Meetings/Workshops on Algebra in the United States (USA)

Mathematical Sciences Research Institute (MSRI)

The study of discrete subgroups of Lie groups and the associated locally symmetric manifolds has a long and rich history, with powerful interconnections between the geometry of the locally symmetric space, topology of towers of its finite covers, and number-theoretic aspects. More recently dynamical and probabilistic techniques have been fruitfully employed to study these groups and spaces. The workshop will take stock of recent developments in these highly active fields from a variety of backgrounds.

American Institute of Mathematics, San Jose, California

This workshop, sponsored by AIM and the NSF, will bring together mathematicians from a variety of backgrounds to discuss a central problem in mirror symmetry: the existence of special Lagrangian submanifolds, and their holomorphic mirrors, stable vector bundles. These two classes of objects form a set of canonical geometric objects, described by fully nonlinear partial differential equations (PDEs), which play a central role in mirror symmetry. Dating back to work of Thomas-Yau, it has long been conjectured that the existence of solutions to these nonlinear PDEs is equivalent to a purely algebraic notion of stability. This conjectural picture connects diverse fields of mathematics, ranging from stability conditions on derived categories, to symplectic geometry and the Fukaya category, to the study of the Lagrangian mean curvature flow and fully nonlinear systems of PDEs.

The central topics for the workshop are: The Lagrangian Mean Curvature Flow, singularity analysis, and connections with the Fukaya category. The deformed Hermitian-Yang-Mills equation, infinite dimensional GIT, and fully nonlinear systems. Understanding the Thomas-Yau conjecture for toric Fano manifolds and Landau-Ginzburg models.

American Institute of Mathematics, San Jose, CA

This workshop, sponsored by AIM and the NSF, will be devoted to recent advances in arithmetic intersection theory on Shimura varieties. This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The main topics for the workshop are: Kudla's program: modularity of arithmetic generating series, Kudla-Rapoport conjectures, and connections with L-functions Arithmetic Gan-Gross-Prasad program: arithmetic fundamental lemma, arithmetic transfer conjectures, and connection with L-functions Applications of arithmetic intersections: exceptional isogenies between reductions of abelian varieties, arithmetic of K3 surfaces, Gross-Stark units and singular moduli for real quadratic fields

The overarching objective of this workshop is to bring together researchers at the interface of the rapidly developing areas of the structure and classification of C*-algebras and subfactor theory/tensor categories. Advanced minicourses (making up around half the workshop) will enable a rich dialogue between the two communities, and participants will leave with many new problems to explore, as well as deeper insights about how C*-algebraic and von Neumann algebraic techniques interact.

ICERM

This workshop will focus on the development of software to facilitate research in combinatorial algebraic geometry, based on the SAGE Mathematical Software System and the OSCAR Computer Algebra System. Special attention will be given to efficient computations with multi-variate polynomials, which is a critical part of many algorithms in combinatorial algebraic geometry. Aside from development of software, the workshop will feature a series of talks about polynomial computations, as well as introductory lectures about Sage and Oscar.

Email: info@icerm.brown.edu

Graph Theory and Combinatorics,    Geometry and Topology

This workshop, sponsored by AIM and the NSF, will be devoted to exploration of the recently discovered connections between conformal sympathetic structures, contact topology and the theory of codimension one foliations.

ICERM

The workshop will revolve around the interplay between algebraic geometry and combinatorial structures such as graphs, polytopes, and polyhedral complexes. In particular, the workshop will foster dialogue among groups of researchers who use similar combinatorial geometric tools for different purposes within algebraic geometry and adjacent fields. The topics covered will include Newton-Okounkov bodies, Ehrhart theory, toric geometry, tropical geometry, matroids, and interactions with mirror symmetry.

Email: Info@icerm.brown.edu

Society for Industrial and Applied Mathematics (SIAM)

Linear algebra is an important area of mathematics and it is at the heart of many scientific, engineering, and industrial applications. Research and development in linear algebra include theoretical studies, algorithmic designs and implementations on advanced computer architectures, and applications to various disciplines. The SIAM Conferences on Applied Linear Algebra, organized by SIAM every three years, are the premier international conferences on applied linear algebra, which bring together diverse researchers and practitioners from academia, research laboratories, and industries all over the world to present and discuss their latest work and results on applied linear algebra.

American Institute of Mathematics (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to the use of computational mathematics in computer assisted proofs. There are an increasing number of famous conjectures and theorems that have recently been proven using computer assisted proofs. A highly incomplete list in alphabetical order includes the Dirac-Schwinger conjecture, the double bubble conjecture, Kepler's conjecture (Hilbert's 18th problem), Smale's 14th problem, the 290-theorem, the weak Goldbach conjecture etc. In many of these cases the proofs are based on using numerical computations with approximations, a technique that belongs to the field of computational mathematics and scientific computing rather than computer science.

American Institute of Mathematics, San Jose

This workshop, sponsored by AIM and the NSF, will be devoted to analysis on the hypercube. The topics of the workshop will include harmonic analysis on the hypercube, Markov-Bernstein type inequalities, and martingales and Bellman functions.

Geometry and Topology,    Quantum Mechanics and Quantum Information Theory

MRSI – Mathematical Sciences Research Institute, Berkeley

This summer school will introduce the participants to two of the main techniques in the subject: (i) the filtration method to prove algebraic degeneracy of integral points by means of the subspace theorem, leading to special cases of conjectures by Bombieri, Lang, and Vojta, and (ii) unlikely intersections through o-minimality and bi-algebraic geometry, leading to results in the context of the Manin-Mumford conjecture, the André-Oort conjecture, and generalizations. This SGS should provide an entry point to a very active research area in modern number theory.

MRSI – Mathematical Sciences Research Institute, Berkeley

The goal of the summer school is to introduce students to the foundational aspects of gauge theory, and explore their relations to geometric analysis and low-dimensional topology. By the end of the two-week program, the students will understand the relevant analytic and geometric aspects of several partial differential equations of current interest (including the Yang-Mills ASD equations, the Seiberg-Witten equations, and the Hitchin equations) and some of their most impactful applications to problems in geometry and topology.

Geometry and Topology,    Courses and Events for Math Students and Early Career Researchers

Creighton University, Omaha, NE USA

The 11th International Conference on Path Integrals, hosted by the Creighton University Department of Mathematics, aims to bring together researchers around the world who study path integrals in various settings as well as researchers who use path integrals in their particular areas of study.

MRSI – Mathematical Sciences Research Institute, Berkeley

This Summer Graduate School will cover basic tools that are instrumental in Random Conformal Geometry (the investigation of analytic and geometric objects that arise from natural probabilistic constructions, often motivated by models in mathematical physics) and are at the foundation of the subsequent semester-long program "The Analysis and Geometry of Random Spaces". Specific topics are Conformal Field Theory, Brownian Loops and related processes, Quasiconformal Maps, as well as Loewner Energy and Teichmüller Theory.

Geometry and Topology,    Courses and Events for Math Students and Early Career Researchers

Calculus, Differential Equations and Integration,    Numerical Analysis and Computational Mathematics

University of Alabama, Huntsville

Analysis,    Calculus, Differential Equations and Integration

Mathematical Sciences Research Institute, Berkeley

Society for Industrial and Applied Mathematics (SIAM)

Mathematical Sciences Research Institute, Berkeley

This workshop will focus on cutting-edge research in random matrices and integrable probability. We will explore connections with other branches of mathematics and applications to sciences and engineering. The workshop will feature presentations by both leading researchers and promising newcomers.

Mathematical Physics,    Courses and Events for Math Students and Early Career Researchers

Mathematical Sciences Research Institute, Berkeley

The introductory workshop aims at providing participants with an overview of some of the recent developments in the topics of the semester, with a particular emphasis on universality and applications. This includes universality for Wigner matrices and band matrices and quantum unique ergodicity, universality for beta ensembles and log/coulomb gases, KPZ universality class, universality in interacting particle systems, the connection between random matrices and number theory.

Mathematical Physics,    Courses and Events for Math Students and Early Career Researchers

MRSI – Mathematical Sciences Research Institute, Berkeley

This workshop will explore connections between the regularity theory of minimal surfaces and of mean curvature flow. Recent breakthroughs have improved our understanding of singularity formation in both settings but the current research trends are becoming increasingly disparate. Experts from both areas will present their research and there will be ample free time to establish connections between the topics.

Mathematical Sciences Research Institute (MSRI)

This workshop will focus on the integrable aspect of random matrix theory and other related probability models such as random tilings, directed polymers, and interacting particle systems. The emphasis is on communicating diverse algebraic structures in these areas which allow the asymptotic analysis possible. Some of such structures are determinantal point processes, Toeplitz and Hankel determinants, Bethe ansatz, Yang-Baxter equation, Karlin-McGregor formula, Macdonald process, and stochastic six vertex model.

The development of Floer theory in its early years can be seen as a parallel to the emergence of algebraic topology in the first half of the 20th century, going from counting invariants to homology groups, and beyond that to the construction of algebraic structures on these homology groups and their underlying chain complexes. In continuing work that started in the latter part of the 20th century, algebraic topologists and homotopy theorists have developed deep methods for refining these constructions, motivated in large part by the application of understanding the classification of manifolds. The goal of this program is to relate these developments to Floer theory with the dual aims of (i) making progress in understanding symplectic and low-dimensional topology, and (ii) providing a new set of geometrically motivated questions in homotopy theory.

MRSI – Mathematical Sciences Research Institute, Berkeley

The development of Floer theory in its early years can be seen as a parallel to the emergence of algebraic topology in the first half of the 20th century, going from counting invariants to homology groups, and beyond that to the construction of algebraic structures on these homology groups and their underlying chain complexes. In continuing work that started in the latter part of the 20th century, algebraic topologists and homotopy theorists have developed deep methods for refining these constructions, motivated in large part by the application of understanding the classification of manifolds. The goal of this program is to relate these developments to Floer theory with the dual aims of (i) making progress in understanding symplectic and low-dimensional topology, and (ii) providing a new set of geometrically motivated questions in homotopy theory.