Chow quotients of projective varieties by affine torus actions
provide alternative constructions of interesting geometric objects.
For example, the moduli space of stable genus 0 curves with n
marked points arises as the Chow quotient of the...
We will discuss invariants of lattice polytopes and their
subdivisions arising from Ehrhart and Hodge theory and introduce
their matroid theoretic analogues which are enriched versions of
the characteristic and Tutte polynomials.
I will discuss some regular subdivisions of the permutahedron,
one for each Coxeter element in the symmetric group. These
subdivisions are "Bruhat interval" subdivisions, meaning that each
face is the convex hull of the permutations in a Bruhat...
In his 2018 paper "Some Schubert shenanigans" Richard Stanley
asked for the asymptotic behavior of the maximal principle
specialization of a Schubert polynomial. Motivated by this, still
open, question we explore the generalization to Grothendieck...
The general rule for the interactions between tropical geometry
and moduli spaces of course is the following: everything you may
wish is going to work like a charm in genus zero, and break down
horribly in higher genus. This is the case for the...
The spectral norm on the group of Hamiltonian diffeomorphisms of
a symplectic manifold is defined via a homological min-max process
on the filtered Floer homology. Based on the spectral norm one
defines the spectral capacity of domains which is...
We present new objects called quilts of alternating sign
matrices with respect to two given posets. Quilts generalize
several commonly used concepts in mathematics. For example, the
rank function on submatrices of a matrix gives rise to a quilt
with...
We present a new method to solve algorithmic and combinatorial
problems by (1) reducing them to bounding the maximum, over x in
{-1, 1}^n, of homogeneous degree-q multilinear polynomials, and
then (2) bounding the maximum value attained by these...
For a smooth projective variety, the classical
Hirzebruch--Riemann--Roch (HRR) theorem asserts the isomorphism
between the Chow ring and the Grothendieck K-ring of vector bundles
over rational coefficients. For certain toric varieties, we show
an...
There has been a lot of recent work connecting the two pipe
dream formulae for Schubert polynomials (classic and bumpless). One
strand is the hybrid pipe dreams of Udell and myself, giving 2n
different pipe dream formulae; an orthogonal one is the...
