PhD Oral Exam - Ramtin Sasani, Mathematics

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

In this thesis, we will study the symplectic aspects of classical Gaudin systems, an important type of integrable dynamical systems at both classical and quantum levels. After a review of integrability and the Lax representation of integrable dynamical systems, we will investigate the analytical properties of Gaudin model via its spectral curve. The main focus is to reconstruct the Lax matrix using the analytical information of the system and subsequently, provide a symplectic structure for the phase space. We will also calculate the symplectic potential in terms of action-angle coordinates using Szegö kernel variational method. A brief look into the spectral transform aspect as well as the study of variational properties of vector of Riemann constants will also follow.