Current students

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: HiGHS: Theory, software and Impact

Abstract:

Since Dantzig formulated the simplex algorithm in 1947, the widespread need to solve linear optimization problems drove the development of algorithmic and computational techniques for decades, yielding several high performance commercial and open source software systems. This talk will focus on the Edinburgh-based work on solving large scale sparse linear programming problems that underpins the high performance open source linear optimization software, HiGHS, the challenges of developing such software, and the Impact that it has achieved.

Title: TBA

Abstract: 

Having briefly introduced the key ideas which make interior point methods (IPMs) such a powerful optimization approach, I shall focus on a solution of the Newton systems and in particular on the use of iterative (Krylov-subspace) techniques to perform this task.

The Newton systems arising in IPMs are inherently ill-conditioned and preconditioning is a must to make iterative methods work.

A re-design of IPMs to enable the use of iterative techniques provides a completely new perspective on these methods.

I will address both theoretical and practical aspects of it.

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: 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: 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: 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: 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.