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Please note: The University of Waterloo is closed for all events until further notice.

Events

Thursday, May 20, 2021 — 1:00 PM EDT

Title: q-Whittaker functions, finite fields, and Jordan forms

Speaker: Steven Karp
Affiliation: UQAM
Zoom: Contact Steve Melczer

Abstract:

The q-Whittaker symmetric function associated to an integer partition is a q-analogue of the Schur symmetric function. We give a new formula for the q-Whittaker function in terms of partial flags compatible with a nilpotent endomorphism over the finite field of size 1/q.

Friday, May 21, 2021 — 3:30 PM EDT

Title: Positivity Problems for Linear Recurrences

Speaker: Steve Melczer
Affliliation: University of Waterloo
Zoom: Contact Emma Watson

Abstract:

Although sequences satisfying linear recurrence relations have been studied for centuries, and appear as some of the first examples of combinatorial sequences encountered in an introductory combinatorics class, there are natural examples of simply stated problems related to their basic behaviour whose decidability is unknown. In this talk we survey some open computability and complexity questions related to the positivity of linearly recurrent sequences, before examining a new approach to proving positivity using rigorous numerical methods for functions satisfying linear differential equations.

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