Prix Krieger-Nelson SMC

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    • Stephanie van Willigenburg
      University of British Columbia

      Prof. van Willigenburg is a leading expert in algebraic combinatorics, a vibrant area of mathematics that connects with many other fields of study including representation theory, algebraic geometry, mathematical physics, topology and probability. Her research and subsequent discoveries have focused on Schur functions, skew Schur functions and quasisymmetric Schur functions, central topics within the field of algebraic combinatorics.

    An introduction to quasisymmetric Schur functions
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    In algebraic combinatorics a central area of study is Schur functions. These functions were introduced early in the last century with respect to representation theory, and since then have become important in other areas such as quantum physics and algebraic geometry. These functions also form a basis for the algebra of symmetric functions, which in turn forms a subalgebra of the algebra of quasisymmetric functions that itself impacts areas from category theory to card shuffling. Despite this strong connection, the existence of a natural quasisymmetric refinement of Schur functions was considered unlikely for many years. In this talk we will meet such a natural refinement of Schur functions, called quasisymmetric Schur functions. Furthermore, we will see how these quasisymmetric Schur functions refine many well-known Schur function properties, with combinatorics that strongly reflects the classical case including diagrams, walks in the plane, and pattern avoidance in permutations. This talk will require no prior knowledge of any of the above terms.