Calendar

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
Last modified May 8, 2026

Algebra and Number Theory Seminar Questions or comments?

Caroline Semmens, University of Arkansas
Isogeny-Torsion Graphs of Some Quadratic Number Fields

An elliptic curve over a number field $K$ is a smooth projective curve $E$ with a point defined over $K$. By the Mordell–Weil theorem, the $K$-rational points on elliptic curves form a finitely generated abelian group. Isogenies of elliptic curves are maps between elliptic curves which are also group homomorphisms. We can organize isogeny classes into graphs and label the vertices with the torsion structure of corresponding elliptic curves. These graphs are called isogeny-torsion graphs, and in 2021, Chiloyan and Lozano-Robledo classified all isogeny torsion graphs over $\mathbb{Q}$. In this talk, we explore progress on this classification question over other number fields, using work done by Banwait, Najman, and Padurariu extending Mazur’s theorem. Of particular interest is the quadratic field $K = \mathbb{Q}(\sqrt{213})$. This talk is based on joint work with Clayton Boothe, Michael Logal, and Lance E Miller.

Event contact: Richard Ng and Gene Kopp