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# Events for January 19, 2018 from General and Seminar calendars

## Algebra and Combinatorics Seminar

**Abstract:** The h-vector of a simplicial complex X is a well-studied invariant with connections to algebraic aspects of its Stanley-Reisner ring. When X is the independence complex of a matroid Stanley has conjectured that its h-vector is a ‘pure O-sequence’, i.e. the degree sequence of a monomial order ideal where all maximal elements have the same degree. The conjecture has inspired a good deal of research and is proven for some classes of matroids, but is open in general. Merino has established the conjecture for the case that X is a cographical matroid by relating the h-vector to properties of chip-firing and `G-parking functions' on the underlying graph G. We introduce and study the notion of a ‘coparking’ function on a graph (and more general matroids) inspired by a dual version of chip-firing. As an application we establish Stanley’s conjecture for certain classes of binary matroids that admit a well-behaved `circuit covering'. Joint work with Kolja Knauer

## Hiring Candidate Dr. Li Wang

**Description:**

**Time:** 3:00PM - 4:00PM

**Location:** BLOC 628

**Speaker:** Anton Dochtermann, Texas State University

**Title:** *Coparking functions and h-vectors of matroids*

**Time:** 4:00PM - 5:00PM

**Location:** BLOC 220

**Speaker:** Dr. Li Wang, State University of New York at Buffalo

Title: Front capturing schemes for nonlinear PDEs with a free boundary limit

Abstract:

Evolution in physical or biological systems often involves interplay between nonlinear interaction among the constituent “particles”, and convective or diffusive transport, which is driven by density dependent pressure. When pressure-density relationship becomes highly nonlinear, the evolution equation converges to a free boundary problem as a stiff limit. In terms of numerics, the nonlinearity and degeneracy bring great challenges, and there is lack of standard mechanism to capture the propagation of the front in the limit.

In this talk, I will introduce a numerical scheme for tumor growth models based on a prediction-correction reformulation, which naturally connects to the free boundary problem in the discrete sense. As an alternative, I will present a variational method for a class of continuity equations (such as Keller-Segel model) using the gradient flow structure, which has built-in stability, positivity preservation and energy decreasing property, and serves as a good candidate in capturing the stiff pressure limit.