Fall 2025 Analysis Seminar

Organizers: Lars Niedorf and Andreas Seeger

Emails:

• Lars Niedorf: niedorf at math dot wisc dot edu
• Andreas Seeger: seeger at math dot wisc dot edu

Time and Room: Wednesdays, 3:30--4:30 p.m., Van Vleck B235

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+subscribe (at) g-groups (dot) wisc (dot) edu

Links to previous seminars

Date	Speaker	Institution	Title	Host(s)	Notes (e.g. unusual room/day/time)
September 10	Giorgio Young	UW Madison	Wavepacket spread for almost periodic and partially periodic Schrödinger operators
September 17	Rajula Srivastava	UW Madison	A Fourier Analytic Approach to Count Integer Points near Space Curves
September 24	Ben Johnsrude	UW Madison	Restriction theory, p-adic analysis, and the decoupling bargain
October 1	Lars Niedorf	UW Madison	Spectral multipliers for the Kohn-Laplacian on the Heisenberg group
Friday/Saturday October 3/4	Harmonic Analysis Workshop.	Workshop Titles and Abstracts.		Andreas, Betsy, Brian	Talks in VV 911 or B239 (see the linked schedule)
Friday, October 3, 4:00 p.m.	Hong Wang	NYU & IHES	Restriction theory and projection theorems	Andreas, Betsy, Brian	Colloquium integrated in the workshop, VV B239
October 8	Jaehyeon Ryu	EWHA Womans University		Andreas, Lars
October 15	John Treuer	UC San Diego		Xianghong
October 22	Burak Hatinoglu	Michigan State		Alexei
October 29	Niclas Technau	UW Madison
November 5	Marco Fraccaroli	UMass Lowell		Andreas
November 12, 4.00 pm.	Rachel Greenfeld	Northwestern		Andreas, Betsy	Wednesday Colloquium in VV B239.
November 19	Sarah Tammen	UW Madison
November 26	---				No seminar
December 3	Terry Harris	UW Madison

Abstracts

Giorgio Young

Title: Wavepacket spread for almost periodic and partially periodic Schr\"odinger operators

Abstract: In this talk, we will provide an introduction to quantum dynamics, and introduce some notions of wavepacket spread, including ballistic transport and dispersion. We will then present some results showing ballistic transport for one dimensional continuum Schr\"odinger operators with limit-periodic potentials, as well as ``directional ballistic transport" for higher dimensional discrete and continuum Schr\"odinger operators with potentials supported, and periodic, on a strip. Finally, we will describe a recent result finding dispersion at the optimal rate for periodic discrete Schr\"odinger operators. This talk contains joint work with Adam Black, David Damanik, Jake Fillman, and Tal Malinovitch.

Rajula Srivastava

Title: A Fourier Analytic Approach to Count Integer Points near Space Curves

Abstract: We present recent results giving both upper and lower bounds for the number of integral points lying near smooth nondegenerate curves in $\mathbb{R}^n$. These estimates are new in dimensions $n\geq 4$, and in the case $n\geq 3$ they recover an earlier result of J. J. Huang. Our approach differs significantly from previous work: instead of relying on sharp planar counting results, we employ Fourier analytic methods. A key ingredient is an Arkhipov–Chubarikov–Karatsuba-type oscillatory integral estimate. This is joint work with Jonathan Hickman (Edinburgh).

Ben Johnsrude

Title: Restriction theory, p-adic analysis, and the decoupling bargain

Abstract: Restriction theory is concerned with understanding delicate properties of functions with Fourier support contained in a submanifold of space. The major advancement in the subject of the last ten years has been the development of decoupling theory; the latter has led to the solution of several problems in restriction theory and geometric measure theory, and made substantial quantitative progress in others. On the other hand, the framework of decoupling imposes certain limits on the analysis, which in particular prevents one from solving problems such as Mizohata--Takeuchi without first exiting the framework.

We survey some outstanding problems in restriction theory and the current state of knowledge therein. We discuss Guth's argument that decoupling is insufficient to solve Mizohata--Takeuchi. We then introduce a novel tool that allows one to go beyond the limits of the usual decoupling framework in the topics surveyed.

Lars Niedorf

Title: Spectral multipliers for the Kohn-Laplacian on the Heisenberg group

Abstract: We discuss recent sharp Bochner-Riesz estimates for Kohn-Laplacians on Heisenberg groups. Since favorable restriction estimates fail in this setting, we developed an approach that relies on square function bounds for the wave equation associated with the Kohn-Laplacian. This is joint work with Detlef Müller, Andreas Seeger, and Betsy Stovall.

Hong Wang

Title: Restriction theory and projection theorems

Abstract: Restriction theory studies functions whose Fourier transforms are supported on some curved manifold in R^n (for example, solutions to the linear Schrodinger equation or to the wave equation). Projection theorems study the Hausdorff dimension of fractal sets under orthogonal projections from R^n to its subspaces. We will survey some recent works in both fields and discuss their interactions.