Emanuel Silva

Affiliation: Universidade Federal de Minas Gerais, Brazil

Title: Quantum walks do not like bridges

Abstract: In this talk we consider graphs with two cut vertices joined by a bridge, and prove that there can be no quantum perfect state transfer between these vertices, unless the graph has no other vertex. We achieve this result by applying the 1-sum lemma for the characteristic polynomial of graphs, the neutrino identities that relate entries of eigenprojectors and eigenvalues, and variational principles for eigenvalues (Cauchy interlacing and Weyl inequalities).

The talk will soon be available on YouTube, meanwhile you can view the slides here.

This talk was given on Januray 10th, 2021


Title: Strongly Cospectral Vertices in Trees

Abstract: This talk is about the problem of finding a triple of pairwise strongly cospectral vertices at a tree. We present a construction of trees with cospectral non-similar vertices by looking at the limbs of the vertices. Then, we discuss the difficulties of finding such triples and comment about related problems.

You can view the talk here and the slides are available here.

This talk was given on October 18th, 2021