Events

Title: Some results on spectral Turán's type problem

Title: Critical Points at Infinity for Hyperplanes of Directions

Abstract: Analytic combinatorics in several variables (ACSV) analyzes the asymptotic growth of series coefficients of multivariate rational functions G/H in an exponent direction r. The poly-torus of integration T that arises from the multivariate Cauchy Integral Formula is deformed away from the origin into cycles around critical points of a “height function" h on V = V(H).

Title: Matroids without cliques

Abstract: The class of graphs that omit some fixed complete graph as a minor is very well-studied; in particular, the densest graphs in the class are known. The analogous question for matroids is just as well-motivated, but seems harder to answer. I will discuss some recent progress in this area, which reduces a bound from doubly exponential to singly exponential. This is joint work with Sergey Norin and Fernanda Rivera Omana.

Title: Steiner Cut Dominants

Abstract: For a subset of terminals T of the nodes of a graph G a cut in G is called a T-Steiner cut if it subdivides T into two non-empty sets. The Steiner cut dominant of G is the Minkowski sum of the convex hull of the incidence vectors of T-Steiner cuts in G and the nonnegative orthant.

Title: Quasisymmetric varieties, excedances, and bases for the Temperley--Lieb algebra

Abstract:  This talk is about finding a quasisymmetric variety (QSV): a subset of permutations which (i) is a basis for the Temperley--Lieb algebra TL_n(2), and (ii) has a vanishing ideal (as points in n-space) that behaves similarly to the ideal generated by quasisymmetric polynomials.   While this problem is primarily motivated by classical (co-)invariant theory and generalizations thereof, the course of our investigation uncovered a number of remarkable combinatorial properties related to our QSV, and I will survey these as well. 

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: Inverse eigenvalue problem of a graph

Abstract:  We often encounter matrices whose pattern (zero-nonzero, or sign) is known while the precise value of each entry is not clear. Thus, a natural question is what we can say about the spectral property of matrices of a given pattern. When the matrix is real and symmetric, one may use a simple graph to describe its off-diagonal nonzero support.

Title: Distance-Regular and Distance-Biregular Graphs

Abstract: For a given diameter d and valency k, what is the maximum number of vertices a k-regular graph of diameter d can have, and what graphs meet that bound? Although there is a straightforward counting argument to bound the number of vertices using the structural information, the problem of characterizing the graphs that meet the bound turns out to be a problem in algebraic graph theory, and helps gives rise to the notion of distance-regular graphs.

Title: Arrangements of Pseudolines, Tropical Grassmannians, and Generalized Scattering Amplitudes

Abstract: For each arrangement of (pseudo)lines on the projective plane, it is possible to construct a differential form that captures its combinatorial structure. The forms have simple poles whenever triangles shrink to a point in the arrangement, and share the same residue when two arrangements are connected via a "triangle flip".

Title: The heroes of digraphs: coloring digraphs with forbidden induced subgraphs

Abstract: The chromatic number is one of the most studied graph invariants in graph theory. $\chi$-boundedness, for instance, studies the induced subgraphs present in graphs with large chromatic number and small clique number. Neumann-Lara introduced an analog directed version of this graph invariant: the dichromatic number of digraphs.