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) 


  • 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.

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