Events

Title: A tale of two integrals

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.

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

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].

Title: Feynman integrals as algebraic graph theory

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.

Title: Algebraic structure of the Hopf algebra of double posets

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.

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

Title: Quantum walks on Cayley graphs

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.

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

Title: A Spectral Moore Bound for Bipartite Semiregular Graphs

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.

Title: Quantum independence number

Abstract:

From this talk you will be able to learn what quantum independence number is and how it is different from the classical independence number. I will provide both known individual and infinite families of the graphs where classical and quantum independent numbers are different, as well as some of our generalisations of these examples.  

Title: Interlacing methods in Extremal Combinatorics