Calendar

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.