Seminar

Title: Incompressibility of classical distributions

Abstract:

We prove a general, robust, single-letter lower bound on the achievable rate for ensembles of classical states, which holds even when Alice and Bob share free entanglement and allow a constant local error. 

Title: Resilience of the rank of random matrices

Abstract:

I will discuss the preprint of this title by Ferber, Luh, and McKinley (arXiv:1910.03619).

Title: Disjunctive Cuts through the V-Polyhedral Lens

Abstract:

Cutting planes, or cuts, are a critical component of modern integer programming solvers, but existing cuts implemented in solvers are relatively simple compared to those in the literature. We discuss the primary reasons for this disparity, as well as our recently-proposed V-polyhedral framework for mitigating some of these difficulties encountered by prior "stronger" cuts.

Title: Kummer's Theorem on binomial coefficients, etc.

Abstract: 

Some of us like the primes and call ourselves pure mathematicians. Some of us like the Catalan numbers and call ourselves combinatorialists.

Title: Submodular function maximization via the multilinear relaxation and contention resolution schemes

Abstract:

I will present a general framework for maximizing a nonnegative submodular set function $f$ subject to a variety of packing type constraints including multiple matroid constraints, knapsack constraints, and their intersections.

Title: Halfway to Rota's Basis Conjecture

Abstract:

Rota’s Basis Conjecture is that any rank-n matroid with n disjoint bases B_1, …, B_n has n disjoint transversal bases; a basis is transversal if it contains exactly one element from each B_i.

Title: From weakly separated collections to matroid subdivisions

Abstract:

We study arrangements of slightly skewed tropical hyperplanes, called blades, on the vertices of a hypersimplex $\Delta_{k,n}$.

Title: A deterministic (1/2 + epsilon)-approximation for submodular maximizztion over a matroid

Abstract:

In 1978, it was shown that a natural greedy algorithm gives a 1/2 approximation to submodular maximization subject to a matroid constraint.

Title: Cospectral and strongly cospectral vertices

Abstract:

If $a$ is a vertex in a graph with adjacency matrix $A$, the \textsl{walk module} generated by $a$ is the $A$-invariant subspace spanned by the vectors $A^re_a$, for $r\ge0$.

Title: The combinatorics of parametric Feynman integrals

Abstract:

Feynman integrals are used in perturbative quantum field theory to compute the probabilities of processes involving elementary particles. They can be represented as Feynman graphs and exhibit a rich combinatorial structure. The parametric representation of Feynman integrals is particularly suitable to be studied from a combinatorial perspective since it contains well known objects like the Kirchhoff polynomial.