The 2024 UNC PDE Mini-school will feature a series of lectures by Gigliola Staffilani from MIT. We will have additional complementary "satellite" talks by Gonzalo Cao-Labora (MIT), Felipe Hernandez (MIT), and Xueying Yu (Oregon State University). Analysis and PDE Mini-School Website … Read more
Gravity water waves with constant vorticity at low regularity and balanced energy estimates Abstract. In this talk I will talk about the Cauchy problem of two-dimensional gravity water waves with constant vorticity. The water waves system is a nonlinear dispersive … Read more
Resonances and transmission for waves in truncated media Abstract. In a lot of toy models in quantum mechanics, you can construct “states” that live only at certain ”energies” by trapping things into specific regions, say using an infinite square well … Read more
Interior Hessian estimates for singularities of the Lagrangian mean curvature flow Abstract. In this talk, we discuss the history of the Lagrangian Mean Curvature equation beginning with the special Lagrangian equation of Harvey and Lawson. We consider the hypercritical case … Read more
A geometric flow towards Hamiltonian stationary submanifolds Abstract. In joint work with Jingyi Chen, we introduce a geometric flow for Lagrangian submanifolds in a Kähler manifold which stays in its initial Hamiltonian isotopy class and is a gradient flow for … Read more
