Marcello LUCIA

September 15 (in person):
Prosenjit Roy (Indian Institute of Technology - Kanpur)
Asymptotic Analysis of Eigenvalues Problems on Long Cylindrical Domains
Abstract: The primary aim of this talk is to study the asymptotic behaviour of eigenvalue problems, with Neumann boundary conditions on the sides and Dirichlet boundary conditions on the lateral part of the cylindrical domain, as the length of the cylinder goes to infinity. Before discussing this problem, I will first discuss the case of Dirichlet boundary conditions and present a survey of what is known for such type of problems. This talk is based on a joint work with M. Chipot and I. Shafrir.

October 6:
Learning Seminar
The sub-supersolution method

October 27 (Zoom Meeting):
Learning Seminar
Existence of solutions for a Chern-Simons model in Gauge field Theory

November 3 at 4:15pm (in person): JOINT SEMINAR with Geometric Analysis Seminar
Jian Song (Rutgers University)
Diameter estimates in Kähler geometry
Abstract: We establish diameter estimates for Kähler metrics, requiring only an entropy bound and no lower bound on the Ricci curvature. As a consequence, diameter bounds are obtained for long-time solutions of the Kähler-Ricci flow and finite-time solutions when the limiting class is big, as well as for special fibrations of Calabi-Yau manifolds.

November 10 at 4:15pm (Zoom Meeting): JOINT SEMINAR with Geometric Analysis Seminar
Stefano Nardulli (Universidad Federal do ABC)
Lusternik-Schnirelman and Morse Theory for the Van der Waals-Cahn-Hilliard equation with volume constraint
Abstract: We give a multiplicity result for solutions of the Van der Waals-Cahn-Hilliard two phase transition equation with volume constraints on a closed Riemannian manifold. Our proof employs some results from the classical Lusternik–Schnirelman and Morse theory, together with a technique, the so-called photography method, which allows us to obtain lower bounds on the number of solutions in terms of topological invariants of the underlying manifold. The setup for the photography method employs recent results from Riemannian isoperimetry for small volumes. This is a joint work with Vieri Benci, Luis Eduardo Osorio Acevedo, Paolo Piccione.

November 17 and 24: No Meeting

December 1 (in person):
Guido De Philippis (Courant Institute)
Non-degenerate minimal surfaces as energy concentration sets: a variational approach
Abstract: I will show that every non-degenerate minimal sub-manifold of codimension 2 can be obtained as the energy concentration set of a family of critical points of the (rescaled) Ginzburg Landau functional. The proof is purely variational, and follows the strategy laid by Jerrard and Sternberg in 2009. The same proof applies also to Yang-Mills-Higgs and Allen-Cahn-Hillard energies. This is a joint work with Alessandro Pigati.