### TBA by Shukun Wu

- Series
- Analysis Seminar
- Time
- Wednesday, February 26, 2025 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Shukun Wu – Indiana University Bloomington – shukwu@iu.edu

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- Series
- Analysis Seminar
- Time
- Wednesday, February 26, 2025 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Shukun Wu – Indiana University Bloomington – shukwu@iu.edu

- Series
- Analysis Seminar
- Time
- Wednesday, January 15, 2025 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Leonidas Daskalakis – Wroclaw University – leonidas.e.daskalakis@gmail.com

- Series
- Analysis Seminar
- Time
- Tuesday, December 31, 2024 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Tomasz Szarek – UGA – tzs10705@uga.edu

- Series
- Analysis Seminar
- Time
- Wednesday, December 4, 2024 - 14:00 for
- Location
- Speaker
- ji Li – Macquarie University – ji.li@mq.edu.au

- Series
- Analysis Seminar
- Time
- Wednesday, November 13, 2024 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Alex Stokolos – Georgia Southern University – astokolos@georgiasouthern.edu

I will review some recent results in the theory of differentiation of integrals.

- Series
- Analysis Seminar
- Time
- Wednesday, November 6, 2024 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Tainara Gobetti Borges – Brown University – tainara_gobetti_borges@brown.edu

Let $S^{2d-1}$ be the unit sphere in $\mathbb{R}^{2d}$, and $\sigma_{2d-1}$ the normalized spherical measure in $S^{2d-1}$. The (scale t) bilinear spherical average is given by

$$\mathcal{A}_{t}(f,g)(x):=\int_{S^{2d-1}}f(x-ty)g(x-tz)\,d\sigma_{2d-1}(y,z).$$

There are geometric motivations to study bounds for such bilinear spherical averages, in connection to the study of some Falconer distance problem variants. Sobolev smoothing bounds for the operator

$$\mathcal{M}_{[1,2]}(f,g)(x)=\sup_{t\in [1,2]}|\mathcal{A}_{t}(f,g)(x)|$$

are also relevant to get bounds for the bilinear spherical maximal function

$$\mathcal{M}(f,g)(x):=\sup_{t>0} |\mathcal{A}_{t}(f,g)(x)|.$$

In a joint work with B. Foster and Y. Ou, we put that in a general framework where $S^{2d-1}$ can be replaced by more general smooth surfaces in $\mathbb{R}^{2d}$, and one can allow more general dilation sets in the maximal functions: instead of supremum over $t>0$, the supremum can be taken over $t\in \tilde{E}$ where $\tilde{E}$ is the set of all scales obtained by dyadic dilation of fixed set of scales $E\subseteq [1,2]$.

- Series
- Analysis Seminar
- Time
- Wednesday, October 30, 2024 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Rotem Assouline – Weizmann Institute of Science – rotemassouline@gmail.com

I will present a magnetic version of the Riemannian Brunn-Minkowski and Borell-Brascamp-Lieb inequalities of Cordero-Erausquin-McCann-Schmuckenschläger and Sturm, replacing geodesics by minimizers of a magnetic action functional. Both results involve a notion of magnetic Ricci curvature.

- Series
- Analysis Seminar
- Time
- Wednesday, October 9, 2024 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Martin Hsu – Purdue University – hsu841212@gmail.com

We go over some relevant history and related problems to motivate the study of the Carleson-Radon operator and the difficulty exhibiting in the planar case. Our main result confirms that the planar Carleson-Radon operator along homogenous curve with general monomial \(t^\alpha\) term modulation admits full range \(L^p\) bound assuming the natural non-resonant condition. In the talk, I'll provide a brief overview of the three key ingredients of the LGC based proof:

- A sparse-uniform dichotomy of the input function adapted to appropriate time-frequency foliation of the phase-space;
- A joint structural analysis of the linearizing stopping-time function in the phase in relation to the Gabor coefficients of the input;
- A level set analysis on the time-frequency correlation set.

- Series
- Analysis Seminar
- Time
- Wednesday, October 2, 2024 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Niclas Technau – University of Bonn – ntechnau@uni-bonn.de

Given x in $[0,1]^d$, this talk is about the fine-scale distribution of the Kronecker sequence $(n x mod 1)_{n\geq 1}$.

After a general introduction, I will report on forthcoming work with Sam Chow.

Using Fourier analysis, we establish a novel deterministic analogue of Beck’s local-to-global principle (Ann. of Math. 1994),

which relates the discrepancy of a Kronecker sequence to multiplicative diophantine approximation.

This opens up a new avenue of attack for Littlewood’s conjecture.

- Series
- Analysis Seminar
- Time
- Wednesday, September 25, 2024 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker

<<>>

We discuss the Pointwise Ergodic Theorem for the Gaussian divisor function $d(n)$, that is, for a measure preserving $\mathbb Z [i]$ action $T$, the ergodic averages weighted by the divisor function converge pointwise for all functions in $L^p$, for $p>1$. We obtain improving and sparse bounds for these averages.