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

Date Time 
Location  Speaker 
Title – click for abstract 

09/15 3:00pm 
BLOC 302 
Laura Matusevich TAMU 
Combinatorics of Gorenstein affine semigroup rings
Affine semigroup rings are algebras that are generated by finitely many monomials. They are very suitable for combinatorial treatment, so people in commutative algebra like to translate algebraic properties into combinatorial terms (and vice versa) if possible. In this talk, I will describe the combinatorial mechanics of the Gorenstein property for affine semigroup rings. I will give a definition of "Gorenstein" in the talk that is useful for computations, but is a bit technical. As for an intuitive definition, let me just say that assuming your ring is Gorenstein has a habit of making theorems work...
This is joint work with Byeongsu Yu. 

09/29 3:00pm 
BLOC 302 
Youngho Yoo TAMU 
Path oddcovers of graphs
We study the minimum number of paths needed to express the edge set of a given graph as the symmetric difference of the edge sets of the paths. This problem sits in between Gallai's path decomposition problem and the linear arboricity problem. It is also motivated by the study of the diameter of partition polytopes, and we adapt some techniques therein to prove bounds on the path oddcover number of graphs. Joint work with Steffen Borgwardt, Calum Buchanan, Eric Culver, Bryce Frederickson, and Puck Rombach.


10/13 3:00pm 
BLOC 302 
Jianping Pan North Carolina State University 
Polynomials from Schubert Calculus via Diagrams
Polynomials are powerful tools in many fields, for example, representation theory, geometry, and topology. Understanding the combinatorics of the polynomials may reveal important information in these fields. This talk will focus on four polynomials from Schubert calculus: Schubert, key, Grothendieck, and Lascoux polynomials. I will discuss diagrams related to these polynomials, including Kohnert diagrams, snow diagrams, and rook diagrams. This is joint work with Tianyi Yu. 

10/27 3:00pm 
BLOC 302 
ChunHung Liu TAMU 
AssouadNagata dimension of minorclosed metrics
AssouadNagata dimension addresses both largescale and smallscale behaviors of metric spaces and is a refinement of Gromov’s asymptotic dimension. A metric space is a minorclosed metric if it is defined by the distance function on the vertices of an edgeweighted graph that satisfies a fixed graph property preserved under vertexdeletion, edgedeletion, and edgecontraction. In this talk, we determine the AssouadNagata dimension of every minorclosed metric. It is a common generalization of known results about the asymptotic dimension of Hminor free unweighted graphs, about the AssouadNagata dimension of complete Riemannian surfaces with finite Euler genus, and about their corollaries on weak diameter coloring of minorclosed families of graphs and asymptotic dimension of minorexcluded groups. 

11/17 3:00pm 
BLOC 302 
Shixuan Zhang TAMU (ISEN) 
Certification of sums of squares via lowrank optimization
To certify a sum of k squares on a real projective variety, one can minimize the distance of the sum of squares of k linear forms from it in the space of quadrics. When k is smaller than the dimension of linear forms, the certification problem can be applied in lowrank semidefinite relaxation of polynomial optimization, similar to the BurerMonteiro method. We discuss the existence of spurious local minima in this nonconvex certification problems, and show that in some interesting cases, there is no spurious local minima, or any spurious local minimum would lie on the boundary of the sumofsquare cone. These characterizations could potentially lead to efficient algorithms for polynomial and combinatorial optimization. 

12/01 3:00pm 
BLOC 302 
Catherine Yan TAMU 
Combinatorial Identities for Vacillating Tableaux
Vacillating tableaux are sequences of integer partitions that satisfy specific conditions. The concept of vacillating tableaux stems from the representation theory of the partition algebra and the combinatorial theory of crossings and nestings of matchings and set partitions. In this talk we discuss the enumeration of vacillating tableaux and present multiple combinatorial identities and integer sequences relating to the number of vacillating tableaux and limiting vacillating tableaux. 