Positivity in Algebraic Combinatorics (15w2208)


(Wilfrid Laurier University)

Stephanie Van Willigenburg (UBC)


The Banff International Research Station will host the "Positivity in Algebraic Combinatorics" workshop in Banff from August 14 to August 16.

Symmetric functions form a significant area of research, especially within algebraic combinatorics, in particular because of the fundamental elements, the Schur functions. These functions also arise naturally in many areas of mathematics, computer science, and physics. A deeper understanding of Schur functions, and their many properties, enables many of the beautiful and useful results in these areas, and leads to many applications via connections between diverse areas from pure mathematics to applied mathematics and beyond. A key aspect of such a deeper understanding is knowing exactly how an arbitrary symmetric function can be expressed in terms of Schur functions. Indeed, it is a long-standing and important open question to classify whether an arbitrary function is a positive linear combination of Schur functions, that is, Schur-positive.

The positivity question is a timely one, and advances have recently been made regarding positivity for a diverse range of closely related functions including quasisymmetric functions, Schur Q and P functions and Schubert polynomials. The key goals of the workshop are to exchange ideas and tools on various aspects of this problem, and to create the intense atmosphere that will facilitate new collaborations and jumpstart new research.

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).