Title: Minimum eigenvalue of nonbipartite graphs
|Affiliation:||Simon Fraser University|
|Zoom:||Contact Soffia Arnadottir|
Let \rho and \lambda be the largest and the smallest eigenvalue of a connected graph G. It is well-known that \rho + \lambda \geq 0 and that equality occurs if and only if G is bipartite. The speaker will discuss what else can we say when G is not bipartite.
Title: q-Whittaker functions, finite fields, and Jordan forms
|Zoom:||Contact Steve Melczer|
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.
Title: Positivity Problems for Linear Recurrences
|Affliliation:||University of Waterloo|
|Zoom:||Contact Emma Watson|
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.