Nonlinear Analysis Seminar
Nonlinear Analysis and PDEs
CUNY Graduate Center, 365 Fifth Avenue, NYC
Room 6417, 6:30pm--8:00pm
Goals of these seminars is to discuss techniques that are used nonlinear
problems arising in applied mathematics, physics or differential geometry.
It will also give the opportunity of learning some recent progress in these fields.
Those participating in the Nonlinear Analysis and PDE seminar may
also be interested in the
Geometric Analysis Seminar
which meets also on Thursdays in the same room 6417 starting at 4:15pm.
Spring 2026
March 19th (in person):
Samuel Magill (CUNY Graduate Center)
Variational Sub-super method in some PDE problems with singularities
Abstract:
The sub-super method to detect a solution to nonlinear problems has been reconsidered by Struwe in a variational context.
I will discuss how it can be refined, and discuss how it can be applied to find some solutions for a class of problems
that involve Dirac measures.
March 26th (in person):
Andras Balogh (College of Staten Island)
Global Solutions of the Higgs Boson Equation in de Sitter Spacetime
Abstract:
In this work, we investigate the Higgs Boson Equation in de Sitter Spacetime.
We prove the existence and uniqueness of global–in–time solutions for initial data of arbitrary size with compact support.
The proof uses Galerkin's method, based on a priori energy estimates.
High–performance computer simulations are presented to demonstrate the theoretical results
and to provide further conjectures about bubble formation and long–time behavior.
April 16th (in person):
Inigo Urtiaga Erneta (Rutgers Universoty)
TBA
Abstract:
TBA
April 23rd (in person):
Mohameden Ahmedou (University of Giesseni, Germany)
TBA
Abstract:
TBA
Fall 2025
November 13th (in person):
Yanyan Li (Rutgers University)
Symmetry of hypersurfaces and the Hopf Lemma
Abstract
November 20th
4:15--5:15pm: Ali Maaloui (Clark University)
Conformally Invariant Fractional Dirac Operator: Construction and Associated Sobolev Inequalities
Abstract:
In this talk I will discuss the construction of the fractional Dirac operator via scattering theory.
This provides a continuous family of pseudo-differential operators acting on spinors similar to the case
of the fractional conformal Laplacian.
Then I will introduce a Caffarelli-Silvestre type extension allowing an alternative definition of these operators
as a Dirichlet-to-Neumann type operators and also an associated Sobolev type inequality.
5:30--6:30pm: Philip Korman (University of Cincinnati)
Some special super-critical equations
Abstract:
For special super-critical equations it is possible to determine exactly all positive solutions on a ball in $R^n$, and give precise information on the entire solution curves. These equations can serve as prototypes for other similar equations. The special equations include Gelfand's equation, Lin-Ni equation, MEMS and $\Delta u+u^{\frac{n+2}{n-2}}=0$.
Spring 2025
February 27th (in person):
Jiahua Zou (Rutgers University)
Minimal hypersurfaces in S^{4}(1) by doubling the equatorial three-sphere S3
Abstract:
For each large enough integer m, we construct by PDE gluing
methods a closed embedded smooth minimal hypersurface M_m
by doubling the equatorial three-sphere S3 in
S^4(1).
This answers a long-standing question of Yau in the
case of S^4(1) and long-standing questions of Hsiang.
Similarly we
construct a self-shrinker of the Mean
Curvature Flow in R^4 by doubling the three-dimensional
spherical self-shrinker.
A brief survey on two-dimensional case will also be given. This talk is
based on joint work with Kapouleas.
March 20th (in person):
Hongyi Liu (Princeton University)
Compactness theorems for Einstein 4-manifolds with boundary
Abstract:
Einstein 4-manifolds have been widely studied in both the compact and complete non-compact settings, particularly when additional geometric structures are present. However, the case of Einstein manifolds with boundary remains less explored. In this talk, I will discuss compactness theorems for Einstein 4-manifolds with boundary, considering two distinct frameworks: when the boundary is at a finite distance and in the conformally compact setting.
April 24th (in person):
Zilu Ma(Rutgers University)
Examples of Bubble-Sheet Singularities in Ricci Flow
Abstract:
Two-cylinders or bubble-sheets are new singularities arising in 4D Ricci flow, and they are generally hard to study compared to three-cylinders. In this talk, we shall discuss some recent constructions of compact Ricci flows producing such a singularity model. More precisely, we show that starting from an open set of initial data with warped product geometries over a surface, the Ricci flow develops a unique bubble-sheet singularity. This is based on the join work with J. Isenberg, D. Knopf, and N.Sesum.
PAST SEMINARS