Modern Mathematics in Current Theoretical Physics Research
The lecture course is intended to provide a glimpse of mathematics used to describe monopoles (magnetic, t'Hooft-Polyakov) and instantons, as well the physical consequences of such constructions and the search for them.
The lecture is 15 hourse/semester (8 meetings 1 - 2 hrs each)
Topics:
- Basic notions of connections from differential geometry.
- Gauge theory as seen by mathematics.
- Example of nontrivial connection: magnetic monopole.
- Example of nontrivial configuration of fields: t'Hooft-Polyakov monopole.
- Chern classes of gauge connections.
- Instantons and their role.
- Physics behind all of these and the search for it.