Non UBC
DSpace
Meneses, Claudio
2019-03-29T10:01:30Z
2018-07-04T10:31
Moduli spaces of stable vector bundles carry a natural KÃ¤hler structure, described originally in the Riemann surface case by Narasimhan and in the pioneering work of Atiyah-Bott. Such a KÃ¤hler structure is in many ways analogous to the Weil-Petersson metric on moduli spaces of Riemann surfaces, for which a deep relationship with the Liouville functional in Conformal Field Theory was established by Takhtajan and Zograf.
In this talk I will describe work in progress on how the ideas of Takhtajan-Zograf can be adapted to vector bundles in three different settings: moduli of stable parabolic bundles in genus 0 and 1, moduli of semistable bundles in genus 1, and Jacobians. In all cases the main tool is an adaptation of the WZNW action of Conformal Field Theory---defined by twisting the so-called chiral models with a topological term---to a functional on singular hermitian metrics on a suitable holomorphic gauge. I will also describe briefly how the previous results can be generalized to moduli spaces of parabolic Higgs bundles.
https://circle.library.ubc.ca/rest/handle/2429/69333?expand=metadata
49.0
video/mp4
Author affiliation: University of Kiel
Oaxaca (Mexico : State)
10.14288/1.0377651
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Postdoctoral
BIRS Workshop Lecture Videos (Oaxaca (Mexico : State))
Mathematics
Differential geometry
Global analysis, analysis on manifolds
WZNW actions, holomorphic gauges, and the KÃ¤hler structure of moduli spaces
Moving Image
http://hdl.handle.net/2429/69333