Calendar

Posted March 9, 2026
Last modified March 20, 2026

Informal Analysis Seminar Questions or comments?

Zhiwei Wang, Louisiana State University
Some recent progress on frequency methods to quantitative unique continuation

We study quantitative unique continuation for elliptic equations with lower order terms of H\"older regularity via a frequency function method. We establish quantitative three-ball inequalities and corresponding vanishing-order bounds. Our results are quantitative with explicit dependence of the three-ball constants and the vanishing-order exponents on the H\"older exponent, which has a unified framework matching sharp endpoint results.

Posted March 3, 2026
Last modified March 9, 2026

Harmonic Analysis Seminar

Shuang Guan, Tufts University
The HRT Conjecture for a Symmetric (3,2) Configuration

The Heil-Ramanathan-Topiwala (HRT) conjecture is an open problem in time-frequency analysis. It asserts that any finite combination of time-frequency shifts of a non-zero function in $L^2(\mathbb{R})$ is linearly independent. Despite its simplicity, the conjecture remains unproven in full generality, with only specific cases resolved. In this talk, I will discuss the HRT conjecture for a specific symmetric configuration of five points in the time-frequency plane, known as the (3,2) configuration. We prove that for this specific setting, the Gabor system is linearly independent whenever the parameters satisfy certain rationality conditions (specifically, when one parameter is irrational and the other is rational). This result partially resolves the remaining open cases for such configurations. I will outline the proof methods, which involve an interplay of harmonic analysis and ergodic theory. This is joint work with Kasso A. Okoudjou.

Posted January 15, 2026
Last modified March 23, 2026

Informal Geometry and Topology Seminar Questions or comments?

Saumya Jain, Louisiana State University
Right-angled Mock Reflection Groups

Right-angled Coxeter groups (RACGs) and certain groups arising from blow-ups act isometrically on CAT(0) cube complexes in a reflection-like manner. Right-angled mock reflection groups (RAMRGs) generalize this class of groups. In this talk, I will introduce RAMRGs and explain how their group structure can be encoded combinatorially using graphs with additional local data. We will also discuss examples and see a characterization of all finite RAMRGs.

Posted January 15, 2026
Last modified March 23, 2026

Colloquium Questions or comments?

Kumar Murty, University of Toronto
Non-vanishing of Poincare series

A famous conjecture of Lehmer asserts that there is no positive integer n for which the Ramanujan function tau(n) vanishes. This has been verified numerically for n up to a very large bound, but a general proof still eludes us. In this talk, we view this conjecture in terms of the non-vanishing of a family of cusp forms called Poincare series. We introduce a new method by which it is possible to prove the non-vanishing of many of these cusp forms.

Posted January 5, 2026
Last modified March 9, 2026

Control and Optimization Seminar Questions or comments?

Jonathan How, Massachusetts Institute of Technology AIAA and IEEE Fellow
Resilient Multi-Agent Autonomy: Perception and Planning for Dynamic, Unknown Environments

Unmanned ground and aerial systems hold promise for critical applications, including search and rescue, environmental monitoring, and autonomous delivery. Real-world deployment in safety-critical settings, however, remains challenging due to GPS-denied operation, perceptual uncertainty, and the need for safe trajectory planning in dynamic unknown environments. This talk presents recent advances in planning, control, and perception that together enable robust, scalable, and efficient aerial autonomy. On the planning and control side, I first introduce DYNUS, which enables uncertainty-aware trajectory planning for safe, real-time flight in dynamic and unknown environments. Building on this foundation, MIGHTY performs fully coupled spatiotemporal optimization to generate agile and precise motion by jointly reasoning about path and timing. Together with prior work on Robust MADER, these methods enable fast, safe, multi-robot navigation under uncertainty. On the perception side, I introduce complementary mapping frameworks that support long-term autonomy and planning. GRAND SLAM combines 3D Gaussian splatting with semantic and geometric priors to produce unified scene representations suitable for photorealistic planning. A second example is ROMAN, which builds on ideas from our prior open set mapping work including SOS MATCH and VISTA. ROMAN compresses environments into sparse, object-centric maps that are orders of magnitude smaller than traditional representations, while still enabling accurate re-localization and loop closure under extreme viewpoint changes. I also discuss the interaction between perception and control, with a focus on safety filtering for systems that rely on learned perception models. Finally, I present results from simulation and hardware experiments and conclude with open challenges in building resilient autonomous aerial systems. Together, these advances move us closer to reliable multi-robot autonomy with meaningful real-world impact. [For the speaker's biographical sketch, click here.]

Posted January 2, 2026
Last modified March 11, 2026

Control and Optimization Seminar Questions or comments?

Jia-Jie Zhu, KTH Royal Institute of Technology in Stockholm
Optimization in Probability Space: PDE Gradient Flows for Sampling and Inference

Many problems in machine learning and Bayesian statistics can be framed as optimization problems that minimize the relative entropy between two probability measures. In recent works, researchers have exploited the connection between the (Otto-)Wasserstein gradient flow of the Kullback-Leibler (or KL) divergence and various sampling and inference algorithms, interacting particle systems, and generative models. In this talk, I will first contrast the Wasserstein flow with the Fisher-Rao flows of a few entropy energy functionals, and showcase their distinct analysis properties when working with different relative entropy driving energies, including the reverse and forward KL divergence. Building upon recent advances in the mathematical foundation of the Hellinger-Kantorovich (HK, a.k.a. Wasserstein-Fisher-Rao) gradient flows, I will then show the analysis of the HK flows and its implications in examples of machine learning tasks.

Event contact: Susanne Brenner

Posted March 1, 2026

Harmonic Analysis Seminar

Simon Bortz, University of Alabama
TBA

Posted January 15, 2026

Informal Geometry and Topology Seminar Questions or comments?

Krishnendu Kar, Louisiana State University
TBD

TBD