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

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.

New Mexico State University, Las Cruces, NM

BLAST is a conference series focusing on Boolean Algebras Lattices, Algebraic and Quantum logic Universal Algebra Set Theory Set-theoretic and Point-free Topology

Mathematical Logic and Foundations,    Geometry and Topology

ICERM

This workshop is at the interface of algebra, geometry, and computer science. The major theme deals with a novel domain of computational algebra: the design, implementation, and application of algorithms based on matrix representations of groups and their geometric properties. The setting of linear Lie groups is amenable to calculation and modeling transformations, thus providing a bridge between algebra and its applications. The main goal of the proposed workshop is to synergize and synthesize the independent strands in the area of computational aspects of discrete subgroups of Lie groups. We aim to facilitate solutions of theoretical problems by means of recent advances in computational algebra and additionally stimulate development of computational algebra oriented to other mathematical disciplines and applications.

Phone: [4018635030];     Email: info@icerm.brown.edu

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

ICERM

The adoption of D-module techniques has transformed the interface between commutative algebra and algebraic geometry over the last two decades. The discovery of interactions and parallels with the Frobenius morphism has been an impetus for many new results, include new invariants attached to singularities but also D- and F-module based algorithms for computing quantities that used to be unattainable. Our goal for this workshop is to discuss computational aspects and new challenges in singularity theory, focusing on special varieties that arise from group actions, canonical maps, or universal constructions. By bringing together geometers, algebraists, and invariant theorists, we will address problems from multiple perspectives. These will include comparisons of composition chains for D- and F-modules, the impact of group actions on singularity invariants, and the structure of differential operators on singularities in varying characteristics.

Email: info@icerm.brown.edu

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 purpose of this workshop is to bring together mathematicians interested in foams and their use in low-dimensional topology, representation theory, categorification, mathematical physics, and combinatorics. The workshop will focus on the foam evaluation formula and its applications. More concretely, we aim to: (a) Give a more intrinsic definition of the foam evaluation, in order, for instance, to find similar formulas for the other Lie types; (b) Understand the interplay between foams and matrix factorizations and further use foams for a unified and comprehensive approach to Khovanov-Rozansky link homology theories; (c) Compare combinatorial foam evaluation with the geometric structures and invariants coming from gauge theory and symplectic geometry; (d) Study potential applications of the foamy definition of link homology theories. This workshop is fully funded by a Simons Foundation Targeted Grant to Institutes.

This program is devoted to the investigation of universal analytic and geometric objects that arise from natural probabilistic constructions, often motivated by models in mathematical physics. Prominent examples for recent developments are the Schramm-Loewner evolution, the continuum random tree, Bernoulli percolation on the integers, random surfaces produced by Liouville Quantum Gravity, and Jordan curves and dendrites obtained from random conformal weldings and laminations. The lack of regularity of these random structures often results in a failure of classical methods of analysis. One goal of this program is to enrich the analytic toolbox to better handle these rough structures.

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

The Connections Workshop will feature talks on a variety of topics related to the analysis and geometry of random spaces. It will preview the research themes of the semester program and will highlight the work of women in the field. There will be a panel discussion as well as other social events. This workshop is directly prior to the Introductory Workshop, and participants are encouraged to participate in both workshops. This workshop is open to all mathematicians.

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

This workshop brings together leading experts in quantum numerical linear algebra, to discuss the recent development of quantum algorithms to perform linear algebra tasks for solving challenging problems in science and engineering and for various industrial and technological applications.

This workshop will introduce some of the major themes in probability and geometric analysis that will be relevant for the semester-long program. A series of short mini-courses will give participants the opportunity to learn about important subjects such as the Schramm-Loewner evolution (SLE) or the Gaussian free field (GFF), for example. The workshop will also include "visionary" lectures by prominent researchers who will outline fruitful directions for future research.

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

ICERM

Incarnations of braid groups, or generalizations thereof, naturally arise in a range of active research areas in symplectic and algebraic geometry. This is a rich and diverse ecosystem, and the workshop will aim to bring together speakers from all corners of it. A unifying theme is monodromy: one the one hand, generalized braid groups arise in symplectic and algebraic geometry as fundamental groups of moduli spaces, loosely construed -- for instance, of complements of discriminant loci of singularities or of hyperplane arrangements, or moduli spaces of deformations of complex or symplectic structures. On the other hand, monodromy ideas motivate representations of generalized braid groups as various flavors of geometric automorphisms -- for instance, as (framed) mapping class group elements, symplectic Dehn twists, spherical twists in derived categories, or flop functors for 3-folds. These perspectives lead in turn to a wide array of further geometric applications, from classifications of Stein fillings to the study of spaces of Bridgeland stability conditions.

From a community perspective, one aim of the workshop is to bring together mathematicians from adjacent research communities with a shared interest in braids as they arise in symplectic or algebraic geometry. We hope the conference will accelerate the cross-pollination of ideas, and help foster collaborations, at what is a very exciting time for the field. Much of this research also lies at an interface with other aspects of the thematic semester -- for instance, braids in representation theory (e.g. in connection with cluster algebras or Bridgeland stability conditions), or in low-dimensional topology (e.g. in connection with monodromies of open books) -- and many of the talks should be of interest to a broader set of semester participants.

Phone: [401 863 5030];     Email: info@icerm.brown.edu

The aim of this workshop is to bring together researchers whose work contributes to the study of random structures that exhibit some form of conformal self-similarity. Notable examples include the Schramm-Loewner evolution SLE, the Brownian map and random trees, Liouville Quantum Gravity, and Conformal Field Theory. A particular focus will be the discussion of analytic tools needed to address the challenges arising from the often rough underlying sets and spaces.

This workshop will focus on complex dynamics in one and several variables. We will bring toghether experts in rational dynamics, transcendental dynamics, and dynamics in several complex variables in order to get new perspective and foster discussions in a warm and stimulating atmosphere. A special focus will be put on the interactions between one dimensional and higher dimensional complex dynamics, and on connections with adjacent areas of mathematics.

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.