Nabla Seminar 2026 Fall
Grad Analysis Seminar at Rutgers University
Grad Analysis $\nabla$ Seminar is a graduate seminar at Rutgers University, Department of Mathematics, organized by Qi Ma, Aprameya, and Anupam.
This page is for seminars held in Fall 2026. We will meet every Monday from 4:00 to 5:00 p.m. in the Mathematics Graduate Lounge (Hill 701).
We are looking for speakers. Please let Qi Ma, Aprameya, or Anupam know if you would like to give a talk.
To see seminars in other semesters, please refer to Nabla.
2026 Nov.2nd , Speaker: Qiyuan Song
Title: Łojasiewicz–Simon inequality
Abstract: The Łojasiewicz–Simon inequality controls the energy difference near a critical point by its gradient. I will introduce the classical finite dimensional Łojasiewicz inequality, and then discuss how Leon Simon generalized it to the infinite dimensional case on closed Riemannian manifolds, using Liapunov-Schmidt Reduction. Simon's work has application to many problems in calculus of variations and nonlinear PDEs (which can be thought as limits of infinite dimensional gradient flows of analytic functionals).
2026 Oct.26th , Speaker: Adam
Title: The Tauberian Theorem for Laplace Transforms and a proof of the prime number theorem.
Abstract: Abelian theorems are theorems where information about sums or integrals of a function and used to gain information about transformations of the sum or integral. Tauberian theorems are results about the converses of those statements. Where these results excel is in showing integrability on functions that are otherwise poorly behaved. We will prove a Tauberian Theorem for Laplace Transforms. Time Permitting, we’ll also use this result to prove the prime number theorem.
2026 Oct.12th , Speaker: Dana Zilberberg
Title: Analytic Fredholm Theory and Transmission Eigenvalues
Abstract: In the first part, we will introduce Analytic Fredholm Theory, which states that operator-valued analytic functions can only have a discrete set of eigenvalues. We will then introduce the transmission eigenvalue problem in classical scattering theory and establish the discreteness of transmission eigenvalues. Time permitting, we will also discuss the existence of such eigenvalues and their fractional counterparts.
2026 Oct.5th , Speaker: Junyoung Park
Title: Bubbling of harmonic map heat flow from surface.
Abstract: In my last talk, we discussed the existence, uniqueness and asymptotic behavior of harmonic map heat flow when target was non positively curved. This time, we consider the next simple setup, where the domain is 2 dimensional. We first discuss Struwe’s longtime solution, and discuss its regularity. Then we show that near singular points, one can observe concentration of energy/formation of bubbles, at least along carefully chosen sequence of times.
2026 Sept.28th , Speaker: Owen Drummond
Title: Symmetric Rearrangement and the Pólya–Szegő Inequality, with an Application to Gravity Water Waves
Abstract: Rearrangement inequalities provide a powerful way to compare functions through the geometry of their level sets. In this talk, I will introduce symmetric decreasing rearrangement and its basic properties, including equimeasurability and preservation of \(L^p\) norms, and then discuss the Hardy–Littlewood and Pólya–Szegő inequalities. The latter shows that symmetric rearrangement does not increase the Dirichlet energy. I will conclude by explaining how a directional rearrangement can be used in a constrained variational problem arising in gravity water waves, where the symmetrization preserves the relevant geometric constraints while lowering the energy.
2026 Sept.21st , Speaker: Ryan McGowan
Title: Yau's Liouville Theorem and Evans-Krylov Estimates in the Kähler Setting
Abstract: In this talk, I will briefly introduce the complex Monge-Ampère equation and its relation to Kähler metrics and outline Yau's classical $C^2$ and $C^3$ estimates, which were fundamental in resolving the Calabi conjecture. I will then outline how these estimates allow one to prove a Liouville theorem for Kähler metrics. Time permitting, I will discuss how one can bypass the $C^3$ estimates yet still recover an Evans-Krylov $C^{2,\alpha}$ estimate. We shall see how much I actually get through lol.
2026 Sept.14th , Speaker: Samanthak Thiagarajan
Title: Potential Theory for Lipschitz Domains
Abstract: In this talk, we'll go over some of the basic theory of harmonic functions on Lipschitz domains following the book of Caffarelli-Salsa. Topics include the boundary Harnack inequality, growth estimates, and monotonicity properties.