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Title:ÌýCritical Points at Infinity for Hyperplanes of Directions

Abstract:ÌýAnalytic 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:ÌýMatroids without cliques

Abstract:ÌýThe 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:ÌýSteiner Cut Dominants

Abstract:ÌýFor 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:ÌýOn the complexity of quantum partition functions

Abstract:ÌýQuantum 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:ÌýSets that Support a Joint Distribution

Abstract:ÌýGiven a closed set on the plane and two probability distributions on the real line, when are there random variables with the given distributions whose joint distribution is supported by the given set?

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:ÌýLorentzian polynomials

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

Title: Bounded degree arboricity

Abstract: For a multigraph $G$ together with a positive weight $f(v)$ on every vertex $v$, we study the problem of covering the edge set of $G$ by the minimum number of forests $F$ in which every vertex $v$ has degree at most $f(v)$ in $F$.

Title:ÌýBreaking the Supersingular Isogeny Diffie-Hellman protocol

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

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. ÌýIn 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. Ìý