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 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.



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