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

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