Conferences  >  Mathematics  >  Courses and Events for Math Students and Early Career Researchers  >  United States

Vanderbilt University

The conference will focus on several aspects of constructive function theory, including orthogonal polynomials, potential theory, discrete and continuous energy problems, special functions, polynomial inequalities, as well as various problems relating to optimization and efficiency. The aim is to stimulate collaboration and the exchange of ideas. The conference will be held in conjunction with the 37th Annual Shanks Lecture, to be given by Professor Doron Lubinsky (Georgia Institute of Technology).

Analysis,    Calculus, Differential Equations and Integration

Simons Laufer Mathematical Sciences Institute (SLMath)

The course will present basic concepts of the theory of combinatorial limits related to various combinatorial objects such as graphs, permutations, and hypergraphs, and discuss analytic representations of their limits. We will discuss how the theory of combinatorial limits is related to regularity decompositions and how its analytic tools can be applied to various problems in computer science and mathematics, in particular, in extremal combinatorics where Razborov's flag algebra method has led to advances on long-standing open problems (with solutions of the Erdős-Rademacher Problem and the Erdős Pentagon Problem being among the first results obtained using the method). We will demonstrate how the flag algebra arguments can be applied both directly and in a computer-assisted way, including non-asymptotic settings, e.g., to compute particular Ramsey numbers.

Simons Laufer Mathematical Sciences Institute (SLMath)

The course will present basic concepts of the theory of combinatorial limits related to various combinatorial objects such as graphs, permutations, and hypergraphs, and discuss analytic representations of their limits. We will discuss how the theory of combinatorial limits is related to regularity decompositions and how its analytic tools can be applied to various problems in computer science and mathematics, in particular, in extremal combinatorics where Razborov's flag algebra method has led to advances on long-standing open problems (with solutions of the Erdős-Rademacher Problem and the Erdős Pentagon Problem being among the first results obtained using the method). We will demonstrate how the flag algebra arguments can be applied both directly and in a computer-assisted way, including non-asymptotic settings, e.g., to compute particular Ramsey numbers.

MIP 2025 is supported by the Mixed Integer Programming Society (MIPS), which is a section of the Mathematical Optimization Society (MOS).

The Mixed Integer Programming (MIP) Workshop is a single-track workshop highlighting the latest trends in integer programming and discrete optimization, with speakers chosen by invitation. The 2025 edition of the workshop will be the twenty-second in the MIP series.

Optimization Theory, Operational Research,    Algorithms and Data Structures

This summer school will focus on focus on Legendrian links and the microlocal theory of sheaves and run from June 9th through June 13th, 2025. The summer school will be centered around a mini-course given by Roger Casals (the University of California, Davis). The mini-course will be supplemented by a couple of research talks, opportunities for participants to ask questions and work on problem sets, panel discussions about career paths, and a discussion of open problems.

Simons Laufer Mathematical Sciences Institute (SLMath)

This summer school offers an exceptional opportunity for participants to delve into the intricate realm of statistical optimal transport theory. This captivating field stands at the crossroads of multiple disciplines, drawing from a rich tapestry of mathematical insights from diverse subjects, including partial differential equations, stochastic analysis, convex geometry, statistics, and machine learning, crafting a vibrant and interdisciplinary landscape. The foremost objective of this summer school is to create a dynamic learning environment that unites students from diverse backgrounds such as PDE theory, probability, or optimal transport. Throughout the program, participants will embark on a journey that will not only enhance their comprehension of the distinct elements of statistical optimal transport but will also foster the integration of diverse disciplines. This integration will enable them to tackle the forefront challenges in statistics and machine learning where optimal transport stands as a potent and indispensable tool. By the end of the program, participants will leave with not only a comprehensive skill set but also a profound understanding of the synergy between optimal transport and the realm of statistics and machine learning, ready to apply their knowledge to the forefront of this exciting field.

Probability and Statistics, Game Theory,    Optimization Theory, Operational Research

Institute for Computational and Experimental Research in Mathematics, Brown University, Providence, RI (ICERM)

Summer@ICERM is a residential undergraduate research program hosted at the Institute for Computational and Experimental Research in Mathematics at Brown University. Led by experienced faculty and graduate student teaching assistants, participating undergrads will spend seven weeks learning how to collaborate, engage in data science, and conduct research as a team. The goal of Summer@ICERM 2025: Building Useful Insights from Local Data through Sustainable partnerships (BUILDS) is to introduce students with limited experience to the field of data science through projects related to issues such as global food systems, food production, and food security.

Scientific Computing and Data Science,    Public Lectures and Outreach

IPCO (Integer Programming and Combinatorial Optimization) is a conference that is sponsored by the Mathematical Programming Society. IPCO is a forum for researchers and practitioners working on various aspects of integer programming and combinatorial optimization. The aim is to present recent developments in theory, computation, and applications of integer programming and combinatorial optimization. The conference and summer school will take place at Johns Hopkins University in Baltimore, Maryland, USA.

Graph Theory and Combinatorics,    Algorithms and Data Structures

Northwestern University.

This summer school is being held to celebrate Luigi Ambrosio who won the 2024 Frederic Esser Nemmers Prize in Mathematics for his "deep and numerous contributions to calculus of variations and geometric measure theory, and broad and far-reaching influence of these fields." Ambrosio is Professor of Mathematics, and currently serving as Director, of the Scuola Normale Superiore in Pisa. See here for more information about the Nemmers Prize. The summer school schedule will include three mini-courses and three one-hour research talks given by experts in the field, including a mini-course by Ambrosio himself. The summer school is aimed at mathematics graduate students, postdocs and junior faculty.

American Institute of Mathematics, Pasadena, California (AIM)

This workshop, sponsored by AIM and the NSF, is a week-long summer program for incoming second- or third-year students in graduate programs in the USA. It is designed to support and train a new generation of mathematical scientists in applied and computational mathematics. Applied mathematics research is rapidly shifting from classical applied mathematics, which focuses mainly on physical applications, to one that is more heavily driven by data and technology. In this Big Data era, students must be suitably trained in computational skills such as statistics, optimization, and machine learning.

Simons Laufer Mathematical Sciences Institute (SLMath)

This school will introduce students to a range of powerful combinatorial tools used to understand algebraic objects ranging from the homogeneous coordinate ring of the Grassmannian to symmetric functions. The summer school will center around two main lecture series "Webs and Plabic Graphs" and "Vertex Models and Applications". While the exact applications differ, both courses will center on graphical models for algebraic problems closely related to Grassmannian and its generalizations. This school will be accessible to a wide range of students. Students will leave the school with a solid grasp of the combinatorics of webs, plabic graphs, and the six-vertex model, an understanding of their algebraic applications, and a taste of current research directions.

IAS/Park City Mathematics Institute

Extremal graph theory and Ramsey theory are two of the central branches of modern extremal combinatorics, which seeks to understand the size and structure of discrete objects under certain natural constraints. In this course we will explore these topics, seeing both some of the beautiful techniques developed to study such problems, as well as many innocent-looking problems that seem completely out of reach of the currently-known techniques. We will also see some of the many connections these questions have to other areas of mathematics, including geometry, number theory, probability, and theoretical computer science.

Research Theme: Extremal and Probabilistic Combinatorics

Simons Laufer Mathematical Sciences Institute (SLMath)

Computer assisted proofs are at the forefront of modern mathematics, and have led to many important recent mathematical advances. They provide a way of melding analytical techniques with numerical methods, in order to provide rigorous statements for mathematical models that could not be treated by either method alone. In this summer school, students will review standard computational and analytical techniques, learn to combine these techniques with more specialized methods of interval arithmetic and automatic differentiation, and apply these methods to establish rigorous results in otherwise intractable problems.

Automated Theorem Proving,    Applied Mathematics (in general)

Simons Laufer Mathematical Sciences Institute (SLMath)

The summer school aims to expose participants to formal methods that can facilitate principled scientific discovery. The school will cover some of the basic automated statistical inference (in the form of machine learning techniques) and reasoning methods that are commonly used in scientific discovery, as well as novel techniques developed to tackle open questions and issues. This summer school will address novel computational methods for scientific discovery and focus on fusing axiomatic knowledge and experimental data to enable principled derivations of models of natural phenomena along with certificates of the consistency of these models with background knowledge specified as axioms.

Courses and Events for Physics Students,    Mathematical Physics

Lie groups are central objects in modern mathematics; they arise as the automorphism groups of many homogeneous spaces, such as flag manifolds and Riemannian symmetric spaces. Often, one can construct manifolds locally modelled on these homogeneous spaces by taking quotients of their subsets by discrete subgroups of their automorphism groups. Studying such discrete subgroups of Lie groups is an active and growing area of mathematical research. The objective of this summer school is to introduce young researchers to a class of discrete subgroups of Lie groups, called Anosov subgroups. These subgroups are central objects in the study of higher Teichmuller theory, convex projective geometry, and character varieties. In this summer school, there will be an emphasis on discussing some of the dynamical tools that have recently been successfully used to study Anosov subgroups. The required background in dynamics, hyperbolic geometry, and Lie theory will also be discussed. Aside from providing a stimulating academic environment for learning about Anosov subgroups, this summer school also aims to be a relaxed and friendly space for participants to interact with fellow aspiring mathematicians.

Geometry and Topology,    Group Theory

Organised in partnership with the Clay Mathematics Institute

Simons Laufer Mathematical Sciences Institute (SLMath)

This school will serve as an introduction to the SLMath semester “Topological and Geometric Structures in Low-Dimensions”. The school consists of two mini-courses: one on Teichmüller Theory and Hyperbolic 3-Manifolds and the other on Anosov Flows on Geometric 3-Manifolds. Both topics lie at the interface of low-dimensional geometric topology (specifically, surfaces, foliations, and 3-manifolds) and low-dimensional dynamics. The first course will be targeted towards students who have completed the standard first year graduate courses in geometry, topology, and analysis while the second course will geared towards more advanced students who are closer to beginning research. However, we expect that all students will benefit from both courses.

Institute for Computational and Experimental Research in Mathematics, Brown University, Providence, RI (ICERM)

Linear Algebra over finite fields is a building block for several applications including data storage, error detection and correction, and public-key cryptography. These applications enable the security and possibility of our daily digital lives. This workshop aims to expose and engage junior researchers in the foundations and applications of linear algebra over finite fields.

The program will unite researchers from a number of areas: algebraic and complex geometry, arithmetic geometry, Hodge theory, and mathematical physics. It will bring theoretically and computationally oriented researchers together, expecting that computations will illuminate conjectures made by the theorists and that theory will enlarge the range of what can be computed. We intend to develop databases of certain types of K3 surfaces for the L-Functions and Modular Forms Database and promote the development of software for computations on K3 surfaces in Magma, SageMath, or other systems for public release.

Geometry and Topology,    Number Theory, Arithmetic