∇ Seminar - Graduate Student Analysis Seminar @ Rutgers University

Fall 2026

∇ Seminar (read as “nabla seminar” or “Grad seminar”) is a student run Analysis and Geometry seminar at the Department of Mathematics, Rutgers University. The seminar features various expository and research talks from students meeting every Monday 4-5 PM at Graduate Student Lounge, Math Dept Hill 701, Rutgers University.

The Fall 2026 edition of the ∇ Seminar is being organized by Aprameya Girish Hebbar, Qi Ma and Anupam Nayak.

You may find the titles and abstracts for the past and upcoming talks below.

Those who wish to receive e-mails for latest information of the seminar may subscribe to our mail-list by sending “Subscribe” to grad_analysis-join@email.rutgers.edu or you can email Aprameya at ah1531[at]math[dot]rutgers[dot]edu.

Seminar Schedule

Date: Oct 5, 2026

Speaker:

Title:

Abstract:

Date: Sept 28, 2026

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.

Date: Sept 21, 2026

Speaker: Ryan Mc Gowan

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.

Date: Sept 14, 2026

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.