Student Analysis

Following lecture notes by Michael Struwe, we will continue our exploration of 2+1-dimensional wave maps with symmetries. We will see that a co-rotational wave map into a surface of revolution which blows up necessarily does so in a self-similar way, with the profile given by a non-constant co-…

Following lecture notes by Michael Struwe, we will continue our exploration of 2+1-dimensional wave maps with symmetries. We will see that a co-rotational wave map into a surface of revolution which blows up necessarily does so in a self-similar way, with the profile given by a non-constant co-…

The theme for Student Analysis in the second half of fall quarter is geometric wave equations and wave maps. This will be the second talk on this theme.

This will be the first talk in our series on geometric wave equations, the theme for Student Analysis in the second half of fall quarter.

This will be the fourth Student Analysis talk on kinetic theory, the seminar theme for the first half of Autumn 2024. Detailed abstract to come.

We'll start covering monotonicity of Fisher information for the space homogeneous Boltzmann equation, from the September 2024 paper by Imbert, Silvestre and Villani.

We will prove the global existence and uniqueness of solutions to the Cauchy problem for the Boltzmann equation of a hard sphere, assuming small data. We will also show that such solutions, assuming nonnegative initial data, remain nonnegative, which is what we expect, as a solution represents a…

Derivation of the Boltzmann equation, introduction of the collision operator, the hard sphere case, conservation laws and entropy.

I'll discuss some recent work of Michael Christ which establishes smoothing for the integral of a four-fold product. In particular, I will outline some key ideas involving a reduction to the trilinear case using spicy​ Cauchy-Schwarz, a study of sublevel set estimates for a…

Unlike for pseudodifferential operators, showing even just L²-boundedness for a general Fourier Integral Operators is nontrivial. This is especially true if the corresponding canonical relation cannot be written as a graph over the cotangent bundle of the source manifold. We will have a look at…