Seminars Sorted by Series

Abstract: I will survey new results on several enumerative problems related to the geometry, topology, and arithmetic of moduli spaces of smooth and stable curves. The enumerative problems include counting isomorphism classes of curves of genus $g$...

Sponsored by Dr. John P. Hempel and the Simons Foundation

Organizers: Paolo Aluffi, Dave Anderson, June Huh, and Leonardo Mihalcea

This workshop was dedicated to the exploration of the combinatorial dimensions of intersection theory and enumerative...

Abstract: Chow rings of toric varieties feature a rich combinatorial structure of independent interest. We will begin by surveying four different ways of computing in these rings, due to Billera, Brion, Fulton–Sturmfels, and Allermann–Rau. We will...

Abstract: 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 $2^n$ different pipe dream formulae; an orthogonal...

Abstract: 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...

Abstract: 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...

Abstract: 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...

Abstract: 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...

Abstract: 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...

Abstract: 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.

Abstract: 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...

Abstract: Suppose $X$ is the affine cone of a projective variety. The Hilbert series of the coordinate ring $C[X]$ is the character of an algebraic torus. More generally, one considers a reductive algebraic group $G$ acting rationally on $X$. When...

Abstract: Springer fibers are subvarieties of the flag variety parameterized by partitions. They are central objects of study in geometric representation theory. Given a partition $λ$, one of the key conclusions of Springer theory is that the top...

Abstract: While mirror symmetry for flag varieties and Grassmannians has been extensively studied, Schubert varieties in the Grassmannian are singular, and hence standard mirror symmetry statements are not well-defined. Nevertheless, in joint work...

Abstract: There are two major research trends in the theory of symmetric functions arising from Dyck paths. One is the theory of Catalan symmetric functions and its geometric realization conceived by Chen-Haiman, following the works of Broer and...

Abstract: A Richardson variety R in a cominuscule Grassmannian is defined by a skew diagram of boxes. If this diagram has several connected components, then R is a product of smaller Richardson varieties given by the components. I will show that the...

Organizers: Mariusz Lemanczyk (IAS), Maksym Radziwill (Caltech), Tamar Ziegler (IAS)

Confirmed Speakers:
Teresa Anderson (Carnegie Mellon)
Vitaly Bergerlson (IAS)
Valentin Blomer (Universität Bonn)
Thierry De la Rue...

Abstract: We discuss some consequences of the existence of a Siegel zero for various questions relating to the distribution of the prime numbers, and in particular to conjectures of Hardy-Littlewood and Chowla type.  This is joint work with Joni...

Abstract: Low-lying horocycles are known to equidistribute on the modular curve. Here we consider the joint distribution of two low-lying horocycles of different speeds in the product of two modular curves and show equidistribution under certain...

Abstract: Behaviors of objects of algebraic interest, such as polynomials, elliptic curves and number fields -- many of which are still unknown -- fall into the field of arithmetic statistics..  By bringing in Fourier analysis to interplay with a...

Abstract: We construct examples showing that the correlation in the Mobius disjointness conjecture can go to zero arbitrarily slowly. In fact, our methods yield a more general result, where in lieu of μ(n) one can put any bounded sequence such that...

Abstract: In unpublished lecture notes, William A. Veech considered the following potential property of the Möbius function:
"In any Furstenberg system of the Möbius function, the zero-coordinate is orthogonal to any function measurable with respect...

Abstract: A central question in additive combinatorics is to determine what class of structured functions is enough to determine multilinear averages such as

$\mathbb{E}_{x,a} f_1(x) f_2(x+a) f_3(x+2a) f_4(x+3a)$.

In ergodic theory the analogous...

Abstract: Given $B \subset N$, we consider the corresponding set $FB$ of $B$-free integers, i.e. $n \inFB i_ no b \in B$ divides $n$. We $de_{ne} X \eta_}$ the B-free subshift _ as the smallest subshift containing $\eta := 1FB \in {0, 1}Z$. Such...

Abstract: For a topological dynamical systems (T, X) and a fixed $x \in X$ we are interested in the distribution of prime and semi-prime orbits, i.e. ${T px}p='$ and ${T p1p2 x}p1,p2='$. We are interested in systems for which the related sequences...

Abstract: Given a fractal set E in $R^n$ and a set F in $Gr(k,n)$, can we find k-plane S in F such that the orthogonal projection of E onto S is large? 

We will survey some classical and recent projection theorems and discuss their applications. ...