Informal Analysis Seminar

Welcome

Welcome to the Informal Analysis Seminar! We are a seminar run by graduate students with an emphasis on providing a space for graduate students to give analysis talks. Everyone is encouraged to participate.

Next Week

Speaker: Long Teng

Title: Nodal Sets of Harmonic Functions

Abstract: 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.

Schedule – Fall 2025

Aug 26: Organizational Meeting
Sept 2: Hari Narayanan- Intro to Spectral Theory (Intro to Moises's Talk)
Sept 9: Moises Gomez-Solis- What Is Absolutely Continuous Spectrum and Transport?
Sept 16: Gowri Priya Sunkara- The Elvis Problem with Convex Bifunctions and Shalini Shalini- The Minimal Time Function Under More General Assumptions
Sept 23: Matthew McCoy- Introduction to Ergodic Theory, Chebyshev Polynomial Expansions, and Schur Complements (Introduction to Ken's Talk)
Sept 30: Ken Beard- Momentum Space Algorithm for Electronic Structure of Double-Incommensurate Trilayer Graphene
Oct 7: Bart Rosenzweig (Ohio State University)- Borel Summability in Quantum Theory
Oct 14: Long Teng- Nodal Sets of Harmonic Functions
Oct 21: Laura Kurtz- Stochastic Homogenization
Oct 28: Sanjeet Sahoo- Introduction to Stochastic PDEs: Ito's Formula (Introduction to Chris's Talk)
Nov 4: Christopher Bunting- Ergodicity of solutions to the Navier-Stokes equations
Nov 11: Phuc Cong Nguyen (LSU)- Capacities, Weighted Norm Inequalities, and non-linear partial differential equations
Nov 18: Anan Saha- Learning of Stochastic Differential Equations
Nov 25: Gustavs Tobiss- Bloch's Theorem and Wannier functions
Dec 2: Han Nguyen- Walker et al: Modelling and Simulation of the cholesteric Landau-de Gennes model

Contact Information

Organizers

Name: Moises Gomez-Solis
Email: mgome29@lsu.edu

Name: Laura Kurtz
Email: lkurtz2@lsu.edu

Faculty Sponsor

Name: Stephen Shipman
Email: shipman@math.lsu.edu