
Date Time 
Location  Speaker 
Title – click for abstract 

08/31 3:00pm 
BLOC 628 
Catherine, Sarah, Yue 
Organizing meeting 

09/07 3:00pm 
BLOC 628 
Sarah Witherspoon Texas A&M University 
Lie algebra structure on derivations and Hochschild cohomology
Derivations are linear operators on rings that obey the Leibniz rule,
for example, differentiation on rings of functions. The space of all
derivations on a ring is a Lie algebra. Generalizing from linear to
multilinear operators naturally leads to the subject of Hochschild
cohomology, a source of important algebraic invariants for rings. It
arises in many settings, for example, in representation theory, in
noncommutative geometry, and in algebraic deformation theory. In this
talk, we will give a brief introduction to Hochschild cohomology and
mention some of its applications and some recent work on its structure
as a graded Lie algebra. 

09/14 3:00pm 
BLOC 628 
Jurij Volcic Texas A&M University 
Multipartite rational functions: the universal skew field of fractions of a tensor product of free algebras
A commutative ring embeds into a field if and only if it has no zero divisors; moreover, in this case it admits a unique field of fractions. On the other hand, the problem of noncommutative localization and embeddings into skew fields (that is, division rings) is much more complex. For example, there exist rings without zero divisors that do not admit embeddings into skew fields, and rings with several nonisomorphic "skew fields of fractions". This led Paul Moritz Cohn (19242006) to introduce the notion of the universal skew field of fractions to the general theory of skew fields in the 70's. However, almost all known examples of rings admitting universal skew fields of fractions belong to a relatively narrow family of Sylvester domains. One of the exceptions is the tensor product of two free algebras.
After a decent introduction, we will look at the skew field of multipartite rational functions, whose construction via matrix evaluations of formal rational expressions is inspired by methods in free analysis. This skew field turns out to be the universal skew field of fractions of a tensor product of free algebras (for arbitrary finite number of factors).


09/21 3:00pm 
BLOC 628 
ChunHung Liu Texas A&M University 
Clustered coloring on old graph coloring conjectures
The famous Four Color Theorem states that every graph that can be drawn in the plane without edgecrossing is properly 4colorable, which means that one can color its vertices with 4 colors such that every pair of adjacent vertices receive different colors. It is equivalent to say that every graph that does not contain a subgraph contractible to K_5 or K_{3,3} is properly 4colorable.
Hadwiger in 1943 proposed a far generalization of the Four Color Theorem: every graph that does not contain a subgraph contractible to K_{t+1} is properly tcolorable. Hajos, and Gerards and Seymour, respectively, proposed two strengthening of Hadwiger's conjecture, where only special kinds of edges are allowed to be contracted. More precisely, these three conjectures state that every graph that does no contain K_{t+1} as a minor (topological minor, or odd minor, respectively) is properly tcolorable. These three conjectures are either open or false, except for some very small t. One weakening of these three conjectures is to color the vertices such that every monochromatic component has bounded size, which is called clustered coloring.
In this talk we will show joint work with David Wood about a series of tight results about clustered coloring on graphs with no subgraph isomorphic to a fixed complete bipartite graph. These results have a number of applications, including nearly optimal or first linear bound for the number of colors on the clustered coloring version of the previous three conjectures, as well as results on graphs embeddable in a surface of bounded genus where edgecrossings are allowed.
No background about graph theory is required for this talk.


09/28 3:00pm 
BLOC 628 
Laura Matusevich Texas A&M University 
Standard pairs
Standard pairs are a useful gadget for studying monomial ideals in polynomial rings. I will recall the definition, mention some known applications, and introduce a new generalization to the context of monomial ideals in semigroup rings. 

10/05 3:00pm 
BLOC 628 
Li Ying Texas A&M University 
Generalized stability of Heisenberg coefficients
Stembridge introduced a new concept, Kronecker stable triple, which generalized the classical Murnaghan's stability result of Kronecker coefficients. Sam and Snowden proved a conjecture of Stembridge concerning when a Kronecker triple is stable, and they also showed an analogous result for LittlewoodRichardson coefficients. Heisenberg coefficients are Schur structure constants of the Heisenberg product which generalize LittlewoodRichardson coefficients and Kronecker coefficients. In this talk, I will recall the definition and explain some known results. I will show that any stable triple for Kronecker coefficients or LittlewoodRichardson coefficients also stabilizes Heisenberg coefficients, and I follow Vallejo's idea of using matrix additivity to generate Heisenberg stable triples.


10/12 3:00pm 
BLOC 628 
Andrew Maurer University of Georgia 
Relative Cohomology of Classical Lie Superalgebras
Cohomology is a powerful technique in representation theory. In this
talk, I will define Lie superalgebras and their relative cohomology
theory. We will see two classical results on geometric properties of
relative cohomology, and I will present original results which
relate the two aforementioned results. 

10/19 3:00pm 
BLOC 628 
Frank Sottile Texas A&M University 
A geometric proof of an equivariant Pieri rule for flag manifolds
The Pieri formulas describes the multiplication of Schubert classes in the equivariant cohomology of any manifold of partial flags. I will describe how to use geometric and combinatorial arguments that provide a short proof of an equivariant Pieri rule in the classical flag manifold. This is joint work with Changzheng Li, Vijay Ravikumar, and Mingzhi Yang. 

10/26 3:00pm 
BLOC 628 
Anastasia Chavez University of California, Davis 
Dual Equivalence Graphs and CAT(0) Combinatorics
In this talk we will explore the combinatorial structure of dual equivalence graphs G_lambda. The vertices are Standard Young tableaux of fixed shape lambda that allows us to further understand the combinatorial structure of G_lambda, and the edges are given by dual Knuth equivalences. The graph G_lambda is the 1skeleton of a cubical complex C_lambda. One can ask whether the cubical complex is CAT(0); this is a desirable metric property that allows us to describe the combinatorial structure of G_lambda very explicitly. We will discuss the CAT(0) characterization of ArdilaOwenSullivant. It is constructive and provides an algorithm for determining when a cubical complex is CAT(0). Using their characterization, we prove that C_lambda is CAT(0) if and only if lambda is a hook. This is joint work with John Guo. 

11/02 3:00pm 
BLOC 628 
Emily Witt University of Kansas 
Connectedness and local cohomology
Local cohomology modules are algebraic objects that encode
important properties; e.g., the dimension of a ring, the depth of a ring on
an ideal, and the number of equations needed to define a variety. The
second vanishing theorem of local cohomology characterizes the connectedness
of the punctured spectrum. In this talk, we seek to understand how local
cohomology determines more refined connectedness properties, and introduce a
"third vanishing theorem." This is joint work with Luis NúñezBetancourt
and Sandra Spiroff. 

11/09 3:00pm 
BLOC 628 
Westin King Texas A&M University 
Parking on Directed Graphs
Parking functions were first defined in the 1960s in order to study collision resolution on hashing tables. Since then, they have appeared nearly ubiquitously throughout combinatorics and have several generalizations. I will present a new generalization which can be thought of as drivers with preferred parking spaces searching for an available parking spot (vertices) along a series of oneway streets (directed edges). I will discuss parking functions on several families of directed graphs, their surprisingly nice enumeration, and multiple further research directions for this generalization. 

11/30 3:00pm 
BLOC 628 
Dmitri Nikshych University of New Hampshire 
Quantum Manin pairs and fusion categories
A quantum Manin pair consists of a nondegenerate braided fusion category and a Lagrangian algebra in it. There is a bijection between equivalence classes of such pairs and fusion categories. This allows to study the latter using categorical linear algebra techniques. We explain how various categorical structures related to a fusion category (such as braidings, subcategories, module categories, fiber functors) can be interpreted and classified by means of the corresponding Manin pair. A part of this talk is based on a joint work with Alexei Davydov, Michael Mueger, and Victor Ostrik. 

12/05 3:00pm 
BLOC 628 
YeongNan Yeh Institute of Mathematics, Academia Sinica 
TBD 