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Events - April 2021

Monday, April 26, 2021 — 11:30 AM EDT

Title: A Spectral Moore Bound for Bipartite Semiregular Graphs

Speaker: Sabrina Lato
Affiliation: University of Waterloo
Zoom: Contact Soffia Arnadottir

Abstract:

The Moore bound provides an upper bound on the number of vertices of a regular graph with a given degree and diameter, though there are disappointingly few graphs that achieve this bound. Thus, it is interesting to ask what additional information can be used to give Moore-type bounds that are tight for a larger number of graphs. Cioaba, Koolen, Nozaki, and Vermette considered regular graphs with a given second-largest eigenvalue, and found an upper bound for such graphs.

Friday, April 23, 2021 — 3:30 PM EDT

Title: Robust Interior Point Methods for Key Rate Computation in Quantum Key Distribution

Speaker: Hao Hu
Affliliation: University of Waterloo
Zoom: Contact Emma Watson

Abstract:

We study semidefinite programs for computing the key rate in finite dimensional quantum key distribution (QKD) problems. Through facial reduction, we derive a semidefinite program which is robust and stable in the numerical computation. Our program avoids the difficulties for current algorithms from singularities that arise due to loss of positive definiteness. This allows for the derivation of an efficient Gauss-Newton interior point approach. We provide provable lower and upper bounds for the hard nonlinear semidefinite programming problem.

Monday, April 19, 2021 — 11:03 AM EDT

Title: Quantum walks on Cayley graphs

Speaker: Julien Sorci
Affiliation: University of Florida
Zoom: Contact Soffia Arnadottir

Abstract:

In this talk we will look at the continuous-time quantum walk on Cayley graphs of finite groups. We will show that normal Cayley graphs enjoy several nice algebraic properties, and then look at state transfer phenomena in Cayley graphs of certain non-abelian p-groups called the extraspecial p-groups. Some of the results we present are part of joint work with Peter Sin.

Friday, April 16, 2021 — 3:30 PM EDT

Title: A proof of the Erdős–Faber–Lovász conjecture

Speaker: Tom Kelly
Affliliation: University of Birmingham
Zoom: Contact Emma Watson

Abstract:

The Erdős–Faber–Lovász conjecture (posed in 1972) states that the chromatic index of any linear hypergraph on $n$ vertices is at most $n$.  We prove this conjecture for every sufficiently large $n$.  This is joint work with Dong Yeap Kang, Daniela Kühn, Abhishek Methuku, and Deryk Osthus.

Thursday, April 15, 2021 — 1:00 PM EDT

Title: Algebraic structure of the Hopf algebra of double posets

Speaker: Yannic Vargas
Affiliation: Potsdam University
Zoom: Contact Karen Yeats

Abstract:

A Hopf algebra of double posets was introduced by Claudia Malvenuto and Christophe Reutenauer in 2011, motivated by the study of pictures of tableaux as defined by Zelevinsky. Starting from the correspondence between top-cones in the braid arrangement and partial orders, we investigate several properties of the Hopf algebra of double posets as the image of a Hopf monoid (via the Fock functor). In particular, we obtain a non-cancellative formula for the antipode. A description of the primitive space is also discussed.

Monday, April 12, 2021 — 11:30 AM EDT

Title: Feynman integrals as algebraic graph theory

Speaker: Karen Yeats
Affiliation: University of Waterloo
Zoom: Contact Soffia Arnadottir

Abstract:

I will overview how Feynman integrals should feel very familiar to algebraic graph theorists, and then say a few words about current directions of interest to me, particularly the c_2 invariant.

Friday, April 9, 2021 — 3:30 PM EDT

Title: Circuit QED Lattices: Synthetic Quantum Systems on Line Graphs

Speaker: Alicia Kollár
Affliliation: University of Maryland
Zoom: Contact Emma Watson

Abstract:

After two decades of development, superconducting circuits have emerged as a rich platform for quantum computation and simulation. Lattices of coplanar waveguide (CPW) resonators realize artificial photonic materials or photon-mediated spin models. Here I will highlight the special property that these lattice sites are deformable and allow for the implementation of devices with graph-like configurational flexibility. In particular, I will show that it is possible to create synthetic materials in which microwave photons experience negative curvature, which is impossible in conventional electronic materials [1].

Thursday, April 8, 2021 — 1:00 PM EDT

Title: A tale of two integrals

Speaker: Jonathan Novak
Affiliation: University of California San Diego
Zoom: Contact Karen Yeats

Abstract:

The Harish-Chandra/Itzykson-Zuber (HCIZ) and Brezin-Gross-Witten (BGW) integrals are a pair matrix integrals which play a prominent role in quantum field theory. Remarkably, these ubiquitous special functions are also significant from the perspective of algebraic combinatorics: they are generating functions for certain classes of Hurwitz numbers.

Thursday, April 1, 2021 — 1:00 PM EDT

Title: A combinatorial approach to Minkowski tensors of polytopes

Speaker: Amy Wiebe
Affiliation: Freie Universität Berlin
Zoom: Contact Karen Yeats

Abstract:

Intrinsic volumes of a convex body provide scalar data (volume, surface area, Euler characteristic, etc. ) about the geometry of a convex body independent of the ambient space. Minkowski tensors are the tensor-valued generalization of intrinsic volumes. They provide more complex geometric information about a convex body, such as its shape, orientation, and more.

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