Calendar

Posted December 27, 2025
Last modified April 11, 2026

Control and Optimization Seminar Questions or comments?

Aris Daniilidis, Technische Universität Wien
Variational Stability of Alternating Projections

The alternate projection method is a classical approach to deal with the convex feasibility problem. We shall first show that given two nonempty closed convex sets $A$ and $B$, the consecutive projections $x_{n+1} = P_B(P_A(x_n))$, $n \ge 1$ produce a self-contacted sequence, providing in particular an alternative way to establish convergence in the finite dimensional case [2]. In infinite dimensions, a regularity condition is required to ensure convergence of the above sequence $\{x_n\}_{n\ge 1}$ [4]. In [3], it was established that a regularity condition from [1] also ensures the variational stability of the above method. In this talk, we shall complete this result and show that variational stability is actually equivalent to the aforementioned regularity assumption. REFERENCES: [1] H. Bauschke, J. Borwein, On the convergence of von Neumann’s alternating projection algorithm for two sets, Set-Valued Anal. 1 (1993), 185–212. [2] A. Bohm, A. Daniilidis, Ubiquitous algorithms in convex optimization generate self-contracted sequences, J. Convex Anal. 29 (2022) 119–128. [3] C. De Bernardi, E. Miglierina, A variational approach to the alternating projections method, J. Global Optim. 81 (2021), 323-350. [4] H. Hundal, An alternating projection that does not converge in norm, Nonlinear Anal. 57 (2004), 35–61.

Posted April 13, 2026

Combinatorics Seminar Questions or comments?

Gyaneshwar Agrahari, LSU
Counting $K_{1,t}$ and $K_{2,t}$ in higher connected triangulations

In 1979, Hakimi and Schmeichel initiated the study of the maximum number of copies of a fixed subgraph in planar graphs by determining the maximum number of \( C_3 \) and \( C_4 \) in an \( n \)-vertex planar graph. In 1984, Alon and Caro determined the maximum numbers of copies of $K_{1,t}$ and $K_{2,t}$ in an $n$-vertex planar triangulation. Throughout the years, graph theorists have solved similar problems for longer cycles, including Hamiltonian cycles, paths, and other subgraphs. In the case of Hamiltonian cycles, there are at least quadratically many Hamiltonian cycles in a 4-connected planar triangulation. However, in a 5-connected $n$-vertex planar triangulation, there are exponentially many Hamiltonian cycles, proving that connectivity can play a significant role in enumerating certain subgraphs. We determine the exact maximum number of copies of $K_{1,t}$ and $K_{2,t} $ in a $4$-connected planar triangulation, and that of $K_{1,t}$ in a $5$-connected planar triangulation. We also characterize all extremal graphs that attain these bounds.

Posted April 8, 2026

Informal Analysis Seminar Questions or comments?

Christopher Bunting, LSU
Tbd

Tbd

Posted January 15, 2026
Last modified January 22, 2026

Informal Geometry and Topology Seminar Questions or comments?

Fabian Espinoza de Osambela, Louisiana State University
TBD

TBD

Posted January 2, 2026

Control and Optimization Seminar Questions or comments?

Behçet Açıkmeşe, University of Washington AIAA and IEEE Fellow
Optimization-Based Design and Control for Next-Generation Aerospace Systems

Next-generation aerospace systems (e.g., asteroid-mining robots, spacecraft swarms, hypersonic vehicles, and urban air mobility) demand autonomy that transcends current limits. These missions require spacecraft to operate safely, efficiently, and decisively in unpredictable environments, where every decision must balance performance, resource constraints, and risk. The core challenge lies in solving complex optimal control problems in real time, while (i) exploiting full system capabilities without violating safety limits, (ii) certifying algorithmic reliability for critical guidance, navigation, and control (GNC) systems, and (iii) co-designing hardware and software subsystems for optimal end-to-end performance. Our solution is optimization-based autonomy. By transforming GNC challenges into structured optimization problems, we achieve provably robust, computationally tractable solutions. This approach has already revolutionized aerospace, e.g., reusable rockets land autonomously via real-time trajectory planning, drones navigate dynamic obstacles, and spacecraft perform precision docking, all powered by algorithms that solve optimization problems with complex physics-based equations and inequalities in milliseconds. Emerging frontiers (such on-orbit satellite servicing, multi-vehicle asteroid exploration, large-scale orbital spacecraft swarms, and global hypersonic transport) push these methods further. Yet barriers remain, e.g., handling non-convex constraints, ensuring solver resilience, large-scale optimization for decision making and co-design, and bridging the gap between theory and flight-ready systems. This talk explores how real-time optimization is rewriting the rules of autonomy, and how researchers can turn these innovations into practice, propelling aerospace engineering into an era where aerospace systems think, adapt, and perform at the edge of the possible.

Posted April 14, 2026

Student Colloquium

Evelyn Sander, George Mason University
Stable floating configurations for 3D printed objects

This talk concentrates on the study of stability of floating objects through mathematical modeling and experimentation. The models are based on standard ideas of center of gravity, center of buoyancy, and Archimedes’ principle. In addition to free-floating objects in a single fluid, we are able to extend these theory to consider objects floating in two-fluid interfaces, partially grounded objects, and small objects where surface tension is a critical factor.  There will be a discussion of a variety of floating shapes with two-dimensional cross sections for which it is possible to analytically and/or computationally a potential energy landscape in order to identify stable and unstable floating orientations.  I then will compare the analysis and computations to experiments on floating objects designed and created through 3D printing. This research is joint work with Dr. Dan Anderson at GMU and many graduate and undergraduate students. The talk will be accessible to a wide audience, including undergraduate students.

Posted April 14, 2026

Student Colloquium

Evelyn Sander, George Mason University
Bifurcations with cyclic symmetries in partial differential equations models in biology and materials science

In the study of pattern forming systems of partial differential equations, the bifurcation structure of the equilibrium solutions serves as an organizing structure of the dynamics. Werner and Spence (1984) developed the theory of symmetry-breaking pitchfork  bifurcation structures for dynamical systems with even and odd symmetries. In recent work with P. Rizzi and T. Wanner, we were able to extend these results to cases with dihedral symmetries, giving a computer-assisted proof of such bifurcations in the case of the Ohta-Kawasaki model for diblock copolymers. In current work with M. Breden and T. Wanner, we extend these results beyond pitchfork bifurcations to symmetry-breaking transcritical bifurcations. Additionally, we extend our set of examples to higher dimensions and also to the Shigesada-Kawasaki-Teramoto model, a partial differential reaction-diffusion system for spatial segregation in the coexistence of two competing species.

Posted March 6, 2026

Applied Analysis Seminar Questions or comments?

Yunfeng Zhang, University of Cincinnati
TBA

Event contact: Xiaoqi Huang

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 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.