Nabla Seminar 2026 Spring

Grad Analysis Seminar at Rutgers University

Grad Analysis $\nabla$ Seminar is a graduate seminar at Rutgers University, Department of Mathematics, Orgnised by Qi Ma, Aprameya and Anupam since Nov. 2024.

This page is for seminars held in 2026 Spring. This semester we meet regularly on Monday at 4:00 p.m. in the Mathematics Graduate Lounge (Hill 701). We are looking for speakers. Please let me, Aprameya or Anupam know if you want to give a talk.

To see seminars in other semesters, please refer to Nabla.

2026 Feb.23rd , Speaker: Aprameya Girish Hebbar

Title: Metric Flows: Heat Kernels, F-convergence and Compactness

Abstract: In his landmark 2020 work, R. Bamler introduced metric flows which are weak synthetic analogues of smooth flows. Roughly, a metric flow consists of time-slices of metric spaces equipped with heat kernel type measures, providing a "parabolic analogue of a metric space". I will explain how the axioms of metric flows arise naturally from smooth Ricci flow, the convergence notion (“F-convergence”), and if time permits, how this yields a compactness theory for sequences of (super) Ricci flows.

2026 Feb.16th , Speaker: Qi Ma

Title: About Liouville’s Theorem – From harmonic function to nonlinear PDEs

Abstract: Liouville’s Theorem plays a fundamental role in the uniqueness of solutions. In this talk, we will start from the most trivial case – harmonic function. Classical proof, proof by energy estimation and proof by Fourier transform will be presented. Finally, we will generalize our result to nonlinear equations and introduce the some results of removable singularities in Navier-Stokes.

2026 Feb.9th , Speaker: Sammy Thiagarajan

Title: Schauder Estimates three different ways.

Abstract: Schauder estimates are classical estimates for second order, uniformly elliptic PDEs. Naturally, there are lots of ways to prove them! We will discuss three interesting ways in this talk.

2026 Feb.2nd , Speaker: Junyoung Park

Title: On Eells and Sampson theorem

Abstract: The idea of using heat type equations to solve problems in geometry has been proven to be an extremely powerful method. In this talk, we will discuss one of the earliest success of such approach, which is the use of harmonic map heat flow to find minimizing harmonic maps in a given homotopy class, under a geometric constraint on the target manifold.