Calendar
Posted September 9, 2025
Algebra and Number Theory Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett 233 or click here to attend on Zoom
Kalani Thalagoda, Tulane University
A summation formula for Hurwitz class numbers
The Hurwitz class numbers, $H(n)$, count ${\rm SL}(2,\mathbb{Z})$-classes of binary quadratic forms inversely weighted by stabilizer size. They are famously connected to the sum of three squares problem and to class numbers of imaginary quadratic fields. The work of Zagier in 1975 showed that their generating functions are related to a weight $3/2$ Harmonic Maass form. In this talk, I will discuss a summation formula for mock modular forms of moderate growth, with an emphasis on its application to Hurwitz class numbers. This is joint work with Olivia Beckwith, Nicholas Diamantis, Rajat Gupta, and Larry Rolen.
Posted October 27, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Monday, October 27, 2025 Lockett 136
Sanjeet Sahoo, LSU
Introduction to Invariant Measures and Ergodicity for Markov Processes
In this talk, we will introduce the concept of transition probability measures and establish criteria for the existence and uniqueness of invariant measures.
Posted August 27, 2025
Last modified October 27, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Nilangshu Bhattacharyya, Louisiana State University
Khovanov Homology
Continuing our discussion of Khovanov Homology following Melissa Zhang's notes.
Posted September 1, 2025
Last modified October 27, 2025
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Chen Zhang, Simons Center for Geometry and Physics
Plane Floer homology and the odd Khovanov homology of 2-knots
In this talk, I will discuss joint work with Sypropoulous and Vidyarthi in which we prove a conjecture of Migdail and Wehrli regarding the maps which odd Khovanov homology associates to knotted spheres. Our main tool is the spectral sequence from reduced OKH to Plane Floer homology.
Posted October 7, 2025
Last modified October 9, 2025
Control and Optimization Seminar Questions or comments?
9:30 am – 10:20 am Note: First of 2 Seminars for 10/31. Zoom (click here to join)
Alexandre Mauroy, Université de Namur
Dual Koopman Operator Formulation in Reproducing Kernel Hilbert Spaces for State Estimation
The Koopman operator acts on observable functions defined over the state space of a dynamical system, thereby providing a linear global description of the system dynamics. A pointwise description of the system is recovered through a weak formulation, i.e. via the pointwise evaluation of observables at specific states. In this context, the use of reproducing kernel Hilbert spaces (RKHS) is of interest since the above evaluation can be represented as the duality pairing between the observables and bounded evaluation functionals. This representation emphasizes the relevance of a dual formulation for the Koopman operator, where a dual Koopman system governs the evolution of linear evaluation functionals. In this talk, we will leverage the dual formulation to build a Luenberger observer that estimates the (infinite-dimensional) state of the Koopman dual system, and equivalently the (finite-dimensional) state of the nonlinear dynamics. The method will be complemented with theoretical convergence results that support numerical Koopman operator-based estimation techniques known from the literature. Finally, we will extend the framework to a probabilistic approach by solving the problem of moments in the RKHS setting.
Posted October 8, 2025
Last modified October 9, 2025
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Note: Second of 2 Seminars for 10/31. Zoom (click here to join)
Umesh Vaidya, Clemson University
TBA
Posted October 27, 2025
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Matthew Mizell, LSU
Unavoidable minors of matroids with minimum cocircuit size four
When a graph $G$ is a 2-connected and loopless, the set of edges that meet a fixed vertex of $G$ is a bond of $G$ and a cocircuit of its cycle matroid $M(G)$. Because of this, it is common in matroid theory to take minimum cocircuit size as a matroid analog of minimum vertex degree in a graph. Halin and Jung proved in 1963 that every simple graph with minimum degree at least four has $K_5$ or $K_{2,2,2}$ as a minor. In this talk, we will provide a characterization of matroids with minimum cocircuit size four in terms of their unavoidable minors. This talk is based on joint work with James Oxley.
Posted October 21, 2025
Colloquium Questions or comments?
3:30 pm Lockett 232
Michael Lacey, Georgia Institute of Technology
Prime Wiener Wintner Theorem
The classical Wiener Wintner Theorem has an extension to prime averages. Namely, for all measure preserving system $(X,m,T)$, and bounded function $f$ on $X$, there is a set of full measure $X_f\subset X$ so that for all $x\in X_f$, the averages below $$ \frac 1N \sum_{n=1}^N \phi(n) \Lambda (n) f(T^n x ) $$ converge for all continuous $2\pi$ periodic $\phi $. Above, $\Lambda$ is the von Mangoldt function. The proof uses the structure theory of measure preserving systems, the Prime Ergodic Theorem, and higher order Fourier properties of the Heath-Brown approximate to the von Mangoldt function. Joint work with J. Fordal, A. Fragkos, Ben Krause, Hamed Mousavi, and Yuchen Sun.
Posted October 22, 2025
Last modified October 23, 2025
Southern Regional Harmonic Analysis Conference
The Southern Regional Harmonic Analysis Conference will focus on current research in harmonic analysis and its applications, featuring plenary talks by Michael Lacey and Irina Holmes. For more details, please refer to conference webpage: https://www.math.lsu.edu/~ha2025/
Event contact: Rui Han, Gestur Olafsson, Naga Manasa Vempati, Fan Yang