Calendar
Posted August 16, 2025
Last modified August 21, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 232
Moisés Gómez-Solís, Louisiana State University
Laura Kurtz, Louisiana State University
Organizational Meeting
Posted August 30, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 232
Hari Narayanan, Louisiana State University
Introduction to Spectral Theory and Schrödinger Operators
This talk concentrates on the spectral theory of Schrödinger operators with a view toward modern research. The huge literature in this field was spawned by non-relativistic quan- tum mechanics and has led to rich advances in pure spectral theory and applications. After a brief review of finite dimensions, the talk first develops abstract spectral theory of self-adjoint operators in Hilbert space with some emphasis on classical ideas of harmonic analysis, namely spectral resolutions induced by symmetry groups. Then we introduce continuous and discrete Schrödinger operators with electric and magnetic potentials and some of the standard theorems. We treat periodic, quasi-periodic, and ergodic operators, in decreasing detail. The treatment of periodic operators will emphasize the connections to commutative algebra centering around the Fermi and Bloch algebraic or analytic varieties. This is followed by analysis in physical, momen- tum (dual), configuration, and reciprocal space; and a brief look at ergodic and quasi-periodic operators.
Posted September 10, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 136
Shalini Shalini, LSU
Gowri Priya Sunkara, LSU
The Elvis Problem with Convex Bifunctions/The Minimal Time Function Under More General Assumptions
The Elvis problem models a time optimal control problem across two regions having a common interface Sigma, each with a constant convex velocity set. We generalized this framework by introducing convex bifunctions of the form F_i(r, v) which are convex, lower semicontinuous, and proper. The minimization problem is min [ F_0(r_0, y - x_0) + F_1(r_1, x_1 - y) ], over r_0 > 0, r_1 > 0 and y in Sigma. The bifunctions F_i are jointly convex in (r, v) and convex analysis is used to derive optimality conditions. Under general assumptions on the target set S and the system dynamics, we show that the minimal time function is a proximal solution to a pair of Hamilton–Jacobi inequalities. Uniqueness is established via two distinct types of boundary conditions. We also introduce a new propagation result, which characterizes proximal sub gradients of the minimal time function in terms of normal cones and a boundary inequality condition. Furthermore, we provide necessary and sufficient conditions for the Lipschitz continuity of the minimal time function near S. In particular, a Petrov-type modulus condition is shown to guarantee such continuity. Our results extend earlier results to a broader class of time dynamics, even within non-Euclidean settings.
Posted September 18, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 136
Matthew McCoy, Louisiana State University
Introduction to Ergodic Theory, Chebyshev Polynomial Expansions, and Schur Complements
This talk will serve as an introductory talk to Ken Beard's talk on 9/30: Momentum Space Algorithm for Electronic Structure of Double-Incommensurate Trilayer Graphene. We will introduce relevant concepts in spectral theory.
Event contact: Laura Kurtz
Posted September 18, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 136
Ken Beard, LSU
Momentum Space Algorithm for Electronic Structure of Double-Incommensurate Trilayer Graphene
Although recent experimental results seem to indicate the existence of flat bands for twisted trilayer graphene (TTG), at present there is no convergent algorithm for approximating the density of states (or other desirable observables). We attempt to address this by using kernel polynomial approximation with an ab initio momentum-space tight-binding model. The unique challenge in the case of TTG is the lack of a periodic moir\'{e} supercell. This is addressed by modifying the truncation to account for more complex Umklapp scattering.
Event contact: Laura Kurtz
Posted October 5, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 136
Bart Rozenweig, Ohio State University
Borel Summability in Quantum Theory
Borel summation is a canonical summation technique which associates to a divergent power series an analytic function, for which the power series is its asymptotic expansion. This talk gives an overview of asymptotic expansions and the fundamental results on Borel summability, before surveying two major applications of the theory: first, in building actual solutions out of divergent formal power series solutions of ODEs and PDEs; and second, in making sense of divergent Rayleigh-Schrödinger perturbation expansions in quantum mechanics. Along the way, we will touch upon some key aspects of “resurgence theory”, a paradigm for the application of Borel summation ideas in quantum field theory.
Posted October 10, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 136
Long Teng, LSU
Nodal Sets of Harmonic Functions
In this talk, we study the size of nodal sets of harmonic functions. We introduce the frequency function N(r), which quantifies the growth rate of a harmonic function and plays a crucial role in understanding its zero set. I will first define this frequency function and show its monotonicity property. Then, using this tool, we establish that the (n−1)-dimensional Hausdorff measure of the nodal set is bounded above by C(n)N, where C(n) depends only on the dimension. This result highlights how quantitative unique continuation connects analytic growth properties of harmonic functions to the geometric complexity of their nodal sets.
Event contact: Laura Kurtz
Posted October 19, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 136
Laura Kurtz, Louisiana State University
Stochastic Homogenization
In this talk, we develop tools of stochastic homogenization of elliptic operators. We focus mainly on the periodic case and discuss the implications of the stochastic case.
Event contact: Moises Gomez-Solis
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 October 29, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm Lockett 136
Christopher Bunting, LSU
Ergodicity of solutions to the stochastic Navier-Stokes equations
The stochastic Navier-Stokes equations has been extensively studied over the past few decades. In this talk, we consider the 2D stochastic Navier-Stokes equations perturbed by an additive noise. We begin by establishing results regarding solutions and provide essential estimates. Using these results, we prove the existence and uniqueness of invariant measure for the solutions of the equations.
Event contact: Laura Kurtz
Posted November 4, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 136
Phuc Nguyen, Department of Mathematics, Louisiana State University
Capacities, weighted norm inequalities, and nonlinear partial differential equations
I will present a survey of trace inequalities for fractional integrals, highlighting the role of capacities associated to Sobolev spaces and their connections to nonlinear potential theory and nonlinear partial differential equations
Event contact: Laura Kurtz
Posted November 13, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Room 136
Anan Saha, LSU
Learning of Stochastic Differential Equations with integral-drift
Stochastic differential equations (SDEs) with integral drift arise naturally in multiscale systems and in applications where effective dynamics are obtained by averaging over latent or unobserved processes. In such settings, the drift takes the form b̅(x) = ∫ b(x, y) π(dy), with π an unknown probability measure. Our primary goal is the nonparametric estimation of the averaged drift b̅ directly from observable data on X, thereby bypassing the need to recover the unidentifiable measure π, which is of secondary importance for understanding the dynamics of these types of SDE models. In this paper, we develop a nonparametric Bayesian framework for estimating b̅ based on L´evy process priors, which represent π via random discrete supports and weights. This induces a flexible prior on the drift function while preserving its structural relationship to b(x, y). Posterior inference is carried out using a reversible-jump Hamiltonian Monte Carlo (RJHMC) algorithm, which combines the efficiency of Hamiltonian dynamics with transdimensional moves needed to explore random support sizes. We evaluate the methodology on multiple SDE models, demonstrating accurate drift recovery, consistency with stationary distributions, and robustness under different data-generating mechanisms. The framework provides a principled and computationally feasible approach for estimating averaged dynamics in SDEs with integral drift.
Event contact: Laura Kurtz