Posted September 27, 2024
Last modified October 1, 2024
Mathematical Physics and Representation Theory Seminar
2:30 pm – 3:20 pm Lockett 233
Tom Gannon, UCLA
Quantization of the universal centralizer and central D-modules
We will discuss joint work with Victor Ginzburg that proves a conjecture of Nadler on the existence of a quantization, or non-commutative deformation, of the Knop-Ngô morphism—a morphism of group schemes used in particular by Ngô in his proof of the fundamental lemma in the Langlands program. We will first explain the representation-theoretic background, give an extended example of this morphism for the group GL_n(C), and then present a precise statement of our theorem. Time permitting, we will also discuss how the tools used to construct this quantization can also be used to prove conjectures of Ben-Zvi and Gunningham, which predict a relationship between the quantization of the Knop-Ngô morphism and the parabolic induction functor.
Posted August 21, 2024
Last modified August 29, 2024
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Wanlin Li, Washington University in St. Louis
TBA
Posted August 30, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Locket 233
Krishnendu Kar, Louisiana State University
TBD
Posted September 11, 2024
Last modified September 18, 2024
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Rushikesh Kamalapurkar, University of Florida
Operator Theoretic Methods for System Identification
Operator representations of dynamical systems on Banach spaces provide a wide array of modeling and analysis tools. In this talk, I will focus on dynamic mode decomposition (DMD). In particular, new results on provably convergent singular value decomposition (SVD) of total derivative operators corresponding to dynamic systems will be presented. In the SVD approach, dynamic systems are modeled as total derivative operators that operate on reproducing kernel Hilbert spaces (RKHSs). The resulting total derivative operators are shown to be compact provided the domain and the range RKHSs are selected carefully. Compactness is used to construct a novel sequence of finite rank operators that converges, in norm, to the total derivative operator. The finite rank operators are shown to admit SVDs that are easily computed given sample trajectories of the underlying dynamical system. Compactness is further exploited to show convergence of the singular values and the right and left singular functions of the finite rank operators to those of the total derivative operator. Finally, the convergent SVDs are utilized to construct estimates of the vector field that models the system. The estimated vector fields are shown to be provably convergent, uniformly on compact sets. Extensions to systems with control and to partially unknown systems are also discussed. This talk is based in part on joint works [RK23], [RK24], and [RRKJ24] with J.A. Rosenfeld.
Posted October 4, 2024
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett Hall 233 (simulcasted via Zoom)
Zilin Jiang, Arizona State University
Beyond the classification theorem of Cameron, Goethals, Seidel, and Shult
The classification of graphs with smallest eigenvalues at least −2 culminated in a beautiful theorem of Cameron, Goethals, Seidel and Shult, who related such graphs to root systems from the representation theory of semisimple Lie algebras. In this talk, I will explore graphs with smallest eigenvalues between −2 and −λ*, where λ* is about 2.0198, and I will explain why the mysterious number λ* is a barrier for classification. Joint work with Alexander Polyanskii and Hricha Acharya.
Posted August 30, 2024
Last modified September 16, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Locket 233
Adithyan Pandikkadan, Louisiana State University
TBD
Posted August 29, 2024
Geometry and Topology Seminar Seminar website
3:30 pm
Bin Sun, Michigan State University
TBD
Posted September 27, 2024
Mathematical Physics and Representation Theory Seminar
2:30 pm – 3:20 pm Lockett 233
Xinchun Ma, University of Chicago
TBA
TBA
Posted August 14, 2024
Algebra and Number Theory Seminar Questions or comments?
Brian Grove, LSU
TBA
Posted August 30, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Locket 233
Megan Fairchild, Louisiana State University
TBD
Posted August 19, 2024
Last modified September 27, 2024
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Andrii Mironchenko, University of Klagenfurt
IEEE CSS George S. Axelby Outstanding Paper Awardee
Superposition Theorems for Input-to-State Stability of Time-Delay Systems
We characterize input-to-state stability (ISS) for nonlinear time-delay systems (TDS) in terms of stability and attractivity properties for systems with inputs. Using the specific structure of TDS, we obtain much tighter results than those possible for general infinite-dimensional systems. The subtle difference between forward completeness and boundedness of reachability sets (BRS) is essential for the understanding of the ISS characterizations. As BRS is important in numerous other contexts, we discuss this topic in detail as well. We shed light on the differences between the ISS theories for TDS, generic infinite-dimensional systems, and ODEs.
Posted October 1, 2024
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Friday, October 4, 2024 Zoom Link
Andrew Fulcher, University College Dublin
The cyclic flats of L-polymatroids
In recent years, $q$-polymatroids have drawn interest because of their connection with rank-metric codes. For a special class of $q$-polymatroids called $q$-matroids, the fundamental notion of a cyclic flat has been developed as a way to identify the key structural features of a $q$-matroid. In this talk, we will see a generalization of the definition of a cyclic flat that can apply to $q$-polymatroids, as well as a further generalization, $L$-polymatroids. The cyclic flats of an $L$-polymatroid is essentially a reduction of the data of an $L$-polymatroid such that the $L$-polymatroid can be retrieved from its cyclic flats. As such, in matroid theory, cyclic flats have been used to characterize numerous invariants.
Posted September 27, 2024
Mathematical Physics and Representation Theory Seminar
2:30 pm – 3:20 pm Lockett 233
Nikolay Grantcharov, University of Chicago
TBA
TBA
Posted September 26, 2024
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett 232
Matias Delgadino, University of Texas at Austin
Generative Adversarial Networks: Dynamics
Generative Adversarial Networks (GANs) was one of the first Machine Learning algorithms to be able to generate remarkably realistic synthetic images. In this presentation, we delve into the mechanics of the GAN algorithm and its profound relationship with optimal transport theory. Through a detailed exploration, we illuminate how GAN approximates a system of PDE, particularly evident in shallow network architectures. Furthermore, we investigate known pathological behaviors such as mode collapse and failure to converge, and elucidate their connections to the underlying PDE framework through an illustrative example.
Posted August 21, 2024
Last modified August 29, 2024
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Brett Tangedal, University of North Carolina, Greensboro
TBA
Posted August 30, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Locket 233
Matthew Lemoine, Louisiana State University
TBD
Posted August 26, 2024
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Angelia Nedich, Arizona State University
TBA
Posted August 30, 2024
Last modified September 16, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Locket 233
Nilangshu Bhattacharyya, Louisiana State University
TBD
Posted September 6, 2024
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Laura Menini, Università degli Studi di Roma Tor Vergata
TBA
Posted August 30, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Locket 233
Sean Boros, Louisiana State University
TBD
Posted September 17, 2024
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Arka Banerjee, Auburn University
TBD
Posted August 29, 2024
Last modified September 12, 2024
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Piernicola Bettiol, Université de Bretagne Occidentale, France
TBA
Posted September 11, 2024
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett 232
Michael Novack, Louisiana State University
TBA
Posted August 30, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Locket 233
Saumya Jain, Louisiana State University
TBD
Posted August 21, 2024
Last modified September 12, 2024
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Benedetto Piccoli, Rutgers University, Camden
AMS Fellow, SIAM W. T. and Idalia Reid Prize Awardee
Control Theory in Traffic Applications: 100 Years of Traffic Models
In 1924, in The Quarterly Journal of Economics, Frank H. Knight debated on social costs using an example of two roads, which was the base of the Wardrop’s principle. The author suggested the use of road tolls and it was probably the first traffic model ever. A few other milestones of a long history include the traffic measurements by Greenshields in 1934, the Lighthill-Whitham-Richards model in late 1950s, and follow-the-leader microscopic models. After describing some of these milestones, we will turn to modern theory of conservation laws on topological graphs with application to traffic monitoring. The theory required advance mathematics such as BV spaces and Finsler-type metrics on L1. In the late 2000s, this theory was combined with Kalman filtering to deal with traffic monitoring using data from cell phones and other devices. Then we will turn to measure-theoretic approaches for multi-agent systems, which encompass follow-the-leader-type models. Tools from optimal transport allow us to deal with the mean-field limit of controlled equations, representing the action of autonomous vehicles. We will conclude by discussing how autonomy can dissipate traffic waves and reduce fuel consumption, then illustrating the results of a 2022 experiment with 100 autonomous vehicles on an open highway in Nashville.
Posted August 29, 2024
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Jiuya Wang, University of Georgia
TBA
Posted August 30, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Locket 233
Huong Vo, Louisiana State University
TBD
Posted August 13, 2024
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Karl Johansson, KTH Royal Institute of Technology, Sweden
Fellow of IEEE, IEEE CSS Hendrik W. Bode Lecture Prize Awardee
TBA
Posted September 4, 2024
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
María Soledad Aronna, Escola de Matematica Aplicada, Brazil
TBA
Posted September 19, 2024
Colloquium Questions or comments?
3:30 pm Lockett 232
Bogdan Suceava, California State University Fullerton
TBD