, discuss innovative methodologies, and develop interdisciplinary approaches to apply the techniques of dynamical systems and bifurcation theory to approach complex problems in scientific fields. The session should feature presentations by senior researchers delivering expository talks giving an overview of some area and mid-career to early-career researchers showcasing their recent advances.

Session 50: Algebraic Logic

Organizers:
Noemí Lubomirsky (National University of La Plata, Argentina, contact organizer)
Hernán Javier San Martın (National University of La Plata, Argentina)
Nikolaos Galatos (University of Denver, USA)
Xavier Caicedo (University of Los Andes, Colombia)

Brief Summary: Algebraic logic is a field that explores the connections between logic and algebra, specifically focusing on the algebraic structures that correspond to logical systems. Its historical roots can be traced back to the 19th century with the pioneering work of George Boole, who developed Boolean algebras to represent logical propositions. Over time, the field expanded to include various types of algebras corresponding to different logical systems, such as lattice theory and relation algebras. In the mid-20th century, the field advanced significantly with the emergence of abstract algebraic logic, which generalized the principles of algebraic logic to encompass broader classes of algebras and logical systems. This modern approach, driven by key figures like Helena Rasiowa, Wim Blok, and Don Pigozzi, focuses on understanding the relationships between metalogical properties of logical systems and their algebraic counterparts. A significant achievement in abstract algebraic logic is the development of the Leibniz hierarchy, a classification system that organizes propositional logics based on the strength of their ties to associated algebraic structures. This hierarchy facilitates the application of algebraic methods to a wide range of logics, making algebraic logic a robust and versatile tool for investigating the foundations of logic.

The growing diversity of logics, including nonclassical logics, such as intuitionistic, many-valued, and modal logics, necessitates a unified general approach, with algebraic logic being a natural candidate. This branch of mathematical logic uses algebraic structures to provide semantics for logical systems and has effectively unified the study of various non-classical logics. Over the past forty years, algebraic logic has evolved into abstract algebraic logic, which explores how logical systems can be given algebraic semantics. In this session we bring together experts who apply algebraic logic to study a wide range of different logics and applications.

Session 51: Discrete Stochastic Models and Applications

Organizers:
Pablo Rodríguez (Universidade Federal de Pernambuco, Brazil, contact organizer)
Fabio Lopes (Universidad Tecnológica Metropolitana, Chile)

Brief Summary: The field of discrete stochastic models has its origins from modeling seemingly unrelated problems arising in diverse areas such as statistical physics, population dynamics, genetics, and communication systems. Over the past decades, the study of such models has evolved into an extensive set of tools and methods which are devoted to understanding the large-scale behavior of discrete random structures and systems of many interacting components and their scaling limits, providing a powerful framework to model phenomena arising in social, applied, and natural sciences. This area of research is very active and interconnected throughout the Americas.

The aim of this session is to bring together a diverse group of young and senior experts who approach problems from different perspectives to highlight their recent contributions, share new ideas and inspire further research and collaborations. This session will cover recent developments and a variety of aspects of this field in the Américas.

Session 52: Extremal and Probabilistic Combinatorics

Organizers:
Guilherme Mota (Universidade de Sao Paulo, Brazil, contact organizer)
Maya Stein (Universidad de Chile, Chile)
Robert Morris (IMPA, Brazil)
Yoshiharu Kohayakawa (Universidade de Sao Paulo, Brazil)

Brief Summary: Extremal and probabilistic combinatorics is concerned with both the extreme and the typical behaviour of discrete objects such as graphs, colourings, and sets of integers. Many fundamental open problems in the area were first raised by Erdős (and his many collaborators), whose numerous seminal contributions either initiated or stimulated the development of several of the topics covered by the session. These include extremal graph theory, Ramsey theory, random graphs and processes, additive combinatorics, the application of combinatorial techniques in areas such as statistical physics and number theory, and the application of techniques from analysis and topology in combinatorics. In recent decades, many deep connections have been discovered between these seemingly disparate areas of study, and an extensive array of tools, techniques and theory have been developed. This session aims to cover a wide range of recent developments in the subject, and to showcase some of the brightest young talents in the area.

Session 54: Emergence, Spread, and Control of Mosquito-borne Diseases: Insights from Mathematical Modeling

Organizers:
Michael A. Robert (Virginia Tech, USA, contact organizer)
Omar Saucedo (Virginia Tech, USA)
Claudia Pio Ferriera (Universidade Estadual Paulista, Brazil)

Brief Summary: The incidence and global distribution of mosquito-borne diseases, such as dengue, malaria, Zika, and West Nile, have increased substantially in the past two decades, largely driven by changes in climate, urbanization, and global travel. As morbidity and mortality associated with these diseases continues to increase, there is a growing need for improved mathematical tools to understand the spread and mitigation of these infectious diseases. Mosquito-borne disease mechanisms are often complicated by processes such as mosquito population dynamics, environmental and meteorological changes, and anthropogenic factors. Control of mosquito-borne diseases most often relies primarily on mosquito management; however, many traditional measures of control have limited efficacy, and novel methods for regulation are being investigated aggressively. Mathematical models have proven to be an incredibly useful tool both for characterizing the dynamics of complex disease transmission and for developing and evaluating potential mitigation strategies. This session will examine the mathematics of mosquito-borne diseases by featuring models that integrate ecological and epidemiological dynamics across different scales to understand the mechanisms underlying disease spread and control. The session highlights a diverse group of mathematical biologists from different countries who are implementing traditional and novel methods to study important questions in mosquito-borne diseases.

Session 55: Post-Quantum Cryptography

Organizers:
Vaĺerie Gauthier-Umaña (Universidad de los Andes, Colombia, contact organizer)
Henry Chimal-Dzul (University of Notre Dame, USA)
Jason LeGrow (Virginia Tech, USA)

Brief Summary: Post-Quantum Cryptography is a branch of Mathematics that studies cryptographic algorithms that resist attacks implemented on quantum computers. While current cryptosystems, such as RSA and ECC, base their security on the difficulty of factoring large integers and the difficulty of calculating discrete logarithm problems, the security of post-quantum cryptographic algorithms relies on different mathematical problems that are intractable by a large-scale quantum computer if it is ever built. In recent years, Post-Quantum Cryptography has experienced a significant growth to meet the demands of the NIST PQC Standardization Process. This process started in 2015 with the aim of developing a new set of cryptographic standards that will work with our current computers while being resistant to future quantum computers. In 2023, the NIST announced a new competition with the aim of finding a digital signature scheme as no such scheme was selected from the 2015 call. Despite the advances the field has experienced, the competition is still ongoing and we need to explore more mathematical and computing areas in order to find new ideas to optimize proposed schemes as well as to propose new cryptographic primitives that can resist quantum attacks. This special session aims to provide an space to promote collaborations and exchange ideas among scientists as well as to introduce young researchers to the most recent advances and venues of research in Post-Quantum Cryptography.

Session 56: Recent Developments in Commutative Algebra

Organizers:
Luis Núñez-Betancourt (CIMAT, Mexico, contact organizer)
Jack Jeffries (University of Nebraska-Lincoln, USA)
Aron Simis (Universidade Federal de Pernambuco, Brazil)

Brief Summary: Commutative algebra stands as a vibrant and dynamic field within the mathematical community of the Americas. The field has grown within the Americas where new centers of Commutative Algebra have surfaced. The proposed special session aims to showcase recent developments across various fronts in the discipline, such as differential operators, homological algebra, perfectoid algebras, syzygies, DG algebras, and multiplicity theory; and to showcase the broad geographical footprint of the field throughout the Americas.

Session 57: Differential Equations and Geometric Structures

Organizers:
Jesús Muciño Raymundo (Universidad Nacional Autónoma de México, Mexico, contact organizer)
John Alexander Arredondo (Fundación Universitaria Konrad Lorenz, Colombia)
Ronaldo García (Universidad Federal de Goiás, Brasil)
Mikhail Malakhaltsev (Universidad de los Andes, Colombia)

Brief Summary: The aim of the special session is to gather researches who work in various aspects of the interaction between Differential Geometry and Differential Equations together, in order they could share the recent results and approaches concerning the topics. At the session there will be presented results in such important areas, among the others, as differential equations on submanifolds, dynamical systems and their singularities, applications of dynamical systems, complex differential equations and geometric structures on curves, Fuchsian groups, geodesic flows on surfaces of constant negative curvature, partially hyperbolic dynamics in dimension three, Hamiltonian systems.

Session 58: Recent Advances in Convex and Riemannian Optimization

Organizers:
Orizon Pereira Ferreira (Federal University of Goiás, Brazil, contact organizer)
Yunier Bello Cruz (Northern Illinois University, USA)
Douglas Soares Gonçalves (Federal University of Santa Catarina, Brazil)

Brief Summary: Many constrained optimization problems involve minimizing a function subject to either convex constraints or constraints defined on a Riemannian manifold, or finding a common point between convex sets. These topics are interconnected in various ways, and we aim to gather experts working on different aspects of both convex and Riemannian optimization such as theory, algorithms, complexity and applications to exchange new ideas and results. Convex optimization has long been a cornerstone of mathematical optimization, focusing on minimizing a convex function over a convex set or computing a common point between convex sets. The properties of convexity guarantee global optimality and enable the development of efficient algorithms. Convex optimization problems are prevalent across numerous fields such as operations research, economics, machine learning, and engineering. Projection methods, such as alternating projections, the Douglas-Rachford algorithm, the circumcentered-reflection method, projected gradient descent, and the alternating direction method of multipliers (ADMM), are particularly crucial for handling constraints in convex optimization. Recent advances have improved the efficiency and scalability of these methods, addressing the challenges of large-scale and high-dimensional problems. Riemannian optimization extends classical optimization algorithms to problems with constraints forming a Riemannian manifold by introducing appropriate metrics. This framework leverages the manifold’s geometric structure to enhance algorithmic efficiency and accuracy. By modifying numerical methods used in Euclidean spaces, such as those mentioned above, Riemannian optimization effectively addresses inherently non-convex and high-dimensional problems using ideas from convex optimization, often encountered in machine learning applications. Examples include optimization on the Stiefel manifold for principal component analysis and on the Grassmann manifold for subspace clustering. By bringing together specialists from diverse fields, this thematic session will provide a platform for identifying new research directions and fostering collaborations among researchers, stimulating discussions that will advance the state-of-the-art in optimization and address the emerging challenges in these topics.

Session 59: Harnessing Mathematics in Artificial Intelligence: Implications and Innovations

Organizers:
Juan B. Gutiérrez (University of Texas at San Antonio, USA, contact organizer)
José Morales Escalante (University of Texas at San Antonio, USA)
Joaquin Fontbona (University of Chile, Chile)

Brief Summary: This session will explore the profound interplay between mathematics and artificial intelligence, emphasizing the foundations, development, analysis and uses tools and methods in artificial intelligence, e.g. large language models, deep learning, reinforcement learning, etc. Mathematics underpins the theoretical frameworks that model complex algorithms and data structures within AI. The speakers will discuss their cutting-edge research which spans various aspects of these models, from algorithmic foundations to ethical implications and practical applications. This session aims to foster a deeper understanding of how mathematical principles can drive innovations in AI, enhancing both theoretical and applied perspectives.

Session 60: Frames and Generalized Functions

Organizers:
Diana Stoeva (University of Vienna, Austria, contact organizer)
Peter G. Casazza (University of Missouri, USA)
Maximilian Hasler (Université des Antilles, Martinique)
Stevan Pilipović (University of Novi Sad, Serbia)

Brief Summary: The concept of frames, introduced in the 60s in Hilbert spaces, has become of keen interest since the 90s with the beginning of the so called wavelet era. Frames have been shown to be a very powerful tool in signal and image processing, with numerous applications, and deep theoretical investigation has attracted attention in various directions, in particular in extension of the frame concept to Banach and Frechet spaces and relating frame theory to the theory of generalized functions. In the last decades frames were applied to derive series expansion in certain spaces of generalized functions and to provide asymptotic analysis of generalized functions. Many new questions arise in relation to the development of frame theory for distributions. The aim of this special session is the meeting of experts in the two areas - frame theory and theory of generalized functions, in order to present recent work, to discuss new ideas and to determine joint research lines for further work.

Session 61: Recent Advances in Mathematical Finance and Related Fields

Organizers:
Bahman Angoshtari (University of Miami, USA, contact organizer)
Christian Keller (University of Central Florida, USA)
Jinniao Qiu (University of Calgary, Canada)
Yuri F. Saporito (Fundação Getulio Vargas, Brazil)

Brief Summary: Since the seminal works of Harry Markowitz in the 50’s on portfolio optimization and those of Fischer Black and Myron Scholes in the 70’s on option pricing, mathematics has played a central role in Finance. Conversely, these complex financial applications have facilitated the development of various mathematical theories, as it is exemplified by the revolutionary thesis Théorie de la spéculation (1900) of Louis Bachelier, which laid the mathematical foundations of the Brownian motion. Nowadays, Mathematical Finance is a broad and interdisciplinary field. It includes research in wide ranging topics such as optimal investment, asset pricing, risk measures, stochastic optimal control, backward stochastic differential equations, rough path theory, random networks, optimal transport, stochastic games, mean field games and, more recently, machine learning.

This special session will bring together researchers, ranging from early career mathematicians to established experts, to discuss recent developments, open problems, and new directions in mathematical finance and related fields.

Session 62: Complex, Dynamic Equations on Time Scales and Difference Equations and their Applications

Organizers:
Sabrina Streipert (University of Pittsburgh, USA, contact organizer)
Jaqueline Godoy Mesquita (Universidade de Brasília, Brazil)
Mina Teicher (University of Miami, USA)

Brief Summary: Mathematical modeling is a powerful tool in understanding underlying mechanisms of complex systems and dynamic processes in life sciences. Given the various global challenges in ecology, epidemiology, neuroscience, and social sciences, the formulation of mathematical models, their analyses and interpretation are of utmost importance. Dependent on the application and the modeled underlying time domain, the study of such mathematical models utilizes the theory of differential equations, difference equations, and dynamic equations on time scales. Dynamic equations on time scales unify the discrete and continuous analysis and allow for the modeling of processes that are neither fully discrete nor fully continuous. Hence, time scales theory allows for realistic modeling and is a powerful tool for applications in several scientific fields such as biology, population models, economics, statistics, finance, physics, among others. Other benefits of time scales models include numerical stability and simplification of nonautonomous continuous models by incorporating model complexity in the underlying time domain.

Each modeling area benefits from their own experts and techniques to study these systems. In this session, we aim to connect researchers working in these areas to advance the study of dynamical systems. The goal of this session is to promote stimulating discussions and foster collaborations. We look forward to bringing together internationally renowned researchers of different career stages and foster advances in difference equations, dynamic equations on time scales, complex systems, and their applications.

Session 64: Dynamics of Infectious Diseases: From Within-host to Population-level

Organizers:
Xi Huo (University of Miami, USA, contact organizer)
Shigui Ruan (University of Miami, USA)
Jianhong Wu (York University, Canada)

Brief Summary: The scope of infectious disease models varies significantly depending on the purpose of the study, ranging from within-host dynamics of cells and pathogens to population-level dynamics of human and vector populations. This special session will bring together researchers working on different scales of infectious disease modeling, aiming to stimulate ideas and foster interdisciplinary collaborations across multiple-scale models. The invited speakers have backgrounds in within-host models, specializing in the treatment of viral and bacterial infections, pharmacokinetics/pharmacodynamics (PK/PD) models, vector-borne diseases affecting mosquitoes or humans, and cancer research. Based on the speakers’ expertise, advanced techniques in biomedical research will be discussed in the session, such as model development, mathematical analysis, data fitting, parameter identifiability, model validation, and communication with experimentalists.

Particularly, this special session focuses on the development of within-host mathematical models for disease and treatment dynamics. Most of the talks will concentrate on the real-world application of such models, as well as the necessity and advances in the development of novel within-host models with complex structures. Additionally, we aim to initiate discussions on how individual-level models can be used to infer and assist in the improvement of population-level models, and vice versa.

Session 65: Variational Problems of Physical Origin

Organizers:
Duvan Henao (Universidad de O’Higgins, Chile, contact organizer)
Robert Jerrard (University of Toronto, Canada)

Brief Summary: This special session brings together active contributors to theories of copolymerization, ferromagnetism, liquid crystals, phase separation, nanomaterials, nonlinear elasticity, nonlocal interactions, quasiconvexity, and superconductivity, from the perspective of the calculus of variations. Working under the common umbrella of energy minimization, these theories formally explain and predict the formation of patterns with energy concentration at structures having various length scales and dimensions, such as dislocations, domain walls, fractures, optical defects, self-assembly lattices, vortex filaments or wrinkles. Rigorous verification of these predictions may involve the derivation of reduced models describing the geometry of patterns, as well as the study of regularity, symmetry, or other relevant properties of minimizers. These problems lead to deep mathematical challenges, related to the high non-convexity and the vectorial nature of the associated functionals and partial differential equations. These challenges have stimulated the discovery in the last decades of novel developments in compensated compactness, differential inclusions, Gamma-convergence, geometric flows, isoperimetric and functional inequalities, Young measures, and other methods. The exchange between researchers on these connected topics will foster new perspectives and synergies to confront the demanding open problems.

Session 66: Recent Developments in Interacting Particle Systems and their Applications

Organizers:
Kavita Ramanan (Brown University, USA, contact organizer)
Claudio Landim (IMPA, Brazil)

Brief Summary: Interacting particle systems refer to coupled systems of interacting stochastic processes that describe phenomena in a variety of fields including physics, biology and engineering. Though the origins of this field go back more than half a century to the pioneering works of Spitzer and Dobrushin, it remains a very active area of research, with many open questions related to both the fundamental theory of stochastic process, and those driven by applications. This session will showcase some of the latest developments in this field.