Previous Special Year Seminar

Apr
02
2025

Special Year Seminar I

Schubert Calculus on Peterson Varieties
Rebecca Goldin
2:00pm|Simonyi 101

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...

Mar
27
2025

Special Year Seminar II

Expressive Curves
Sergey Fomin
11:00am|Simonyi 101

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...

Mar
27
2025

Special Year Seminar II

Phylogenetic Trees and the Moduli of n Points
Herwig Hauser
10:00am|Simonyi 101

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...

Mar
26
2025

Special Year Seminar I

Incidence Geometry and Tiled Surfaces
Sergey Fomin
2:00pm|Simonyi 101

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...

Mar
20
2025

Special Year Seminar II

The Quasisymmetric Flag Variety
Hunter Spink
10:00am|Simonyi 101

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...

Mar
19
2025

Special Year Seminar I

Quasisymmetric Divided Differences and Forest Polynomials
Vasu Tewari
2:00pm|Simonyi 101

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...

Mar
13
2025

Special Year Seminar II

Equalities and Inequalities on Products of Schur Functions
10:00am|Simonyi 101

The ring of symmetric functions has a linear basis of Schur functions $s_{\lambda}$ indexed by partitions $\lambda = (\lambda_1 \geq \lambda_2 \geq \ldots \geq 0 )$. Littlewood-Richardson coefficients $c^{\nu}_{\lambda, \mu}$ are the structure...

Mar
12
2025

Special Year Seminar I

Log-concavity of Polynomials Arising from Equivariant Cohomology
Yairon Cid-Ruiz
2:00pm|Simonyi 101

A remarkable result of Brändén and Huh tells us that volume polynomials of projective varieties are Lorentzian polynomials. The dual notion of covolume polynomials was introduced by Aluffi by considering the cohomology classes of subvarieties of a...

Mar
06
2025

Special Year Seminar II

Introduction to Equivariant K-theory
10:00am|Simonyi 101

K-theory arose in the 1950s from Grothendieck’s formulation of the Riemann-Roch theorem – that is, from attempts to calculate spaces of sections of vector bundles on a variety X via intersection theory on X.  An equivariant version was introduced...

Mar
05
2025

Special Year Seminar I

Introduction to Equivariant K-theory
2:00pm|Simonyi 101

K-theory arose in the 1950s from Grothendieck’s formulation of the Riemann-Roch theorem – that is, from attempts to calculate spaces of sections of vector bundles on a variety X via intersection theory on X.  An equivariant version was introduced...