Algebra and Combinatorics Seminar
The current seminar's organizers are
ChunHung Liu and
Catherine Yan.

Date Time 
Location  Speaker 
Title – click for abstract 

08/28 3:00pm 
Zoom 
Catherine Yan Texas A&M 
Enumeration with Moon Polyominoes and Beyond
A polyomino is a shape made by connecting certain numbers of equalsized
squares, each jointed together with at least one other square along an
edge. A combinatorial model, the model of fillings of polyominoes, is
obtained by assigning a nonnegative integer to each square of the polyomino.
This model emerged from the study of maximal monotone chains in various
combinatorial structures, including permutations, words, matchings, set
partitions, integer sequences, graphs, and multigraphs. It provides a
unified frame in enumerative combinatorics and allows us to apply different
algebraic tools and combinatorial transformations. In this talk I will
show how to use this model to analyze some basic combinatorial
statistics. 

09/04 3:00pm 
Zoom 
ChunHung Liu Texas A&M 
Asymptotic dimension of minorclosed families and beyond
The asymptotic dimension of metric spaces is an important notion in geometric group theory. The metric spaces considered in this talk are the ones whose underlying spaces are the vertexsets of (edge)weighted graphs and whose metrics are the distance functions in weighted graphs. A standard compactness argument shows that it suffices to consider the asymptotic dimension of classes of finite weighted graphs.
We prove that the asymptotic dimension of any minorclosed family of weighted graphs, any class of weighted graphs of bounded treewidth, and any class of graphs of bounded layered treewidth are at most 2, 1, and 2, respectively.
The first result solves a question of Fujiwara and Papasoglu; the second and third results solve a number of questions of Bonamy, Bousquet, Esperet, Groenland, Pirot and Scott.
These bounds for asymptotic dimension are optimal and generalize and improve some results in the literature, including results for Riemann surfaces and Cayley graphs of groups with a forbidden minor.


09/18 3:00pm 
Zoom 
Jacob White UT Rio Grande Valley 
Combinatorial Hopf monoids and flag fvectors
A combinatorial Hopf monoid in species provides an algebraic framework for understanding many polynomial and quasisymmetric function invariants in combinatorics. In this talk, we will discuss the problem of determining when the quasisymmetric functions associated to a combinatorial Hopf monoid are related to the flag fvector of a family of relative simplicial complexes. We also discuss inequalities we obtain for the quasisymmetric functions in this situation, and describe some new examples of quasisymmetric functions, and combinatorial Hopf monoids. If there is time, we will also discuss Fpositivity. 

09/25 3:00pm 
Zoom 
Erika Ordog Texas A&M 
Minimal resolutions of monomial ideals
The problem of finding minimal free resolutions of monomial
ideals in polynomial rings has been central to commutative
algebra ever since Kaplansky raised the problem in the 1960s and
his student, Diana Taylor, produced the first general
construction in 1966. The ultimate goal along these lines is a
construction of free resolutions that is universal  that is,
valid for arbitrary monomial ideals  canonical, combinatorial,
and minimal. This talk describes a solution to the problem
valid in characteristic 0 and almost all positive characteristics. 

10/02 3:00pm 
Zoom 
Bridget Tenner DePaul University 


10/09 3:00pm 
Zoom 
Cvetelina Hill Georgia Tech 
Tropical convex hulls of polyhedral sets
This talk is based on joint work with Sala Lamboglia and Faye Pasley Simon. During the first part of the talk we will focus on the tropical convex hull of convex sets and polyhedral complexes. We will introduce results on the tropical convex hull of a line segment and a ray, show that for sets in two dimensions tropical convex hull and ordinary convex hull commute, and give a characterization of tropically convex polyhedra. In the second part of the talk we will use these results to show that the dimension of a tropically convex fan depends on the coordinates of its rays and give a lower bound on the degree of a fan tropical curve using only tropical techniques.
The talk will be based on the work in this paper: https://arxiv.org/abs/1912.01253v2.


10/23 3:00pm 
Zoom 
Kassie Archer UT Tyler 


10/30 3:00pm 
Zoom 
Tekin Karadag Texas A&M 


11/06 3:00pm 
Zoom 
Lauren Snider Texas A&M 


11/13 3:00pm 
Zoom 
Jay Yang U of Minnesota 


11/20 3:00pm 
Zoom 
Pablo Ocal Texas A&M 
