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September 2017

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Thursday, September 14, 2017 — 3:30 PM EDT

Title: Using eigenvalues to bound the independence number of a graph

Speaker: John  Sinkovic Affiliation: University of Waterloo Location: MC 6486

Abstract:

Finding a maximum independent set (or clique) in an arbitrary graph has been shown to be NP-hard.  As any independent set gives a lower bound on the independence number, determining an upper bound is usually more useful. 

Thursday, September 14, 2017 — 3:30 PM EDT

Title: Geometric drawings of graphs (Part I)

Speaker: Alan Arroyo Affiliation: University of Waterloo Room: MC 5479

Abstract:

This is the first of two talks about drawings of graphs that arise from geometry.

Part I: Understanding rectilinear drawings.

Friday, September 15, 2017 — 3:30 PM EDT

Title: Periodic Vertices in Graphs

Speaker Chris Godsil Affiliation: University of Waterloo Room: MC 5501

Abstract:

If $X$ is a graph with adjacency matrix $A$, then any question about the continuous quantum walk on $X$ is a question about the entries of the unitary matrices \[U(t) = \exp(itA)\]

Two pertinent questions are:

Friday, September 22, 2017 — 3:30 PM EDT

Title: Symmetric group characters as symmetric functions

Speaker: Mike Zabrocki Affiliation: York University Room: MC 5501

Abstract:

The irreducible polynomial representations have Schur polynomials as characters. Similarly there is an in-homogeneous basis of symmetric functions that we call the "irreducible character basis" which are characters of irreducible symmetric group modules when the symmetric group is represented as the subgroup of permutation matrices.

Thursday, September 28, 2017 — 3:30 PM EDT

Title: Quantum Walks and State Transfer

Speaker: Christopher van Bommel Affiliation: University of Waterloo Room: MC 6486

Abstract:

Quantum walks are the quantum analogues of classical random walks and can be used to model quantum computations. If a quantum walker starts at a vertex of a graph and after some length of time, has probability 1 of being found at a different vertex, we say there is perfect state transfer between the two vertices.

Thursday, September 28, 2017 — 3:30 PM EDT

Title: The 1,2,3-Conjecture and a related problem for bipartite graphs

Speaker: Kasper Lyngsie Affiliation: University of Waterloo Room: MC 5479

Abstract:

Friday, September 29, 2017 — 3:30 PM EDT

Title: The quantum and private capacities of quantum channels, and the solution in the low-noise regime

Speaker: Debbie Leung Affiliation: University of Waterloo Room: MC 5501

Abstract:

We first summarize background on the quantum capacity of a quantum channel, and explain why we know very little about this fundamental quantity, even for the qubit depolarizing channel (the quantum analogue of the binary symmetric channel) despite 20 years of effort by the community.

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