Title: Maximal Subellipticity Abstract: The theory of elliptic PDE stands apart from many other areas of PDE because sharp results are known for very general linear and fully nonlinear elliptic PDE. […]
Title: On the isoperimetric profile of the hypercube Abstract: The isoperimetric problem in the hypercube is a strikingly simple topic which is not yet completely understood. We will review the known […]
Title: Mean curvature flow with multiplicity 2 convergence Abstract: Mean curvature flow (MCF) has been widely studied in recent decades, and higher multiplicity convergence is an important topic in the study […]
Title: Three theorems about asymptotic expansions of harmonic functions at the boundaryAbstract: Consider a harmonic function on a domain, vanishing along a part of its boundary, and a point on […]
Title: Boundary behavior of the Allen-Cahn equation and the construction of free boundary minimal hypersurfacesAbstract: In the late 70s, the work of Modica, Mortola, De Giorgi, and many others established […]
Title: Soap films, Plateau's laws, and the Allen-Cahn equation Abstract: Plateau's problem of minimizing area among surfaces with a common boundary is the basic model for soap films and leads to […]
Title: First eigenvalue estimates on asymptotically hyperbolic manifolds and their submanifolds. Abstract: I will report on joint work with Samuel Pérez-Ayala. We derive a sharp upper bound for the first […]
Title: Recovery of time-dependent coefficients in hyperbolic equations on Riemannian manifolds from partial data.Abstract: In this talk we discuss inverse problems of determining time-dependent coefficients appearing in the wave equation […]
Title: A family of Kahler flying wing steady Ricci solitonsAbstract: Steady Kahler-Ricci solitons are eternal solutions of the Kahler-Ricci flow. I will present new examples of such solitons with strictly […]
Title: Strichartz estimates for the Schrödinger equation on the sphere. Abstract: We will discuss Strichartz estimates for solutions of the Schrödinger equation on the standard round sphere, which is related to […]
Title: The geometry and topology of lower bounds on scalar curvatureAbstract: In this talk, I will discuss some recent results about controlling the geometry and topology of manifolds from a […]
Title: On isolated singularities and generic regularity of min-max CMC hypersurfacesAbstract: Smooth constant mean curvature (CMC) hypersurfaces serve as effective tools to study the geometry and topology of Riemannian manifolds. […]