Gauge Theory Ideas for Number Theory

ag.algebraic-geometry mp.mathematical-physics nt.number-theory
Start Date
2018-12-17 
End Date
2018-12-21 
Institution
International Centre for Theoretical Sciences 
City
Bengaluru 
Country
India 
Meeting Type
discussion meeting 
Homepage
https://www.icts.res.in/discussion-meeting/gtnt2018 
Contact Name
 

Description

This discussion meeting is aimed at promoting fruitful interactions between theoretical physicists and mathematicians in areas that could be of common interest. In the past few decades, the interaction between algebraic geometry and quantum field theory has contributed substantial insights to both areas. Now seems to be an opportune moment to extend the areas of cross-fertilisation to include arithmetic geometry, comprising the study of arithmetic schemes and their Diophantine geometry, the theory of Galois representations, and the arithmetic Langlands programme.

The ICTS discussion meeting will focus on some ideas that Minhyong Kim and others have been pursuing (see Link). There are analogies between the moduli spaces of arithmetic principal bundles and constructions in quantum field theory, in particular, Chern-Simons theory. The idea of the meeting is to have about a dozen number theorists and string theorists (and some other local participants) to explore this common ground. There will be informal lectures by Minhyong Kim as well as a few others explaining these as well as related ideas but the main purpose is to have time for discussions and throwing ideas around in an informal setting. It would also be an opportunity to learn concepts as well as approaches and interesting questions across the walls of these two distinct communities.

Problems?

If you notice a problem with this entry, please contact the curators by email.