##### Department of Mathematics,

University of California San Diego

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### Advancement to Candidacy

## Yuchao Yi

#### UCSD (yuyi@ucsd.edu)

## Bounded inverse scattering problem for nonlinear Dirac equation

##### Abstract:

Inverse problem is the study of the recovery of parameters or the governing equations of a system based on given observational data. In this talk I will focus on the techniques used in inverse scattering problems for hyperbolic type equations. Scalar wave equation will be used as an example for showing how one can use higher order linearization and microlocal analysis to retrieve information about the unknown nonlinearity. I will also explain the main ideas used in proving that the bounded time scattering map uniquely determines the nonlinearity in the semilinear 4 by 4 Dirac system, with some mild assumptions.

Advisor: Ioan Bejenaru

### November 1, 2024

### 9:30 AM

APM 6402 & Zoom: https://ucsd.zoom.us/j/

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