Events

Title: Orthogonal basis of eigenvectors for the Johnson and Kneser graphs

Abstract: The Johnson and Kneser graphs have the same eigenspaces. How explicitly can we describe these eigenspaces? 

Title: The matching polytope has exponential extension complexity

Abstract: This Friday we will build off of some previous results by looking at the paper “The matching polytope has exponential extension complexity” by Thomas Rothvoss! At the beginning of the semester, we saw that the matching (and TSP) polytopes cannot be expressed by a polynomial sized symmetric LP.

Title: A brief introduction to lattice-based cryptography

Abstract: A brief introduction to lattice-based cryptography, one of the leading candidates for building quantum-resistant cryptosystems.

Title: Snake decomposition of lattice path matroids

Abstract: Lattice path matroids (LPMs) are positroids whose base polytopes have a nice decomposition. We provide a geometric perspective to this decomposition in terms of fences and their order polytopes, which correspond to a certain class of LPMs we call snakes.

Title: Lorentzian polynomials

Abstract: Lorentzian polynomials on cones are intimately connected to Hodge theory, matroid theory and the geometry of zeros of polynomials.

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: 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.