Fall 2024 Analysis Seminar

Organizers: Shengwen Gan, Terry Harris and Andreas Seeger

Emails:

• Shengwen Gan: sgan7 at math dot wisc dot edu
• Terry Harris: tlharris4 at math dot wisc dot edu
• Andreas Seeger: seeger at math dot wisc dot edu

Time and Room: Wed 3:30--4:30 Van Vleck B119.

In some cases the seminar may be scheduled at different time to accommodate speakers.

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Links to previous seminars

Link to Spring 2025 Analysis Seminar

Date	Speaker	Institution	Title	Host(s)	Notes (e.g. unusual room/day/time)
We, 9-11	Gevorg Mnatsakanyan	UW Madison	Almost everywhere convergence of the Malmquist Takenaka series
We, 9-18	Lars Niedorf	UW Madison	Restriction type estimates and spectral multipliers on Métivier groups
Th, 9-26, 2:25-3:25, VV B215	Niclas Technau	University of Bonn	Rational points on/near homogeneous hyper-surfaces	Andreas	Note changes of time/date/room, joint with Number Theory Seminar
We, 10-2	Sergey Denisov	UW Madison	Applications of inverse spectral theory for canonical systems to NLS.
We, 10-9	Shukun Wu	Indiana University	On almost everywhere convergence of planar Bochner Riesz means	Shengwen
We, 10-16	Nathan Wagner	Brown University	Dyadic shifts, sparse domination, and commutators in the non-doubling setting	Andreas
We, 10-23	Betsy Stovall	UW Madison
We, 10-30	Burak Hatinoglu	Michigan State University		Alexei
We, 11-6	Bingyuan Liu	University of Texas Rio Grande Valley		Xianghong
We, 11-13	Maxim Yattselev	Indiana University (Indianapolis)		Sergey
We, 11-20	Li Ji	Macquarie University		Brian
We, 11-27	No seminar
We, 12-4	Dallas Albritton	UW Madison		Andreas
We, 12-11

Abstracts

Gevorg Mnatsakanyan

Title: Almost everywhere convergence of the Malmquist Takenaka series

Link to Abstract: [1]

Lars Niedorf

Title: Restriction type estimates and spectral multipliers on Métivier groups

Abstract: We present a restriction type estimate for sub-Laplacians on arbitrary two-step stratified Lie groups. Although weaker than previously known estimates for the subclass of Heisenberg type groups, these estimates turn out to be sufficient to prove an Lp-spectral multiplier theorem with sharp regularity condition s > d|1/p-1/2| for sub-Laplacians on Métivier groups.

Niclas Technau

Title: Rational points on/near homogeneous hyper-surfaces

Abstract: How many rational points are on/near a compact hyper-surface? This question is related to Serre's Dimension Growth Conjecture. We survey the state of the art, and explain a standard random model. Furthermore, we report on recent joint work with Rajula Srivastava (Uni/MPIM Bonn). Our arguments are rooted in Fourier analysis and, in particular, clarify the role of curvature in the random model.

Sergey Denisov

Title: Applications of inverse spectral theory for canonical systems to NLS

Abstract: For nice initial data, NLS can be integrated using the inverse scattering theory for the Dirac equation on the line. We will discuss the connection of the Dirac equation to canonical systems and use the recent characterization of the Szegő class of measures on the real line to obtain a new semi-conserved quantity for the NLS. The bounds for the negative Sobolev norms will be presented as an application for the L2 NLS solutions (based on joint work with Roman Bessonov).

Shukun Wu

Title: On almost everywhere convergence of planar Bochner Riesz means

Abstract: We prove that the planar Bochner Riesz mean converges almost everywhere for any L^p function in the optimal range, for 5/3<p<2. Our approach is based on a weighted L^2 estimate, which may be of independent interest. For example, up to an epsilon loss, we can reprove Cordoba's L^4 orthogonality by solely considering L^2 space and using L^2 orthogonality. This is a joint work with Xiaochun Li.