Seminar

Title: The size Ramsey numbers of graphs and hypergraphs

Abstract:

The s-colour size-Ramsey number of a graph ( hypergraph) H is the minimum number of edges in a graph (hypergraph) G whose every s-edge-colouring contains a monochromatic copy of H. While the   study of size Ramsey numbers for graphs  goes back to 70's to the work of Erdos, Faudree, Rousseau and Schelp, the systematic study of these numbers for hypergraphs have been initiated much more recently in 2017  by Dudek, La Fleur, Mubayi, and Rödl. In this talk we will present the current known results in the literature, and some recent progress we have made on several questions in the area.

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.

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

Description

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.