Special Year 2024-25: Algebraic and Geometric Combinatorics - Seminar

In the third talk, I will concentrate on inequalities for linear extensionsof finite posets.  I will start with several inequalities which do have a combinatorial proof.  I will then turn to Stanley's inequality and outline the proof why its defect...

In the second talk, I will concentrate on polynomial inequalities and whether the defect (the difference of two sides) has a combinatorial interpretation.  For example, does the inequality  $x^2+y^2 \geq 2xy$  have a combinatorial proof and what...

In the first talk, I will give a broad survey of classical inequalities that arise in enumerative and algebraic combinatorics.  I will discuss how these inequalities lead to questions about combinatorial interpretations, and how these questions...

The Kronecker coefficients of the Symmetric group $S_n$ are the multiplicities of an irreducible $S_n$ representation in the tensor product of two other irreducibles. They were introduced in 1938 by Murnaghan and generalize the beloved Littlewood...

In this talk, I will describe a new definition, joint with Bivas Khan, for a tropical toric vector bundle on a tropical toric variety. This builds on the tropicalizations of toric vector bundles, and can be used to define tropicalizations of vector...

This will be an expository talk on the structure and classification of equivariant vector bundles on toric varieties. I will emphasize Klyachko's classification results from the 1980s and 1990s and discuss more recent re-formulations of this...