Calendar

Posted February 9, 2026
Last modified February 23, 2026

Informal Analysis Seminar Questions or comments?

12:30 pm – 1:30 pm Lockett 233

Gustavs Tobiss, Louisiana State University
Bloch's Theorem, Wannierization, and Tight-binding

This talk presents the mathematical framework and numerical methods behind tight-binding models for electrons in a one-dimensional periodic potential, focusing on the transition from Bloch states to Wannier functions. We start by revisiting Bloch’s theorem, which leads to a decomposition into independent Hamiltonians for each wavevector in the Brillouin zone. This immediately allows us to describe the system in terms of its band structure. We then introduce Wannier functions, localized eigenstates derived from band eigenfunctions. The Wannier functions possess many nice qualities, such as being exponentially localized and orthonormal, with the decay tied to the analyticity of the band structure. Next, we derive the tight-binding Hamiltonian by projecting onto a single band subspace. This Hamiltonian is expressed as a sum of hopping terms, with hopping amplitudes related to the band structure, providing a link to the system's dispersion relation and physical properties. Finally, we discuss how this simple model will be used to analyze more complicated structures.

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Posted January 28, 2026
Last modified February 17, 2026

Geometry and Topology Seminar Seminar website

1:30 pm 233 Lockett Hall

Nir Gadish, University of Pennsylvania
Letter braiding invariants of words in groups

How can we tell if a group element can be written as k-fold nested commutator? One way is to find a collection of computable function that vanish only on nested commutators. This talk will introduce letter-braiding invariants - these are elementarily defined functions on words, inspired by the homotopy theory of loop-spaces and carrying deep geometric content. They give a universal finite-type invariant for arbitrary groups, extending the influential Magnus expansion of free groups that already had countless applications in low dimensional topology. As a consequence we get new geometric formulas for braid and link invariants, and a way to linearize automorphisms of general groups that specializes to the Johnson homomorphism of mapping class groups.

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Posted January 15, 2026
Last modified February 20, 2026

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett Hall 233

Hailey Garcia, Louisiana State University
The Cohomology of the Complement of Hyperplane Arrangements

We consider linear hyperplane arrangements 𝓐 in V=ℂ^n. Of interest is the complement of the arrangement M(𝓐)=M(𝓐)=V\(∪_{H_i∈𝓐}H_i). We will demonstrate the definition and some properties of the Orlik-Solomon algebra A(𝓐) of 𝓐. Then, by considering the deletion-restriction triple (𝓐',𝓐,𝓐''), we demonstrate that the cohomology ring of M(𝓐) is isomorphic to A(𝓐) and hence determined by the combinatorics of the intersection lattice L(𝓐).

Posted January 8, 2026

Control and Optimization Seminar Questions or comments?

9:30 am – 10:20 am Zoom (click here to join)

Lars Gruene, University of Bayreuth SIAM Fellow
Can Neural Networks Solve High Dimensional Optimal Feedback Control Problems?

Deep reinforcement learning has established itself as a standard method for solving nonlinear optimal feedback control problems. In this method, the optimal value function (and, in some variants, the optimal feedback law also) is stored using a deep neural network. Hence, the applicability of this approach to high-dimensional problems relies crucially on the network's ability to store a high-dimensional function. It is known that for general high-dimensional functions, neural networks suffer from the same exponential growth of the number of coefficients as traditional grid based methods, the so-called curse of dimensionality. In this talk, we use methods from distributed optimal control to describe optimal control problems in which this problem does not occur.

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Posted February 24, 2026

Combinatorics Seminar Questions or comments?

2:30 pm – 3:30 pm Zoom (click here to join)

Steven Noble, University of Leeds
Critical groups for embedded graphs

Critical groups are finite Abelian groups associated with graphs. They arise in many different ways, for example, via the chip-firing game, through the Laplacian and via fundamental cycles and cocycles. Several results in the literature on critical groups only hold for planar graphs and their proofs rely on a plane drawing. This suggests the natural setting for the critical group might be graphs embedded on surfaces. We show how various definitions of the critical group may be extended to embedded graphs, and crucially that they give isomorphic groups. No knowledge of topology or group theory is required!

Posted February 10, 2026

Mathematical Physics and Representation Theory Seminar

1:30 pm – 2:20 pm Lockett 233

Milo Moses, Caltech
Four-colorings, recoverability, and topological quantum matter

In ongoing joint work with A. Kitaev, D. Ranard, I. Kim, we have been developing a formalism for exploring topologically ordered quantum states using recovery maps. In this talk, I will explain the potential applicability of these recovery maps to the study of 4-colorings of planar graphs. Conditioned on an unproven technical lemma (which perhaps someone in the audience can demonstrate!), I can show that bridgeless planar graphs quasi-isometric to the Euclidean plane obey a medley of properties reminiscent of topological quantum order.

Posted February 9, 2026

Informal Analysis Seminar Questions or comments?

12:30 pm – 1:30 pm Lockett 233

Basit Abdulfatai, Louisiana State University
Dolapo Onifade, Louisiana State University
Introduction to deep adaptive sampling and physics informed neural networks

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Posted January 19, 2026

Geometry and Topology Seminar Seminar website

1:30 pm Virtual

Ettore Marmo, Università degli Studi di Milano-Bicocca
TBA

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Posted January 15, 2026
Last modified January 16, 2026

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett Hall 233

Benjamin Appiah, Louisiana State University
TBD

TBD

Posted January 12, 2026

Applied Analysis Seminar Questions or comments?

3:30 pm Lockett Hall 232

Daniel Massatt, New Jersey Institute of Technology
TBA

Event contact: Stephen Shipman

Posted November 15, 2025
Last modified January 21, 2026

Algebra and Number Theory Seminar Questions or comments?

2:00 pm – 3:00 pm Lockett 233 or click here to attend on Zoom

Kiran Kedlaya, University of California San Diego
TBA

Event contact: Gene Kopp

Posted January 15, 2026

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett Hall 233

Sayani Mukherjee, Louisiana State University
TBD

TBD

Posted December 1, 2025

Control and Optimization Seminar Questions or comments?

9:30 am – 10:20 am Zoom (click here to join)

Khai Nguyen, North Carolina State University
TBA

Posted January 11, 2026

Applied Analysis Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett 223

Zhiyuan Geng, Purdue University
TBA

Posted January 15, 2026

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett Hall 233

Saumya Jain, Louisiana State University
TBD

TBD

Posted January 15, 2026

Colloquium Questions or comments?

3:30 pm Lockett 232

Kumar Murty, University of Toronto
TBA

Posted January 5, 2026

Control and Optimization Seminar Questions or comments?

9:30 am – 10:20 am Zoom (click here to join)

Jonathan How, Massachusetts Institute of Technology AIAA and IEEE Fellow
TBA

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Posted January 2, 2026
Last modified January 8, 2026

Control and Optimization Seminar Questions or comments?

10:30 am – 11:20 am Joint Computational Mathematics and Control and Optimization Seminar to Be Held In Person at Location TBA and on Zoom (click here to join)

Jia-Jie Zhu, KTH Royal Institute of Technology in Stockholm
TBA

Posted January 15, 2026

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett Hall 233

Krishnendu Kar, Louisiana State University
TBD

TBD

Posted January 15, 2026

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett Hall 233

Nilangshu Bhattacharyya, Louisiana State University
TBD

TBD

Posted February 5, 2026
Last modified February 6, 2026

Control and Optimization Seminar Questions or comments?

9:30 am – 10:20 am Zoom (click here to join)

Wonjun Lee, Ohio State University
Linear Separability in Contrastive Learning via Neural Training Dynamics

The SimCLR method for contrastive learning of invariant visual representations has become extensively used in supervised, semi-supervised, and unsupervised settings, due to its ability to uncover patterns and structures in image data that are not directly present in the pixel representations. However, this success is still not well understood; neither the loss function nor invariance alone explains it. In this talk, I present a mathematical analysis that clarifies how the geometry of the learned latent distribution arises from SimCLR. Despite the nonconvex SimCLR loss and the presence of many undesirable local minimizers, I show that the training dynamics driven by gradient flow tend toward favorable representations. In particular, early training induces clustering in feature space. Under a structural assumption on the neural network, our main theorem proves that the learned features become linearly separable with respect to the ground-truth labels. To support the theoretical insights, I present numerical results that align with the theoretical predictions.

Posted January 15, 2026

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett Hall 233

Anurakti Gupta, Louisiana State University
TBD

TBD

Posted December 27, 2025

Control and Optimization Seminar Questions or comments?

9:30 am – 10:20 am Zoom (click here to join)

Aris Daniilidis, Technische Universität Wien
TBA

Posted January 15, 2026
Last modified January 22, 2026

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett Hall 233

Fabian Espinoza de Osambela, Louisiana State University
TBD

TBD

Posted January 2, 2026

Control and Optimization Seminar Questions or comments?

9:30 am – 10:20 am Zoom (click here to join)

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 January 15, 2026

Informal Geometry and Topology Seminar Questions or comments?

3:30 pm – 4:30 pm Lockett Hall 233

Huong Vo, Louisiana State University
TBD

TBD

Posted January 24, 2026

Control and Optimization Seminar Questions or comments?

10:30 am – 11:20 am Note the Special Seminar Time. Zoom (click here to join)

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

Control and Optimization Seminar Questions or comments?

9:30 am – 10:20 am Zoom (click here to join)

Necmiye Ozay, University of Michigan IEEE Fellow, and ONR Young Investigator, NASA Early Career Faculty, and NSF CAREER Awardee
TBA