Geometric Quantisation, the Hitchin-witten Connection and Quantum Operators in Complex Chern-simons Theory

PhD defence, Monday 12 March 2018, Alessandro Malusà.

2018.03.12 | Trine Berndt Turtiainen Scheelke

Alessandro Malusà

One of the most ambitious goals of present-day mathematical physics is that of understanding some of the formal techniques employed in quantum field theories from a purely mathematical viewpoint. As a first step in this direction, it is interesting to study those particular instances of such theories which can be defined and handled mathematically, of which Chern-Simons theory is a good example. During the past three decades, this theory has been studied thoroughly for the compact structure group SU(n), being approached and solved in several different ways. During his PhD studies, Alessandro Malusà considered the problem of extending known results for the theory with group SU(n) to its complexification SL(n,C). The approach of geometric quantisation produces a family of quantum Hilbert spaces for this theory, which are tied together by the so-called Hitchin-Witten connection. Alessandro Malusà studied some asymptotic properties of this object in the semi-classical limit, especially in the case of a surface of genus 1. Furthermore, he studied certain quantum operators arising in this case and formulated, together with his supervisor Jørgen Ellegaard Andersen, a complex version of the AJ conjecture relating two invariants for knots.

The PhD degree was completed at the Centre for Quantum Geometry of Moduli Spaces (QGM), Department of Mathematics, Science and Technology, Aarhus University.

This summery was prepared by the PhD student.

Time: Monday, 12 March 2018
, 15:00
Place: Aud D1 (1531-113)
Title of PhD thesis: Geometric quantisation, the Hitchin-Witten connection and quantum operators in complex Chern-Simons theory

Contact information: Alessandro Malusà, e-mail:
Members of the assessment committee:
Professor Martin Schlichenmaier, Mathematics Research Unit, University of Luxembourg
Professor Nicolai Reshetikhin, Department of Mathematics, University of California Berkeley
Professor Marcel Bökstedt (chair), Department of Mathematics, Aarhus University

Main supervisor:
Professor Jørgen Ellegaard Andersen, Department of Mathematics, Aarhus University

 The PhD thesis will be defended in English

The defence is public.
The dissertation is available for reading at the Graduate School of Science and Technology/GSST,
Ny Munkegade 120, building 1520, rooms 128-134, 8000 Aarhus C.

PhD defence
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Revised 23.03.2018