Chao Li, NYU, Stable minimal hypersurfaces in R^4.
ZoomIn this talk, I will discuss the Bernstein problem for minimal surfaces, and the recent solution to the stable Bernstein problem for minimal hypersurfaces in R^4. Precisely, we show that…
In this talk, I will discuss the Bernstein problem for minimal surfaces, and the recent solution to the stable Bernstein problem for minimal hypersurfaces in R^4. Precisely, we show that…
We show that the moduli space of all smooth fibrations of a 3-sphere by oriented simple closed curves has the homotopy type of a disjoint union of a pair of…
Broadly speaking, there are two classes of inverse problems — those that are concerned with the analysis of PDEs, and those that are geometric in nature. In this talk, I…
In an inverse boundary problem, one seeks to determine the coefficients of a PDE inside a domain, describing internal properties, from the knowledge of boundary values of solutions of the…
In this talk I will introduce a geometric inverse problem that is motivated by geophysical imaging and seismology. Specifically, I will reconstruct a compact Riemannian manifold with strictly convex boundary…
Waists and widths measure the size of a manifold with respect to measures of families of submanifolds. We’ll discuss related area estimates for minimal submanifolds, as well as applications to…
The Laplacian is a canonical second order elliptic operator defined on any Riemannian manifold. The study of optimal upper bounds for its eigenvalues is a classical problem of spectral geometry…
As described in the previous week's talk by Mikhail Karpukhin, there is a rich interplay between isoperimetric problems for Laplace eigenvalues on surfaces and the study of harmonic maps and minimal…
Numerical simulations on infinite domains are challenging. In this talk, we will take geometric approaches to analyze the problems and provide new solutions. One problem we tackle is the perfectly…
In this talk we provide new Myers–Steenrod theorem based proofs to confirm that: travel time data, travel time difference data and the broken scattering relations determine a simple Riemannian metric…
Neutrinos are very weakly interacting particles that have unique properties that allow indirect measurements that cannot be realized with any other particle or field. I will give an introduction to…
Shape-shifting materials from 2D thin sheets to 3D shapes are attractive for broad applications in programmable machines and robots, functional biomedical devices, and four-dimensional printing. Kirigami, the art of paper cutting, has recently…
In this talk, we will discuss bordered aspects of the Heegaard Floer surgery formulas of Ozsvath--Szabo and Ozsvath--Manolescu. In particular, we will explain how their theories naturally define bordered invariants…
I will talk about the new construction of genus-zero free boundary minimal surfaces embedded in the unit ball in the Euclidean three-space which are compact and lie arbitrarily close to…
I will discuss the travel time tomography problem for elastic media in the transversely isotropic setting. The mathematical study of this problem relates to X-ray tomography and boundary rigidity problems…
We introduce a method of solving inverse boundary value problems for wave equations on Lorentzian manifolds, and show that zeroth order coefficients can be recovered under certain curvature bounds. The…
A free boundary minimal surface (FBMS) in a given three-dimensional Riemannian manifold is a critical point of the area functional with respect to variations that constrain its boundary to the…
Let Σ be a closed surface (i.e. a 2-dimensional Riemannian manifold) satisfying the following condition: the first eigenvalue of the elliptic operator -Δ+βK is nonnegative, where K is the Gauss…
In this talk I will show that the Morse index of the critical Moebius band in the 4-dimensional Euclidean ball equals 5. This result makes use of the quartic Hopf differential technique and a…
In this talk, we will survey G2-structures, which are cross product structures on 7-manifolds, and we will discuss recent developments on a natural geometric flow of G2-structures called Laplacian flow.…