Meetings/Workshops on Numerical Analysis and Computational Mathematics in the United States (USA)

ICERM

Braid groups were introduced by Emil Artin almost a century ago. Since then, braid groups, mapping class groups, and their generalizations have come to occupy a significant place in parts of both pure and applied mathematics. In the last 15 years, fields with an interest in braids have independently undergone rapid development; these fields include representation theory, low-dimensional topology, complex and symplectic geometry, and geometric group theory. Braid and mapping class groups are prominent players in current mathematics not only because these groups are rich objects of study in their own right, but also because they provide organizing structures for a variety of different areas. For example, in modern representation theory, important equivalences of categories are organized into 2-representations of braid groups, and these same 2-representations appear prominently in parts of geometry and mathematical physics concerned with mirror dualities; in low-dimensional topology, manifolds are presented and related to each other via braids and mapping classes. Computational applications and questions about braid groups have also emerged in disparate mathematical contexts; in some cases, these coalesce around the same computational problem. For example, developing fast machine-based calculations of link homology invariants is a goal shared by representation theorists, low-dimensional topologists, symplectic and algebraic geometers, and string theorists. The proposed semester program aims to bring together researchers working in diverse areas through the common thread of their interaction with braid and mapping class groups. The overarching goals of the program are to establish and clarify the key questions driving each field, and to improve each group’s understanding of the tools, techniques, and perspectives of the others.

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

This regional conference series is a collaborative event between the research groups in analysis and PDE at the University of Cincinnati and the University of Kentucky. It meets once a year alternating between the two universities. The goal is to foster closer research collaborations between the two departments and to bring leading experts in the field to the region.

Analysis,    Calculus, Differential Equations and Integration

The PCMI graduate summer school program in 2022 will consist of a sequence of 11 minicourses. Each minicourse is accompanied by a problem session. The topics are arranged so that there is good material and opportunities for learning both for less experienced students as well as more advanced students. Beyond their attendance in these minicourse sessions, all graduate participants will be able to take part in the substantial other benefits of a PCMI session. This includes the opportunity to interact with the researchers in residence and take part in the research seminar component of PCMI. Many graduate students also interact in significant ways with the undergraduate cohort,,the undergraduate faculty cohort, and may also participate in the many pedagogically focused activities which form part of the K-12 Teacher Leadership Program and the Workshop for Equity in Mathematics Education. PCMI includes numerous cross-program activities to help members from all these groups interact with one another.

Courses and Events for Math Students and Early Career Researchers,    Number Theory, Arithmetic