Department of Mathematics Weekly Seminars

MONDAY - 12/5/22

Analysis Seminar

Location:  ICERM - 121 South Main Street, 11th Floor, Room 1115

Time: 3:00-4:00pm

Speaker:  Naga Manasa Vempati, Georgia Tech & ICERM

Title:  Compactness of the Bloom sparse operators and applications.

Abstract:   We discuss the characterization of compactness for the sparse operator (associated with symbol in weighted VMO space) in the two-weight setting on the spaces of homogeneous type. As a direct application we obtain the compactness characterization for the maximal commutators with respect to the weighted VMO functions and the commutator of Calderon–Zygmund operators on the homogeneous spaces. We will look at the applications of this approach to multilinear Bloom setting. 

Algebra Seminar

Location:  Kassar 105

Time: 4:00-5:00pm

Speaker:  Sameeera Vemulapalli, Princeton

Title:  The relationship between scrollar invariants of curves and successive minima of orders in number fields, and related counting problems

Abstract:  Let n >= 2 be an integer. To a degree n cover of P^1, we may attach n integers called the scrollar invariants. Similarly, to an order in a degree n number field, we may attach n real numbers called the successive minima. In this talk I will explain the relationship between scrollar invariants of curves and successive minima of orders in number fields, and I will prove bounds on both. When n < 6, I'll also discuss a related counting question: how many orders in degree n number fields are there with bounded discriminant and prescribed successive minima? 

WEDNESDAY - 12/7/22

Geometry & Topology Seminar

Location:  Kassar 105

Time: 3:00-4:00pm

Speaker:  Sara Maloni, University of Virginia

Title:  Pleated surfaces in PSL_d(C)

Abstract:   Pleated surfaces are an important tool introduced by Thurston to study hyperbolic 3-manifolds and can be described as piecewise totally geodesic surfaces, bent along a geodesic lamination lambda. Bonahon generalized this notion to representations of surface groups in PSL_2(C) and described a holomorphic parametrization of the resulting open charts of the character variety in term of shear-bend cocycles. In this talk I will discuss joint work with Martone, Mazzoli and Zhang, where we generalize this theory to representations in PSL_d(C). In particular, I will discuss the notion of d-pleated surfaces, and their holomorphic parametrization.

Analysis Seminar

Location:  ICERM - 121 South Main Street, 11th Floor, Room 1115

Time: 4:00-5:00pm

Speaker:  Francesco Di Plinio, Università degli Studi di Napoli "Federico II"  

Title:  Wavelet representation and Sobolev regularity of quasiconformal mappings on domains

Abstract:   This work devises a new smooth representation formula for the compression of CZ operators on domains. As a first order consequence of this representation, we obtain a weighted, sharply quantified T(1)-type theorem on Sobolev spaces. Previous results of Prats and Prats-Tolsa are limited to unweighted bounds for convolution-type operators. Our weighted Sobolev inequalities are subsequently applied to obtain quantitative regularity results for solutions to the Beltrami equation with symbol in the critical class W^{k,2}(Omega). Alll past results, due to Prats among others,  based on the Iwaniec scheme are of qualitative nature.Talk is based on current and ongoing joint work with Walton Green and Brett Wick (WUSTL)

Colloquium

Location:  Foxboro Auditorium

Time: 4:30-5:30pm

Speaker:  Joe Harris, Harvard

Title:  Lang's conjectures and the boundedness of rational points

Abstract:   In this talk, I'd like to revisit and update a paper from almost 30 years ago.
At issue are two questions that arise from Faltings' proof of the Mordell Conjecture, which asserts that a curve of genus 2 or more defined over a number field can have only finitely many rational points. The first question is, is that number bounded if we fix the genus g and the number field K, and consider all curves of genus g defined over K? A "universal" upper bound on the number of solutions would be striking.
The second question is perhaps more open-ended: we can ask, what is the analogue of Faltings' theorem for higher-dimensional varieties? Lang and others have conjectured a far-reaching (but very plausible) answer, which I'll describe.
The result I want to discuss relates the two questions: we show that Lang's conjecture implies the existence of a bound on the number of rational points on curves of genus g over a number field K, and give a strong form of this implication.

Graduate Student Seminar

Location:  Kassar 105

Time: 5:00-6:00pm

Speaker:  Sam Freedman

Title:  Untitled Square-Tiled Surfaces Talk

Abstract:   TBA

FRIDAY - 12/9/22

Algebraic Geometry Seminar

Location:  Kassar 105

Time: 3:00-4:00pm

Speaker:  Samir Canning, ETH

Title:  The Chow ring of the moduli space of degree 2 K3 surfaces

Abstract:   The intersection theory of the moduli space of K3 surfaces polarized by a lattice is a subject of recent interest because of its deep connections with a wide variety of mathematics, including the intersection theory of moduli spaces of curves and the study of modular forms. Oprea and Pandharipande conjectured that the tautological rings of these moduli spaces of K3 surfaces are highly structured in a way that mirrors the picture for the moduli space of curves. I will discuss the proof of this conjecture in the case of K3 surfaces polarized by a degree 2 line bundle. This is joint work with Dragos Oprea and Rahul Pandharipande.

PDE Seminar

Location:  170 Hope Street, Room 108

Time: 3:00-4:00pm

Speaker:  Zongyuan Li, Rutgers

Title:  TBA

Abstract: TBA

PDE Seminar

Location:  170 Hope Street, Room 108

Time: 4:00-5:00pm

Speaker:  Gonzalo Cao-Labora, MIT

Title:  TBA

Abstract: TBA

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