Speaker:  Matias von Bell

Title:  The ASMCRY(n) Polytope: An Interesting Face of the Alternating Sign Matrix Polytope.

Abstract:
This talk showcases some of the work done by Karola Meszaros, Alejandro Morales, and Jessica Strikerin their 2015 paper titled ``On Flow Polytopes, Order Polytopes, and Certain Faces of the Alternating Sign Matrix Polytope".
The alternating sign matrix polytope is the convex hull of alternating sign matrices. We will focus on one of its faces known as the Alternating Sign Matrix Chan-Robbins-Yuen polytope (ASMCRY(n)). It is part of a larger family: The ASM-CRY family of polytopes. After a discussion of flow- and order polytopes, we'll prove that the polytopes in the ASM-CRY family are both flow- and order polytopes. Then using Stanley's results for order polytopes, we show that ASMCRY(n) has Catalan many vertices, and its volume is the number of Standard Young Tableaux of staircase shape.

This is Matias von Bell's Masters Exam.

Speaker:  Tefjol Pllaha, U Kentucky

Abstract:

This talk will be about Laplacian simplices, that is, simplices whose vertices are rows of the Laplacian matrix of a simple connected graph. We will focus on graphs and graph operations that yield reflexive Laplacian simplices. We spot such graphs by showing that the $h^*$-vector of the simplex is symmetric. We use the same approach as Batyrev and Hofscheier by considering the fundamental parallelepiped lattice points as a finite abelian group. This is joint work with Marie Meyer.

www.math.uky.edu/~readdy/Seminar

Speaker:  Fernando Shao, U Kentucky

Title Maximizing the number of solutions to a linear equation

Speaker:  Yuan Zhou, U Kentucky

Title:  Integer optimization, cutting planes, and approximation theory

Speaker:  Ricky Liu, NC State

Title:  P-partition generating functions of naturally labeled posets

Speaker:  Alex Chandler, NC State

Title:  Thin posets and homology theories

Abstract:

Inspired by Bar-Natan's description of Khovanov homology, we discuss

thin posets and their capacity to support homology and cohomology

theories which categorify rank-statistic generating

functions. Additionally, we present two main applications. The first,

a categorification of certain generalized Vandermonde determinants

gotten from the Bruhat order on the symmetric group by applying a

special TQFT to smoothings of torus link diagrams. The second is a

broken circuit model for chromatic homology, categorifying Whitney's

broken circuit theorem for the chromatic polynomial of graphs.

www.math.uky.edu/~readdy/Seminar

Speaker:  Matthias Köppe, UC Davis

Title:  Normalized antics: Polyhedral computation in an irrational age

Classic polyhedra such as the dodecahedron have irrational coordinates. How do we compute with them if we need exact answers? In this hands-on lecture using the SageMath system, intended to be accessible to advanced undergraduate students, I explain how to compute with polyhedral representations and with real embedded algebraic number fields. I then report on an ongoing project with W. Bruns, V. Delecroix, and S. Gutsche to obtain an efficient implementation in Normaliz, integrated with SageMath, involving the existing software libraries ANTIC, arb, and FLINT.

Speaker:  Ben Braun, U Kentucky