Fall 2022 analysis seminar

The 2022-2023 Analysis Seminar will be organized by Shaoming Guo. The regular time and place for the Seminar will be Tuesdays at 4:00 p.m. in Van Vleck B139 (in some cases the seminar may be scheduled at different time to accommodate speakers). If you would like to subscribe to the Analysis seminar list, send a blank email to analysis+join (at) g-groups (dot) wisc (dot) edu. If you are from an institution different than UW-Madison, please send as well as an additional email to Shaoming. If you'd like to suggest speakers for the spring semester please contact Shaoming.

All talks will be in-person unless otherwise specified.

Analysis Seminar Schedule

date	speaker	institution	title	host(s)
08.23	Gustavo Garrigós	University of Murcia	Approximation by N-term trigonometric polynomials and greedy algorithms	Andreas Seeger
08.30	Simon Myerson	Warwick	Forms of the Circle Method	Shaoming Guo
09.13 (first week of semester)	Zane Li	UW Madison	A decoupling interpretation of an old argument for Vinogradov's Mean Value Theorem	Analysis group
09.16 (Friday, 1:20-2:10, Room B139)	Franky Li	UW Madison		Analysis group
09.20	Andrej Zlatoš	UCSD	Title	Hung Tran
09.23-09.25	RTG workshop in Harmonic Analysis			Shaoming Guo and Andreas Seeger
09.27 (online, special time, 3-4pm)	Michael Magee	Durham	Title	Simon Marshall
10.04	Philip Gressman	UPenn	Title	Shaoming Guo
10.11	Detlef Müller	CAU Kiel	Title	Betsy Stovall and Andreas Seeger
10.14 (1:00 PM Friday. Joint with Geometry & Topology Seminar)	Min Ru	U of Houston	The K-stability and Nevanlinna/Diophantine theory	Xianghong Gong
10.18	Madelyne M. Brown	UNC	Fourier coefficients of restricted eigenfunctions	Betsy Stovall
10.24 (Monday, B135)	Milivoje Lukic	Rice	Title	Sergey Denisov
11.01	Ziming Shi	Rutgers	Title	Xianghong Gong
11.08	Robert Fraser	Wichita State University	Title	Andreas Seeger
11.15	Brian Cook	Virginia Tech	Title	Brian Street
11.22	Thanksgiving
11.29	(tent reserved)		Title	Betsy Stovall
12.06	Shengwen Gan	MIT	Title	Shaoming Guo and Andreas Seeger
12.13	Óscar Domínguez	Universidad Complutense Madrid and University of Lyons	Title	Andreas Seeger and Brian Street

Abstracts

Gustavo Garrigós

Title: Approximation by N-term trigonometric polynomials and greedy algorithms

Link to Abstract: [1]

Simon Myerson

Title: Forms of the circle method

Abstract: The circle method is an analytic proof strategy, typically used in number theory when one wants to estimate the number of integer lattice points in some interesting set. Traditionally the first step is to evaluate the innocent integral $ \int_0^1 e^{2 \pi i t n} dt $ to give 1 if $ n = 0 $ and 0 if $ n $ is any other integer. Since Heath-Brown’s delta-method in the 90s this simplest step has been embellished with carefully constructed partitions of unity. In this informal discussion I will interpret these as different versions of the circle method and suggest how to understand their relative advantages.

Zane Li

Title: A decoupling interpretation of an old argument for Vinogradov's Mean Value Theorem

Abstract: There are two proofs of Vinogradov's Mean Value Theorem (VMVT), the harmonic analysis decoupling proof by Bourgain, Demeter, and Guth from 2015 and the number theoretic efficient congruencing proof by Wooley from 2017. While there has been recent work illustrating the relation between these two methods, VMVT has been around since 1935. It is then natural to ask: What does old partial progress on VMVT look like in harmonic analysis language? How similar or different does it look from current decoupling proofs? We talk about a refinement of a 1973 argument of Karatsuba that showed partial progress towards VMVT and interpret this in decoupling language. This yields an argument that only uses rather simple geometry of the moment curve. This is joint work with Brian Cook, Kevin Hughes, Olivier Robert, Akshat Mudgal, and Po-Lam Yung.

Madelyne M. Brown

Title: Fourier coefficients of restricted eigenfunctions

Abstract: We will discuss the growth of Laplace eigenfunctions on a compact manifold when restricted to a submanifold. We analyze the behavior of the restricted eigenfunctions by studying their Fourier coefficients with respect to an arbitrary orthonormal basis for the submanifold. We give an explicit bound on these coefficients depending on how the defect measures for the two collections of functions, the eigenfunctions and the basis, relate.

Min Ru

Title: The K-stability and Nevanlinna/Diophantine theory

Abstract: In the recent paper with P. Vojta, we introduced the so-called beta-constant, and used it to extend the Cartan's Second Main Theorem in Nevanlinna theory and Schmidt's subspace theorem in Diophantine approximation. It turns out the beta-constant is also used in the algebro-geometric stability criterion in the Fano's case. In this talk, I'll describe and explore the somewhat mysterious connection. The talk is based on the recent joint paper with Yan He entitled "The stability threshold and Diophantine approximation", Proc. AMS, 2022.

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Links to previous analysis seminars