
Date Time 
Location  Speaker 
Title – click for abstract 

01/25 3:00pm 
BLOC 628 
Aleksandra Sobieska TAMU 
Minimal Free Resolutions over Rational Normal Scrolls
Free resolutions of monomial ideals over the polynomial ring are wellstudied and
reasonably wellunderstood, though they are still an active area of research in commutative algebra.
However, resolutions over quotients of the polynomial ring are much more mysterious, and even simple
examples can violate the nicer properties that the polynomial ring provides. Starting in the 1990's,
there is some work on resolutions over toric rings, a particular (and wellbehaved) quotient of the
polynomial ring. In this talk, we will present a minimal free resolution of the ground field over a
specific toric ring that arises from rational normal scrolls. We also provide a computation of the
Betti numbers for the resolution of the ground field for all rational normal $k$scrolls. 

02/01 3:00pm 
BLOC 628 
Qing Zhang TAMU 
Classification of Supermodular Categories
I will explain the connection between topological quantum computing and tensor
categories. The most promising proposal for topological quantum computation is
anyon braiding in 2D topological phases of matter. The algebraic theory of 2D
topological phases corresponds to tensor category theory in a very precise way.
I will focus on supermodular categories, a type of tensor category related to
fermionic topological phases similarly to the way that modular categories are
related to bosonic phases.
Supermodular categories are interesting from a purely mathematical standpoint
as well. For example, any unitary premodular category is the
equivariantization of a modular or supermodular category. In this talk, I will
discuss a number of properties of supermodular categories parallel to those of
modular categories. Time permitting, I will also discuss the classification of
supermodular categories of rank 8.


02/08 3:00pm 
BLOC 628 
Sarah Witherspoon TAMU 
Hopf algebras and the cohomological finite generation conjecture
A powerful tool for understanding representations of finite groups
is group cohomology. One reason why it is so powerful is that the
group cohomology ring is finitely generated and graded commutative,
thus pointing to geometric methods. Hopf algebras generalize groups
and include many important classes of algebras such as Lie algebras
and quantum groups. Their cohomology rings are known to be graded
commutative, and it is conjectured that they are finitely generated
whenever the Hopf algebra is finite dimensional.
In this introductory talk, we will define Hopf algebras, their
cohomology rings, and mention their uses in representation theory.
We will discuss Hopf algebras for which the conjecture has been
proven and those for which it has not, including recent and ongoing
research.


02/15 3:00pm 
BLOC 628 
Galen DorpalenBarry University of Minnesota 
Whitney Numbers for Cones
An arrangement of hyperplanes dissects space into connected
components called chambers. A nonempty intersection of halfspaces from the
arrangement will be called a cone. The number of chambers of the
arrangement lying within the cone is counted by a theorem of Zaslavsky, as
a sum of certain nonnegative integers that we will call the cone's "Whitney
numbers of the 1st kind". For cones inside the reflection arrangement of
type A (the braid arrangement), cones correspond to posets, chambers in the
cone correspond to linear extensions of the poset, and these Whitney
numbers refine the number of linear extensions. We present some basic
facts about these Whitney numbers, and interpret them for two families of
posets. 

02/22 3:00pm 
BLOC 628 
Westin King TAMU 
Decompositions of Parking Functions on Trees
Parking functions describe a sequence of drivers attempting to
find a place to park in a oneway linear parking lot. We can introduce a
more complicated "parking lot" by considering directed trees and again
ask if all the drivers can park. In this talk, I will give enumerative
results concerning certain types of these generalized parking functions
by considering decompositions based on the movement of drivers while
they attempt to park. Additionally, I will discuss the number of "lucky
drivers," those who park in the first parking space they encounter, and
will find they are related to the Narayana numbers, which refine the
ubiquitous Catalan numbers. 

03/01 3:00pm 
BLOC 628 
Benjamin Briggs University of Utah 
Reflection Groups and Derivations
If you start with a polynomial ring (say over the complex numbers) and you factor out by the ideal generated by symmetric polynomials (of positive degree), then you get a very interesting ring. For example, it is isomorphic to the cohomology ring of a flag manifold.
How many derivations does this ring have (i.e. what is the dimension of the space of Clinear derivations)? The ring is also graded: how many derivations does it have in each degree? These are tricky to count, but it turns out there is a surprisingly nice formula. You get this formula by writing down a free resolution of the module of derivations, which for some reason turns out to be periodic.
You can do all this by messing around with symmetric polynomials (but the combinatorics get quite complicated). It turns out though that this all works for certain reflection groups (all the real reflection groups included, and some complex reflection groups). I'll talk about this too, mainly focusing on the symmetric group example. 

03/08 3:00pm 
BLOC 628 



03/22 3:00pm 
BLOC 628 



03/23 09:00am 
Blocker building 

CombinaTexas 2019 

03/24 09:00am 
Blocker Building 

CombinaTexas 2019 

03/29 3:00pm 
BLOC 628 
Ayo Adeniran TAMU 
Combinatorial Theory of Goncarov polynomials 

04/05 3:00pm 
BLOC 628 



04/06 08:00am 
Rice University 

AWM Research Symposium April 67 

04/12 3:00pm 
BLOC 628 
Michael Brannan Texas A&M University 


04/19 3:00pm 
BLOC 628 
Anton Dochtermann Texas State University 


04/26 3:00pm 
BLOC 628 

