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Faye Pasley, Molly Lynch, NC State

April 26, 2018 | 3:00 pm - 4:00 pm EDT

Speaker 1: Faye Pasley
Title: Determinantal Representations, the Numerical Range, and Invariance
We study hyperbolic polynomials with symmetry and express them as the determinant of a Hermitian matrix with special structure. By properly modifying a construction of Dixon (1902), we show for every hyperbolic polynomial of degree $n$ invariant under the cyclic group of order $n$ there exists a determinantal representation admitted via some cyclic weighted shift matrix. Moreover, this gives a nice result related to the numerical range of a matrix with the same invariance.
Speaker 2: Molly Lynch
Title: Combinatorics of crystal graphs
Abstract: In this talk, we explore the combinatorics of crystal graphs. One of our main goals is to understand relations among so called crystal operators. We can assign a certain graph to the crystal base associated to a highest weight representation of classical Cartan type. These graphs are endowed with a natural partial order.  We use tools from poset topology, particularly lexicographic discrete Morse theory, to study relations among crystal operators. We end by discussing the special case of crystals of two rowed shapes.

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Date:
April 26, 2018
Time:
3:00 pm - 4:00 pm EDT
Event Category:

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