Events

Title: The $k$-Independence Number

Abstract:

An independent set, also known as a stable set or coclique, in a graph is a set of vertices, no two of which are adjacent. The size of a largest independent set is called the independence number. Two classical eigenvalue bounds on the independence number, proved using eigenvalue interlacing are the Hoffman's ratio bound and the Cvetkovi\'{c}'s inertia bound.

Title: Asymptotic quantum state transfer using two loops with large weights

Abstract:

We study the question of asymptotic transfer strength between two nodes of a graph when large weight loop edges are located at these nodes.  It turns out that the limiting strength can be exactly computed and depends only on the extended neighborhoods of the nodes.

Title: Two conjectures on the spread of graphs

Abstract:

Given a graph $G$ let $\lambda_1$ and $\lambda_n$ be the maximum and minimum eigenvalues of its adjacency matrix and define the spread of $G$ to be $\lambda_1 - \lambda_n$. In this talk we discuss solutions to a pair of 20 year old conjectures of Gregory, Hershkowitz, and Kirkland regarding the spread of graphs.

Title: In Memoriam: Tom Coleman’s Contributions to Applied Mathematics and Optimization

Description:

Thomas F. Coleman—a leader in optimization and scientific computing, professor at the University of Waterloo, and a SIAM Fellow—passed away on April 20, 2021. Tom served as the Director of the Theory Center at Cornell and then as Dean of the Faculty of Mathematics at the University of Waterloo. His research spanned continuous optimization, combinatorial scientific computing, automatic differentiation, financial optimization, mathematical software, etc. In this session, his wife and collaborator, Yuying Li, and five of his students and colleagues will describe the pioneering contributions that Tom made to these fields in his research.

Title: In Memoriam: Tom Coleman’s Contributions to Applied Mathematics and Optimization

Description

Title: The spectrum of the random-to-below Markov chain

Abstract:

The random-to-below shuffle of a deck of cards consists of removing any card randomly (with uniform probability), and inserting it anywhere below (with uniform probability). When looking at the eigenvalues of its transition matrix, they all seem to be rational and positive.

Title: Algebraic formulations of Zauner's conjecture

Abstract:

Tight complex projective 2-designs are simultaneously maximal sets of equiangular lines and minimal complex projective 2-designs. In quantum information theory, they define optimal measurements known as SIC-POVMs (Symmetric Informationally Complete Positive Operator-Valued Measures).  They are conjectured by Zauner to exist in every dimension, even as specific group orbits.  Yet, they have only so far been proven to exist in a finite-but-growing list of dimensions via exact, explicit constructions over increasingly high-degree number fields, since identified as specific class fields of real quadratic number fields.

Title: Equivalent Laplacian and Adjacency Quantum Walks on Irregular Graphs

Abstract: 

The continuous-time quantum walk is a particle evolving by Schrödinger's equation in discrete space. Encoding the space as a graph of vertices and edges, the Hamiltonian is proportional to the discrete Laplacian. In some physical systems, however, the Hamiltonian is proportional to the adjacency matrix instead.

Title: A primal-dual interior-point algorithm fo rnonsymmetric conic optimization

Abstract:

It is well known that primal-dual interior-point algorithms for linear optimization can easily be extended to the case of symmetric conic optimization, as shown by Nesterov and Todd (NT) in their 1997 paer about self-scaled barriers. Although many convex optimization problems can be expressed using symmetric cones then models involving for instance exponential functions do not belong to the class of symmetric conic optimization problems.

Title: Macdonald polynomials and the multispecies zero range process

Abstract:

Over the last couple of decades, the theory of special functions and symmetric functions have found unexpected connections to various interacting particle systems. Macdonald polynomials are a family of symmetric functions that are known to have remarkable connections to a well-studied particle model called the ASEP. It is natural to ask whether the modified Macdonald polynomials can be obtained using a combinatorial gadget for some other particle system.