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

The Mathematics Academy is a unique opportunity for students interested in examining mathematical concepts rarely offered at the high school level. This rigorous, proof-oriented program will fuse lectures, problem sessions, demonstrations, and exploratory research to engage students.

Discrete Mathematics, Algebra and Number Theory, Geometry and Topology

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

This workshop, sponsored by AIM and the NSF, will be devoted to the zero distribution of random polynomials spanned by various deterministic bases.

Group theory is a fundamental and highly active field of research within the mathematical sciences and has ramifications throughout all of mathematics and the sciences. There are large communities of group theory researchers in all continents, and they keep in touch through international meetings and conferences. However, local conditions and cultural circumstances under which mathematical research is done differ quite a bit between different regions of the world. The focus of this conference is on research in group theory in the USA and in China. One major goal of the conference is to establish and strengthen ties between group theorists in China and the US. It is the first conference in group theory with this focus. We will have about 15 invited talks and a limited number of contributed talks. The speakers from both countries will cover a large variety of the subjects in the area, which include representations of solvable groups, representations of simple groups, character theory, classes of groups, groups and combinatorics, recognizing simple groups from group invariants, p-groups, and fusion systems.

Phone: [5122453735];     Email: tk04@txstate.edu

Representations of solvable groups, representations of simple groups, character theory, classes of groups, groups and combinatorics, recognizing simple groups from group invariants, p-groups, and fusion systems

American Institute of Mathematics

The LMFDB contains a wealth of information on L-functions, modular forms of several types, elliptic curves and genus 2 curves, number fields, and much more. In addition to detailed information about individual objects, the LMFDB also includes information about connections between objects, including the connections described by the Langlands Program. The workshop will involve a mixture of demonstrations, explorations, discussions about mathematical content, and discussions about the future of the LMFDB.

The Illustrating Mathematics program brings together mathematicians, makers, and artists who share a common interest in illustrating mathematical ideas via computational tools. The goals of the program are to: introduce mathematicians to new computational illustration tools to guide and inform their research; spark collaborations among and between mathematicians, makers and artists; and find ways to communicate research mathematics to as wide an audience as possible.

Geometry and Topology, Algebra and Number Theory, Dynamics and Probability,

Geometry and Topology,    Number Theory, Arithmetic

This workshop, sponsored by AIM and the NSF, is devoted to the working on the birational classification of noncommutative surfaces and related problems. The goal is that these related results would deal with important cases in Artin's conjectured classification and make progress towards an ultimate classification.

This workshop, sponsored by AIM and the NSF, will be devoted to the study of the double ramification cycle in the moduli space of stable curves and its relation with the theory of integrable systems of PDEs, with a special stress on the double ramification hierarchy, a construction associating to any cohomological field theory an integrable system of PDEs and its quantization.

This workshop, sponsored by AIM and the NSF, will be devoted to studying geometric realizations of Langlands functoriality via cycles on Shimura varieties.

Mathematical Sciences Research Institute (MSRI), Berkeley

Holomorphic differentials on Riemann surfaces have long held a distinguished place in low dimensional geometry, dynamics and representation theory. Recently it has become apparent that they constitute a common feature of several other highly active areas of current research in mathematics and also at the interface with physics. In some cases the areas themselves (such as stability conditions on Fukaya-type categories, links to quantum integrable systems, or the physically derived construction of so-called spectral networks) are new, while in others the novelty lies more in the role of the holomorphic differentials (for example in the study of billiards in polygons, special - Hitchin or higher Teichmuller - components of representation varieties, asymptotic properties of Higgs bundle moduli spaces, or in new interactions with algebraic geometry).

This workshop, sponsored by AIM and the NSF, will be devoted to reviewing recent progress on K-stability of Fano varieties with an emphasis on the the algebraic theory. The organizing theme will be to investigate connections between various approaches and encourage participants from different backgrounds to share techniques.

This workshop will survey notable developments and applications of higher category theory; it will be a venue for end-users to share their vision of how to apply the theory, as well as developers to share technical advancements. It will consist of 6 series of 3 lectures, each given by instrumental end-users & developers of higher category theory, together with a few question-answer sessions. Each lecture series will be tailored to a diverse audience, accessible to graduate students and non-expert researchers with some background in homological also algebra. The content of these lecture series will concern the following topics.

Johns Hopkins University

Mathematical Sciences Research Institute (MRSI)

This workshop will focus on recent developments in factorization homology, parametrized homotopy theory, and algebraic K-theory. These seemingly disparate topics are unified by a common methodology, which leverages universal properties and unforeseen descent by way of higher category theory. Furthermore, they enjoy powerful and complementary roles in application to the cyclotomic trace.

This workshop, sponsored by AIM and the NSF, will be devoted to bringing together physicists and mathematicians to concentrate on a variety of problems concerning special holonomy compactifications of M-theory.

This workshop, sponsored by AIM and the NSF, will explore the applications to chromatic homotopy and algebraic K-theory of the new computational techniques in equivariant stable homotopy. The recent renaissance in equivariant stable homotopy theory has provided several new tools which allow us to better understand classical problems and carry out new computations.

The goal is to air fresh perspectives and open problems in combinatorics and algebra, those that the speakers think will be important for the future.

This workshop, sponsored by AIM and the NSF, will be devoted to the study of the geometry and arithmetic of moduli spaces associated to dynamical systems on algebraic varieties, with a particular emphasis on dynamical systems on projective space.

University of Michigan in Ann Arbor