Calendar

Posted May 5, 2026

Harmonic Analysis Seminar

Yaghoub Rahimi, Louisiana State University
A Density Theorem for Higher Order Sums of Prime Numbers

Let \(P\) be a subset of the primes with lower density strictly larger than \(1/2\). We prove that every sufficiently large even integer can be written as a sum of four primes from \(P\). More generally, we establish analogous results for sums of \(k\) primes, for every \(k\geq 4\), as well as for sums involving \(k\geq 4\) distinct subsets of the primes. These results extend work of H. Li and H. Pan, X. Shao, and A. Alsetri and X. Shao on additive problems for dense subsets of primes. We will also discuss connections with the classical quadratic Waring--Goldbach problem, which concerns representations of large integers as sums of squares of primes.

Posted January 5, 2026
Last modified April 10, 2026

Control and Optimization Seminar Questions or comments?

Necmiye Ozay, University of Michigan IEEE Fellow, and ONR Young Investigator, NASA Early Career Faculty, and NSF CAREER Awardee
Fundamental Limitations of Learning for Dynamics and Control

Data-driven and learning-based methods have attracted considerable attention in recent years both for the analysis of dynamical systems and for control design. While there are many interesting and exciting results in this direction, our understanding of fundamental limitations of learning for control is lagging. This talk will focus on the question of when learning can be hard or impossible in the context of dynamical systems and control. In the first part of the talk, I will discuss a new observation on immersions and how it reveals some potential limitations in learning Koopman embeddings. In the second part of the talk, I will show what makes it hard to learn to stabilize linear systems from a sample-complexity perspective. While these results might seem negative, I will conclude the talk with thoughts on how they can inspire interesting future directions.

Posted April 28, 2026

Algebra and Number Theory Seminar Questions or comments?

Caroline Semmens, University of Arkansas
TBA

Event contact: Richard Ng and Gene Kopp