Fall 2023 Analysis Seminar
Organizer: Shaoming Guo
Email: shaomingguo (at) math (dot) wisc (dot) edu
Time: Wed 3:30--4:30
Room: B223
We also have room B211 reserved at 4:25-5:25 for discussions after talks.
All talks will be in-person unless otherwise specified.
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
| Week | Date | Speaker | Institution | Title | Host(s) | Notes (e.g. unusual room/day/time) |
|---|---|---|---|---|---|---|
| 1 | We, Sep. 6 | |||||
| Fr, Sept. 8 | Tushar Das | UW La Crosse | Playing games on fractals: Dynamical and Diophantine | Betsy | Colloquium, 4-5pm in B239 | |
| 2 | Tu, Sept. 12 | Rajula Srivastava | Hausdorff Center of Mathematics, Bonn | Counting Rational Points near Flat Hypersurfaces | Andreas | Tuesday 4:00 pm in VV B135 |
| We, Sept. 13 | Niclas Technau | University of Graz | Oscillatory Integrals Count | Andreas | ||
| 3 | We, Sept. 20 | Terry Harris | UW Madison | Horizontal Besicovitch sets of measure zero and some related problems | analysis group | |
| 4 | We, Sept. 27 | |||||
| 5 | Mo, Oct 2 | Edriss Titi | Texas A&M | On the Solvability of the Navier-Stokes and Euler Equations, where do we stand? | Leslie and Sam | Distinguished Lecture 1 (general audience talk), 4-5pm in B239 |
| 5 | Tu, Oct 3 | Edriss Titi | Texas A&M | Oceanic and Atmospheric Dynamics Models - Global Regularity and Finite-time Singularity. | Leslie and Sam | Distinguished Lecture 2 (Analysis seminar), 4-5pm, B135 |
| 5 | We, Oct 4 | Edriss Titi | Texas A&M | Downscaling Data Assimilation Algorithm for Weather and Climate Prediction | Leslie and Sam | Distinguished Lecture 3 (Applied and Computational math seminar), 901 |
| 5 | We, Oct. 4 | Tristan Leger | Princeton | L^p bounds for spectral projectors on hyperbolic surfaces | Simon | |
| 6 | We, Oct. 11 | Bingyang Hu | Auburn | Brian | ||
| 7 | We, Oct. 18 | Ashley Zhang | Vanderbilt | Alexei | ||
| 8 | Tu, Oct 25 | Gigliola Staffilani | MIT | (See Colloquium page) | Miahela and Leslie | Hilldale Lecture 4-5pm in 1310 Sterling Hall |
| 8 | We, Oct. 25 | Gigliola Staffilani | MIT | (See Colloquium page) | Mihaela and Leslie | Special Colloquium 4-5pm in B239 |
| Fr, Oct 27 | Rodrigo Bañuelos | Purdue | Betsy | Colloquium, 4-5pm in B239 | ||
| 9 | We, Nov. 1 | Tent scheduled distinguished lecture | Distinguished lecture 4-5pm in B239 | |||
| 10 | We, Nov. 8 | Lechao Xiao | Google deepmind | Shaoming | ||
| 11 | We, Nov. 15 | Neeraja Kulkarni | Caltech | Jacob | ||
| 12 | We, Nov. 22 | No talk | No talk | No talk | Thanksgiving week | |
| 13 | We, Nov. 29 | Changkeun Oh | MIT | Shaoming | ||
| 14 | We, Dec. 6 | |||||
| 15 | We, Dec. 13 | Jing-Jing Huang | Nevada | Shaoming | ||
| 1 | We, Jan. 24, 2024 | |||||
| 2 | We, Jan. 31 | |||||
| 3 | We, Feb. 7 | Donald Stull | University of Chicago | Betsy, Shaoming, and Jake F. | ||
| 4 | We, Feb. 14 | Victor Bailey | University of Oklahoma | Betsy | ||
| 5 | We, Feb. 21 | |||||
| 6 | We, Feb. 28 | Alex Rutar | University of St. Andrews | Andreas | ||
| 7 | We, Mar. 6 | Song-Ying Li | UC-Irvine | Xianghong | ||
| 8 | We, Mar. 13 | |||||
| 9 | We, Mar. 20 | |||||
| Fr, Mar. 22 | Jack Lutz | Iowa State University | Shaoming | department colloquium, 4-5pm | ||
| 10 | We, Mar. 27 | Spring recess | spring recess | spring recess | ||
| 11 | We, Apr. 3 | |||||
| 12 | We, Apr. 10 | |||||
| 13 | We, Apr. 17 | |||||
| 14 | We, Apr. 24 | |||||
| 15 | We, May 1 |
Abstracts
Tushar Das
Title: Playing games on fractals: Dynamical & Diophantine
Abstract: We will present sketches of a program, developed in collaboration with Lior Fishman, David Simmons, and Mariusz Urbanski, which extends the parametric geometry of numbers (initiated by Wolfgang Schmidt and Leonhard Summerer) to Diophantine approximation for systems of m linear forms in n variables. Our variational principle (arXiv:1901.06602) provides a unified framework to compute Hausdorff and packing dimensions of a variety of sets of number-theoretic interest, as well as their dynamical counterparts via the Dani correspondence. Highlights include the introduction of certain combinatorial objects that we call templates, which arise from a dynamical study of Minkowski’s successive minima in the geometry of numbers; as well as a new variant of Schmidt’s game designed to compute the Hausdorff and packing dimensions of any set in a doubling metric space. The talk will be accessible to students and faculty whose interests contain a convex combination of homogeneous dynamics, Diophantine approximation and fractal geometry.
Rajula Srivastava
Title: Counting Rational Points near Flat Hypersurfaces
Abstract: How many rational points with denominator of a given size lie within a given distance from a compact hypersurface? In this talk, we shall describe how the geometry of the surface plays a key role in determining this count, and present a heuristic for the same. In a recent breakthrough, J.J. Huang proved that this guess is indeed true for hypersurfaces with non-vanishing Gaussian curvature. What about hypersurfaces with curvature only vanishing up to a finite order, at a single point? We shall offer a new heuristic in this regime which also incorporates the contribution arising from "local flatness". Further, we will describe how ideas from Harmonic Analysis can be used to establish the indicated estimates for hypersurfaces of this type immersed by homogeneous functions. In particular, we shall use a powerful bootstrapping argument relying on Poisson summation, duality between flat and "rough" hypersurfaces, and the method of stationary phase. A crucial role is played by a dyadic scaling argument exploiting the homogeneous nature of the hypersurface. Based on joint work with N. Technau.
Niclas Technau
Title: Oscillatory Integrals Count
Abstract: This talk is about phrasing (number theoretic) counting problems in terms oscillatory integrals. We shall provide a simple introduction to the topic, mention open questions, and report on joint work with Sam Chow, as well as on joint work with Chris Lutsko.
Terry Harris
Title: Horizontal Besicovitch sets of measure zero and some related problems
Abstract: It is shown that horizontal Besicovitch sets of measure zero exist in R^3. The proof is constructive and uses point-line duality analogously to Kahane’s construction of measure zero Besicovitch sets in the plane. Some consequences and related examples are shown for the SL_2 Kakeya maximal function.
Tristan Leger
Title: L^p bounds for spectral projectors on hyperbolic surfaces
Abstract: In this talk I will present L^p boundedness results for spectral projectors on hyperbolic surfaces. I will focus on the case where the spectral window has small width. Indeed the negative curvature assumption leads to improvements over the universal bounds of C.Sogge, thus illustrating how these objects are sensitive to the global geometry of the underlying manifold. I will also explain how this relates to the general theme of delocalization of eigenfunctions of the Laplacian on hyperbolic surfaces. This is based on joint work with Jean-Philippe Anker and Pierre Germain.