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

Special Year Seminar II

April 10, 2025 | 10:00am - 11:00am

Suppose given a class of finite combinatorial structures, such as graphs or total orders. Nate Harman and I recently introduced a notion of measure in this context: this is a rule assigning a number to each structure such that some axioms are...

Special Year Seminar I

April 09, 2025 | 2:00pm - 3:00pm

The Kadomtsev-Petviashvili (KP) Equation has deep connections to algebraic curves, with solutions constructed from Riemann theta functions in the style of Krichever. As a curve undergoes tropical degeneration, its theta function simplifies to a...

Special Year Seminar II

April 03, 2025 | 10:00am - 12:00pm

Given a triple (X,π,s) consisting of a homogeneous space X=G/P, a dominant weight π giving a projective embedding of X, and a reduced expression s for the minimal coset representative of w_0 in the parabolic quotient W/W_P, we construct a polytope...

Special Year Seminar I

April 02, 2025 | 2:00pm - 3:00pm

We will discuss combinatorial and algebraic aspects of regular Hessenberg varieties, a large class of subvarieties of the flag variety G/B. For the special case of Peterson varieties, we show their equivariant structure constants are non-negative...

Special Year Seminar II

March 27, 2025 | 11:00am - 12:00pm

A real plane algebraic curve C is called expressive if its defining polynomial has the smallest number of critical points allowed by the topology of the set of real points of C. We give a necessary and sufficient criterion for expressivity (subject...

Special Year Seminar II

March 27, 2025 | 10:00am - 11:00am

We present a combinatorial approach to the Deligne-Mumford-Knudsen compactification of the moduli space of n distinct points on the projective line $P^1$. The idea is to choose a totally symmetric embedding of the orbits of generic points into a...

Special Year Seminar I

March 26, 2025 | 2:00pm - 3:00pm

We show that various classical theorems of linear incidence geometry, such as the theorems of Pappus, Desargues, Möbius, and so on, can be interpreted as special cases of a general result that involves a tiling of a closed oriented surface by...

Special Year Seminar II

March 20, 2025 | 10:00am - 11:00am

Abstract: In this talk I will construct a “quasisymmetric flag variety”, a subvariety of the complete type A  flag variety built by adapting the BGG geometric construction of divided differences to the newly introduced “quasisymmetric divided...

Special Year Seminar I

March 19, 2025 | 2:00pm - 3:00pm

Postnikov's divided symmetrization, introduced in the context of volume polynomials of permutahedra, possesses a host of remarkable ``positivity'' properties. These turn out to be best understood using a family of operators we call quasisymmetric...