Calendar

Posted April 21, 2026

Algebra and Number Theory Seminar Questions or comments?

Mengwei Hu, Yale University
On certain Lagrangian subvarieties in minimal resolutions of Kleinian singularities

Kleinian singularities are quotients of C^2 by finite subgroups of SL_2(C). They are in bijection with the ADE Dynkin diagrams via the McKay correspondence. In this talk, I will introduce certain singular Lagrangian subvarieties in the minimal resolutions of Kleinian singularities, motivated by the geometric classification of unipotent Harish-Chandra (g,K)-modules. The irreducible components of these singular Lagrangian subvarieties are P^1's and A^1's. I will describe how they intersect with each other through the realization of Kleinian singularities as Nakajima quiver varieties. I will also discuss their connections with nilpotent K-orbits and symmetric pairs in semisimple Lie algebras.

Posted April 8, 2026

Informal Analysis Seminar Questions or comments?

Jackson Knox, Louisiana State University
Tbd

Tbd

Posted January 15, 2026

Informal Geometry and Topology Seminar Questions or comments?

Huong Vo, Louisiana State University
TBD

TBD

Posted January 24, 2026

Control and Optimization Seminar Questions or comments?

Michael Friedlander, University of British Columbia SIAM Fellow
Seeing Structure Through Duality

Duality is traditionally introduced as a source of bounds and shadow prices. In this talk I emphasize a second role: revealing structure that enables scalable computation. Starting from LP complementary slackness, I describe a generalization called polar alignment that identifies which "atoms" compose optimal solutions in structured inverse problems. The discussion passes through von Neumann's minimax theorem, Kantorovich's resolving multipliers, and Dantzig's simplex method to arrive at sublinear programs, where an adversary selects worst-case costs from a set. The resulting framework unifies sparse recovery, low-rank matrix completion, and signal demixing. Throughout, dual variables serve as certificates that decode compositional structure.

Posted April 28, 2026

Combinatorics Seminar Questions or comments?

Rong Luo, West Virginia University
Vector Flows of Graphs

Tutte introduced integer flows as the dual of vertex colorings in planar graphs, and this concept later extended to real-valued and vector-valued flows. In this talk I will talk about $S^1$-flows and $d$-dimentional vector flows. A vector ${S}^d$-flow is a flow whose flow values are vectors in $S^d$, where $S^d$ is the set of all unit vectors in $\mathbb{R}^{d+1}$. A natural question is the relationship between integer nowhere-zero $3$-flows and $S^1$-flows, which was investigated by Thomassen (JCTB, 2014) and further explored in special graph classes by Wang, Cheng, Luo, and Zhang (SIAM Discrete Math, 2015). Motivated by these results, we study the existence of $S^1$-flows in graphs with specific structural properties. In particular, we focus on graphs containing a spanning triangle-tree and triangulated graphs and characterize the existence of $S^1$-flows in such graphs. This extends previous characterizations of integer nowhere-zero $3$-flows to the setting of $S^1$-flows. Mattiolo, Mazzuoccolo, Rajn\'{i}k and Tabarelli recently studied $d$-dimensional $r$-flows with values in $\mathbb{R}^d$ under the Euclidean norm. We generalize this framework by considering arbitrary $p$-norms and introduce \emph{$d$-dimensional $p$-normed nowhere-zero $r$-flows}, with the \emph{$d$-dimensional $p$-normed flow index} $\phi_{d,p}(G)$ defined as the smallest $r \ge 2$ for which $G$ admits such a flow. We establish new upper bounds for $\phi_{d,p}(G)$ This is joint work with Chenxing Li, Jiaao Li, and Bo Su.

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.