Higher codimension area-minimizers: structure of singularities and uniqueness of tangent cones Abstract. The problem of determining the size and structure of the interior singular set of area-minimizing surfaces has been studied thoroughly in a number of different frameworks, with many … Read more
Homogenization of the Einstein equations under symmetry Abstract. Due to their nonlinear nature, the Einstein's equations are not closed under weak convergence. Compactness singulaties associated to highly oscillatory solutions may be identified with additional, non-trivial matter. In 1989, Burnett conjectured … Read more
On Liouville's theorem for conformal maps Abstract. A theorem of Liouville asserts that the simplest conformal transformations on Euclidean space---translations, dilations, reflections, and inversions---generate all conformal transformations when the dimension is at least 3. I will describe a new proof … Read more
Unbounded damped waves: backward uniqueness and polynomial stability Abstract. In this talk, we discuss the wave semigroup with an unbounded damping. In such a setting, there are explicit examples where the linear damped waves would go into finite-time extinction. We … Read more
Join us at the Tate-Turner-Kuralt Auditorium to experience five 15-minute presentations by the recipients of the Phillip and Ruth Hettleman Prizes for Scholarly Achievement. Among these presentations, one will be given by Yaiza Canzani, focusing on her research regarding … Read more
Some recent progress on integrable PDEs Abstract. Integrable PDEs arise as leading-order models in an astoundingly wide range of physical scenarios, such as fluid dynamics, ferromagnetism, and nonlinear optics. For rapidly decaying solutions, the inverse scattering method provides a powerful … Read more
Join us for an informal meet-up where you can delve into the exciting world of research and the pursuit of advanced degrees in mathematics. Our discussion panel features experienced professors and postdocs associated with the NSF RTG project titled “Partial … Read more
Transport of nonlinear oscillations along rays that graze a convex obstacle to any order Abstract. When a wave interacts with a convex obstacle, it creates reflected waves, as well as waves in the geometric shadow of the obstacle. This phenomenon … Read more
Long range wave dependencies and cosine sign correlations Abstract. We’ll introduce and discuss a very strange phenomenon which, approximately, says that quantum particles on nice manifolds can exhibit some very strange form of non-locality and can communicate across very large … Read more
A problem for a material surface attached to the boundary of an elastic semi-plane Abstract. A problem for a nano-sized material surface attached to the boundary of an elastic isotropic semi-plane is considered. A normal external traction is applied to … Read more
Incidences and projections: discrete and continuous Abstract. A number of difficult problems in geometric measure theory stem from discrete geometry results, such as Beck’s theorem about the number of lines spanned by a set of points in the plane, and … Read more
Eigenvalue Optimization and Minimal Surfaces Abstract. I will discuss a new method, developed in collaboration with M. Karpukhin, R. Kusner, and D. Stern, for constructing minimal surfaces embedded in the 3-sphere and the 3-ball, by equivariant eigenvalue optimization. A main … Read more
