Events

Title: Generalized Modular String Averaged Procedure and Its Applications to Iterative Methods

Abstract: A modular string averaging procedure (MSA, for short) for a finite number of operators  was first introduced by Reich and Zalas in 2016. The MSA concept provides a flexible  algorithmic framework for solving various feasibility problems such as common fixed point and convex feasibility problems.

Title: Breaking the Supersingular Isogeny Diffie-Hellman protocol

Abstract: Finding an explicit isogeny between two given isogenous elliptic curves over a finite field is considered a hard problem, even for quantum computers.

Title: Eigenvalues for stochastic matrices with a prescribed stationary distribution

Abstract: A square nonnegative matrix T is called stochastic if all of its row sums are equal to 1. Under mild conditions, it turns out that there is a positive row vector w^T (called the stationary distribution for T) whose entries sum to 1 such that the powers of T converge to the outer product of w^T with the all-ones vector. Further, the nature of that convergence is governed by the eigenvalues of T.

In this talk we explore how the stationary distribution for a stochastic matrix exerts an influence on the corresponding eigenvalues.

Title: Bounding the extended complexity of the stable set polytope on perfect graphs

Abstract: This week we will study the extension complexity of the stable set polytope for perfect graphs. More than 40 years ago, Grötschel et al. gave an algorithm to find maximal weight stable sets on perfect graphs based on a compact semidefinite extension. However, whether there is a compact linear extension is still an open problem.

Title: Chromatic Symmetric Functions: Combining Algebra and Graph Theory

Abstract: The chromatic polynomial, enumerating the proper colorings of a graph by number of colors used, was created by Birkhoff in the early 1900s to study the then Four-Color Conjecture.  In the 1990s, Stanley generalized this to a chromatic symmetric function, which further counts for each proper n-coloring how many times each of the n colors is used.  

Title: Excluded-minor characteristics

Abstract: We review the excluded-minor characterizations for matroids over small fields and discuss the obstacles towards finding such a characterization for GF(5)-representability.

Title: On the complexity of quantum partition functions

Abstract: Quantum complexity theory has been intertwined with the study of quantum many-body systems ever since Kitaev's insight that computing their ground energies is an intractable quantum constraint satisfaction problem that is complete for a quantum generalization of NP.

Title: Approximation algorithms for dense quantum Hamiltonians using convex relaxations

Abstract: Computing ground-state energy and partition functions for quantum Hamiltonian systems are problems of broad applicability in physics. These are also natural generalizations of well-studied classical computational tasks such as maximum constraint satisfaction and computing partition functions of Ising models. In this talk, I will present new classical approximation algorithms for these problems in the case of dense quantum Hamiltonians.

Title: Quantum walk state transfer on a hypercube

Abstract: We investigate state transfer on a hypercube by means of a quantum walk where the sender and the receiver vertices are marked by weighted loops.

Title: Extended Formulations for the Colonel Blotto Game

Abstract: Suppose you want to replace Doug Ford as premier. To beat him, you need to win as many seats as possible. You have some finite amount of resources to allocate across all seats - if you spend more on a seat than Ford does, you will win that seat. How should you allocate your resources to maximize your expected number of seats?