Asymptotic Algebraic Combinatorics (19w5220)

Arriving in Banff, Alberta Sunday, March 10 and departing Friday March 15, 2019


(University of California Los Angeles)

Alejandro Morales (University of Massachusetts Amherst)

(University of Pennsylvania and IAS Princeton)

(University of California Davis)


The Banff International Research Station will host the "Asymptotic Algebraic Combinatorics" workshop in Banff from March 10, 2019 to March 15, 2019.

Algebraic Combinatorics is an area of mathematics that employs methods of abstract algebra,
notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra and representation theory. Many of its problems arise from the need of quantitative and explicit understanding of algebraic phenomena. Its quantitative aspects focused on explicit enumerative formulas, and combinatorial interpretations for dimensions, multiplicities, structure constants. Two highlights of this area are the hook-length product formula for counting standard tableaux and the Littlewood—Richardson rule. However, most often than not, such formulas and rules are a miracle rather than a property. No explicit product formula is known for counting skew tableaux, reduced words, monomials Schubert polynomials nor even discrete interpretations for Kronecker coefficients, Gromov-Witten invariants, Schubert polynomials.

Yet discrete objects of algebraic origins like Schur functions, standard tableaux and plane partitions are also related to integrable models of particle or dimer configurations within Statistical Mechanics. These objects are also central to Asymptotic Representation Theory. In these fields, and, more generally, in Probability, the problems are about understanding the large scale limit or asymptotic behavior rather than having explicit exact formulas and descriptions. Hence we need to find asymptotic formulas for the main objects of Algebraic Combinatorics and study the emerging field of Asymptotic Algebraic Combinatorics.
The main goal of this workshop is to bring together people from all the relevant areas, which are naturally very disjoint --
Algebraic Combinatorics, Analytic Combinatorics, Probability, Representation Theory, to share results and methods and establish the asymptotic study of objects and quantities in Algebraic Combinatorics.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).