Equivariant Combinatorics: A Summer School and Workshop

Drexel University, Philadelphia PA

Investigators

Abstract

This award supports the participation of a diverse group of junior researchers in a summer school and workshop entitled "Equivariant Combinatorics," to be held from June 12-23, 2017 at the Centre de Recherche Mathematiques in Montreal, Quebec. Algebraic combinatorics is the underlying theme of the workshop and school; it is a vast area of mathematics concerned with the development of tools for analyzing, organizing, and arranging discrete data. The workshop and school will enhance the development of combinatorial methods essential in areas such as genomics, computer science, statistics, and physics. Emphasis is on the creation of combinatorial techniques for attacking problems in algebraic and geometric areas such as symmetric function theory, a subject with applications to probability and statistical mechanics. The program will promote the use of and training in an open-source computational symbolic algebra system, SAGE. The workshop is a forum for the communication of recent developments on a body of problems in representation theory, algebraic geometry and topology, and theoretical physics with common combinatorial underpinnings. The focus is on rectangular Catalan combinatorics, relating varied areas such as representation theory of diagonal harmonic polynomials and coinvariant spaces, flag bundles over the Hilbert scheme of points in the plane, affine Springer fibres, and Khovanov-Rozansky homology of torus knots. Three lecture series will run during the summer school preceding the workshop. The speakers, known for both their communication and academic excellence, were choosen for differing viewpoints on similar problems in equivariant combinatorics. The school will broaden participants' perspective and will enable them to more fully benefit from the subsequent workshop talks. There will also be ample opportunity to share code and gain experience with the open-source SAGE-Combinat computer algebra system. Participants will leave equipped to help colleagues at their home institutions begin mathematical experimentation in SAGE. Details of the program can be found at http://www.crm.umontreal.ca/2017/Equivariant17/index_e.php.