Past Seminars: Spring 2023


February 16 (in person):
Eris Runa (Gran Sasso Science Institute, L’Aquila)
Energy driven pattern formation for local/non-local systems
Abstract: In this talk we will consider a class of local/nonlocal interaction functionals motivated by the physics literature. The functionals contain a local term which penalizes interfaces, and a non-local term which favors oscillations. The equilibrium between these two terms is expected to result in the emergence of pattern formation. We will show that minimizers are periodic stripes and in particular that the functional exhibits the phenomenon of symmetry breaking.
February 23 (in person):
Daniele Alessandrini (Columbia University)
Equivariant minimal surfaces in the hyperbolic 3-space
Abstract: I will describe two interesting and closely related moduli spaces: the moduli space of equivariant (possibly branched) minimal surfaces in the hyperbolic 3-space, and the nilpotent cone in the moduli spaces of Higgs bundles for SL_2(C) and PSL_2(C). A deep understanding of these objects is important because of their relations with several fundamental constructions in geometry: branched hyperbolic structures, minimal surfaces in hyperbolic 3-manifolds, singular fibers of the Hitchin fibration, branes, mirror symmetry, and so on.
The moduli space of equivariant minimal surfaces has a natural stratification, given by the degree of branching, and every strata can be parametrized. This work focuses on understanding the closures of the strata, and how these closures interect the other strata. This is necessary to describe the global topology of the moduli space, and, at the same time, to understand how the minimal surfaces can degenerate when the curvature blows up near some points.
This is joint work with Qiongling Li and Andrew Sanders.
March 9 (in person):
Mehdi Lejmi (Bronx Community College)
Special metrics in almost-Hermitian geometry
Abstract: In this talk, we discuss the existence of some canonical metrics on compact almost-Hermitian manifolds. For example, we study an analogue of the Yamabe problem in Hermitian geometry. We also discuss Einstein-like metrics in Hermitian geometry.
April 3-4 (in person):
Two-Day Conference
Tuesday April 4th, 4:15pm (Meeting in Science Center Room 4102 !!): SPECIAL SEMINAR
Pierpaolo Esposito (University of Rome 3)
Green function for quasilinear operators
Abstract: We give some recent result about the property of the Green function for quaslinear operators. Application to the p-Laplacian version of the Brezis-Nirenberg problem will be provided.
April 20 at 4:15pm (in person): JOINT SEMINAR with Geometric Analysis Seminar
Baris Coskunuzer (The University of Texas at Dallas)
Minimal Surfaces in Hyperbolic 3-manifolds
Abstract: In this talk, we will show the existence of smoothly embedded closed minimal surfaces in infinite volume hyperbolic 3-manifolds. The talk will be non-technical, and accessible to graduate students.
May 4 at 4:15pm (in person):
Saïma Khenissy (University of Manouba, Tunisia)
Nonexistence results for biharmonic problems with supercritical growth on h-starlike domains
Abstract