Previous Special Year Seminar
Schubert Calculus on Peterson Varieties
Rebecca Goldin
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...
Sergey Fomin
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...
Phylogenetic Trees and the Moduli of n Points
Herwig Hauser
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...
Incidence Geometry and Tiled Surfaces
Sergey Fomin
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...
The Quasisymmetric Flag Variety
Hunter Spink
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...
Quasisymmetric Divided Differences and Forest Polynomials
Vasu Tewari
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...
Equalities and Inequalities on Products of Schur Functions
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...
Log-concavity of Polynomials Arising from Equivariant Cohomology
Yairon Cid-Ruiz
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...
Introduction to Equivariant K-theory
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...
Introduction to Equivariant K-theory
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...