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Vector bundles on albebraic curves and generalized theta functions

Objective



This research project concerns the study of generalised theta functions on moduli spaces of vector bundles on algebraic curves. Recently, surprising links between certain conformal field theories and moduli spaces could be established, which produced unexpected formulas (Verlinde formula) and new conjectures concerning moduli spaces. This project is a continuation of my PhD thesis, where I extend the work of Beauville and Laszlo to parabolic bundles. Its objective is to study in terms of algebraic geometry the new ideas coming from mathematical physics and in particular from some rational conformal field theories (e.g. multiplication of generalised theta functions, strange duality). In classical algebraic geometry, it seems natural to start with Brill-Noether problems for parabolic bundles, to continue studying reduction problems to Abelian theta functions and their relationship with the classical Schottky-Jung-Prym geometry of the curve.

Funding Scheme

RGI - Research grants (individual fellowships)

Coordinator

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE
Address
Wilberforce Road
CB3 0WB Cambridge
United Kingdom

Participants (1)

Not available
Luxembourg