Title: Pretty Good State Transfer and Minimal PolynomialsSpeaker: Christopher van Bommel Affiliation: University of Manitoba Zoom: Contact Soffia Arnadottir
We examine conditions for a pair of strongly cospectral vertices to have pretty good quantum state transfer in terms of minimal polynomials, and provide cases where pretty good state transfer can be ruled out.
Title: The Hepp bound of a matroid: flags, volumes and integralsSpeaker: Erik Panzer Affiliation: University of Oxford Zoom: Contact Rose McCarty
Invariants of combinatorial structures can be very useful tools that capture some specific characteristics, and repackage them in a meaningful way. For example, the famous Tutte polynomial of a matroid or graph tracks the rank statistics of its submatroids, which has many applications, and relations like contraction-deletion establish a very close connection between the algebraic structure of the invariant (e.g. Tutte polynomials) and the actual matroid itself.