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
Posted November 30, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 136
Han Nguyen, LSU
Modelling and simulation of the cholesteric Landau-de Gennes model
This paper discusses modelling and numerical issues in the simulation of the Landau-de Gennes (LdG) model of nematic liquid crystals (LCs) with cholesteric effects. We propose a fully implicit, (weighted) L2 gradient flow for computing energy minimizers of the LdG model, and note a timestep restriction for the flow to be energy decreasing. Furthermore, we give a mesh size restriction, for finite-element discretizations, that is critical to avoid spurious numerical artifacts in discrete minimizers, particularly when simulating cholesteric LCs that exhibit ‘twist.’ Furthermore, we perform a computational exploration of the model and present several numerical simulations in three dimensions, on both slab geometries and spherical shells, with our finite-element method. The simulations are consistent with experiments, illustrate the richness of the cholesteric model, and demonstrate the importance of the mesh size restriction.
Posted December 29, 2025
Last modified January 9, 2026
Informal Analysis Seminar Questions or comments?
12:30 pm – 1:30 pm 233
Moisés Gómez-Solís, Louisiana State University
Laura Kurtz, Louisiana State University
Organizational Meeting
Posted January 9, 2026
Last modified January 21, 2026
Informal Analysis Seminar Questions or comments?
12:30 pm – 1:30 pm Lockett 233
Maganizo Kapita, Louisiana State University
Statistical Learning of Stochastic Reaction Networks from Event-Time Data
tbd
Posted January 22, 2026
Informal Analysis Seminar Questions or comments?
12:30 pm – 1:30 pm Lockett 233
Han Nguyen, LSU
Introduction to Finite Element Methods
This talk serves as an exposition of ongoing work in Finite Element Methods.
Posted January 22, 2026
Informal Analysis Seminar Questions or comments?
12:30 pm – 1:30 pm Lockett 233
Hari Narayanan, Louisiana State University
Crash Course on Schrödinger Operators (Part 1)
An expository talk in spectral theory.
Posted January 22, 2026
Informal Analysis Seminar Questions or comments?
12:30 pm – 1:30 pm Lockett 233
Matthew McCoy, Louisiana State University
Crash Course on Schrödinger Operators (Part 2)
An expository talk in spectral theory.
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.
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
Posted March 5, 2026
Last modified March 9, 2026
Informal Analysis Seminar Questions or comments?
1:30 pm – 2:30 pm Lockett 233
Long Teng, LSU
Doubling Inequalities for Schrodinger operators with power growth potentials
TBD
Posted March 9, 2026
Last modified March 20, 2026
Informal Analysis Seminar Questions or comments?
12:30 pm – 1:30 pm Lockett 233
Zhiwei Wang, Louisiana State University
Some recent progress on frequency methods to quantitative unique continuation
We study quantitative unique continuation for elliptic equations with lower order terms of H\"older regularity via a frequency function method. We establish quantitative three-ball inequalities and corresponding vanishing-order bounds. Our results are quantitative with explicit dependence of the three-ball constants and the vanishing-order exponents on the H\"older exponent, which has a unified framework matching sharp endpoint results.
Posted March 27, 2026
Last modified March 30, 2026
Informal Analysis Seminar Questions or comments?
12:30 pm – 1:30 pm Lockett 233
Jai Tushar, Louisiana State University
Polytopal finite element methods
Many problems in science and engineering are modelled by partial differential equations, but solutions are often impossible to compute analytically. One of the most successful tools to numerically approximate such solutions of such problems in one, two and three spatial dimensions are the Finite Element Methods (FEMs). FEM approximates the unknown solution over the domain by subdividing the domain into smaller, simpler pieces called finite element. Traditionally these pieces are simple shapes such as triangles/tetrahedra or quadrilaterals/hexahedra. But in many applications, it is useful to allow more general shapes. In this talk, I will give an informal introduction to the design and analysis of polytopal FEMs, where the computational mesh is made of general polytogonal/polyhedral elements.
Posted March 27, 2026
Last modified April 5, 2026
Informal Analysis Seminar Questions or comments?
12:30 pm – 1:30 pm Lockett 233
Yixing Miao, Louisiana State University
Spectra of Magnetic Schrodinger Operators on Hexagonal Graph
In this presentation, I will talk about my ongoing work on the spectral analysis of Hamiltonians defined on the hexagonal graph with delta-like interactions, which is a generalization of previous work by Becker, Han, and Jitomirskaya. The methodology is to reduce the study of spectra of Hamiltonians to that of quasi-periodic Jacobi operators. The main difficulty is due to the parameters of we introduced in the delta-like boundary conditions. It requires us to modify the proofs of several theorems related to the spectral analysis of quasi-periodic Jacobi operators, and results in various spectral types dependent on those parameters. Numerous tools from ODE, Fourier analysis, functional analysis, complex analysis, dynamical systems, etc... are involved.
Posted April 8, 2026
Last modified April 12, 2026
Informal Analysis Seminar Questions or comments?
12:30 pm – 1:30 pm Lockett 233
Arif Ali, Louisiana State University
Introduction to Girsanov's Theorem and Some Application
In this talk, we introduce Girsanov’s Theorem. This theorem is an important result in stochastic calculus that describes how probability measures can be changed to alter the drift of a Brownian motion. After briefly reviewing some concepts from stochastic analysis, we present the theorem and its proof. Then we show how Girsanov’s Theorem can be applied to remove drift from a stochastic process and simplify stochastic differential equations, illustrating its central role in the analysis of SDEs.
Posted April 8, 2026
Informal Analysis Seminar Questions or comments?
12:30 pm – 1:30 pm Lockett 233
Christopher Bunting, LSU
Tbd
Tbd
Posted April 8, 2026
Informal Analysis Seminar Questions or comments?
12:30 pm – 1:30 pm Lockett 233
Jackson Knox, Louisiana State University
Tbd
Tbd