Department of Mathematics,
University of California San Diego
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Math 211A: Seminar in Algebra
Dr. Keller VandeBogert
University of Notre Dame
From Total Positivity to Pure Free Resolutions
Abstract:
Polya frequency sequences are ubiquitous objects with a surprising number of connections to many different areas of mathematics. It has long been known that such sequences admit a "duality" operator that mimics the duality of a Koszul algebra and its quadratic dual, but the precise connection between these notions turns out to be quite subtle. In this talk, we will see how the equivariant analogue of Polya frequency is closely related to the problem of constructing Schur functors "with respect to" an algebra. We will moreover see how these ideas come together to understand the problem of extending Boij--Soederberg theory to other classes of rings, with particular attention given to the case of quadric hypersurfaces. This is based on joint work with Steven V. Sam.
Steven Sam and Karthik Ganapathy
October 14, 2024
3:00 PM
AP&M 7321
Research Areas
Algebra Algebraic Geometry Representation Theory****************************
