PhD Oral Exam - Jordi Pillet, Mathematics and Statistics

When studying for a doctoral degree (PhD), candidates submit a thesis that provides a critical review of the current state of knowledge of the thesis subject as well as the student’s own contributions to the subject. The distinguishing criterion of doctoral graduate research is a significant and original contribution to knowledge.

Once accepted, the candidate presents the thesis orally. This oral exam is open to the public.

Abstract

The results presented in this thesis contribute to the understanding of the interplay between the geometry of Riemann surfaces and their moduli space and the theory of integrable systems. First, in Chapter 2, we present a new degeneration of Fay's trisecant identity leading to algebro-geometric solutions of the Schwarzian Kadomtsev-Petviashvili equation in terms of Riemann theta functions. Then, in Chapter 3, we introduce a new set of log-canonical coordinates on the SL(2,C) character variety of compact Riemann surfaces; these coordinates are constructed by combining shear type coordinates with length-twist type coordinates.