
Date Time 
Location  Speaker 
Title – click for abstract 

09/06 3:00pm 
BLOC 302 
Daniel Perales Anaya TAMU 
A Hopf algebra on noncrossing partitions
In noncommutative probability there are different notions of independence (free, Boolean and monotone), each with a notion of cumulants (analogue of classic cumulants) that linearize the addition of independent random variables. Formulas relating moments and cumulants can be expressed as a sum indexed by set partitions.
Our goal is to construct a Hopf algebra T on noncrossing partitions NC that allows us to systematically study the transitions between distinct brands of cumulants in noncommutative probability. The Hopf algebra T is such that its character group can be identified with a group of 'semimultiplicative' functions on the incidence algebra of NC, used to encode the formulas. While a basic tool of the Hopf Algebra, such as the antipode of T, helps in inverting such formulas.
We will explain how T relates to other (more famous) Hopf algebras and explain some extensions we have worked on.
This is a joint work with Celestino, EbrahimiFard, Nica and Witzman. 

09/20 3:00pm 
BLOC 302 
Nick Veldt Iowa State University 
Chain Saturation on the Boolean Lattice
Given a set X, a collection F ⊂ P(X) is said to be kSperner if it does not contain a chain of length k + 1 under set inclusion, and it is said to be saturated if it is maximal with respect to this property. Gerbner et al. conjectured that, if X is sufficiently large compared to k, then the minimum size of a saturated kSperner system is 2k−1. Noel, Morrison, and Scott disproved this conjecture later by proving that there exists ε such that for every k and X > n_0(k), there exists a saturated kSperner system of cardinality at most 2(1−ε)k .
In particular, Noel, Morrison, and Scott proved this for ε = 1 − 14 log_2 (15) ≈ 0.023277. We find an improvement to ε= 1 − 15 log2 28 ≈ 0.038529. We also prove that, for k sufficiently large, the minimum size of a saturated kSperner
family is at least √k 2^(k/2), improving on the previous Gerbner, et al. bound of 2^(k/2−0.5) 

09/27 3:00pm 
BLOC 302 
Youngho Yoo TAMU 
ErdosPosa property of Apaths in grouplabelled graphs
An Apath is a nontrivial path that intersects a vertex set A exactly at its endpoints. Beginning with a classical result of Gallai from 1961, several families of Apaths have been shown to satisfy an approximate packingcovering duality known as the ErdosPosa property. However, there is very little known about the structures of graphs where this property fails for Apaths, which is in contrast to many similar situations where one can salvage a halfintegral version of the ErdosPosa property. In this talk, we prove a structure theorem that characterizes the obstructions to the ErdosPosa property of Apaths in grouplabelled graphs. This gives a general halfintegral ErdosPosa result as well as a characterization of the full ErdosPosa property for Apaths in grouplabelled graphs. Joint work with Ojoung Kwon. 

10/11 3:00pm 
BLOC 302 
Trevor Karn University of Minnesota 
Equivariant Kazhdan–Lusztig theory of paving matroids
We study the way in which equivariant Kazhdan–Lusztig polynomials change under the operation of relaxation of a collection of stressed hyperplanes. This allows us to compute these polynomials for arbitrary paving matroids, which we do in a number of examples. We focus on the combinatorial consequences of the general theory. This is joint work with George Nasr, Nick Proudfoot, and Lorenzo Vecchi. 

10/18 3:00pm 
BLOC 302 
Galen DorpalenBarry TAMU 
The PoincareExtended abIndex
Motivated by a conjecture of Maglione—Voll concerning Igusa zeta
functions, we introduce and study the Poincaréextended abindex. This
polynomial generalizes both the abindex and the Poincaré polynomial.
For posets admitting Rlabelings, we prove that the coefficients are
nonnegative and give a combinatorial description of the coefficients.
This proves Maglione—Voll’s conjecture as well as a conjecture of the
Kühne—Maglione. We also recover, generalize, and unify results from
Billera—Ehrenborg—Readdy, Ehrenborg, and Saliola—Thomas. This is joint
work with Joshua Maglione and Christian Stump. 

10/25 3:00pm 
BLOC 302 
Chelsea Walton Rice University 


11/01 3:00pm 
BLOC 302 
Oeyvind Solberg Norwegian University of Science and Technology (NTNU) 


11/15 3:00pm 
BLOC 302 
Moxuan (Jasper) Liu UCSD 
