Events

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: Two-colouring hypersurface complements in open Richardson varities

Abstract: 

Given an algebraic hypersurface $H \subset \mathbb{R}^n$, we can always 2-colour the components of the complement $\mathbb{R}^n \setminus H$ such that adjacent components are of opposite colours.

Title: Counting Pentagons in Triangle-free Binary Matroids

Abstract:

Every triangle-free graph with n vertices contains at most (n/5)^5 cycles of length five, and this value is attained by the balanced blowup of the 5-cycle.

Title: Circuit-hyperplane relaxation and matroid representation

Abstract:

Relaxing a circuit-hyperplane in a representable matroid can destroy representability.

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: 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: 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: 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. 

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: 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.