Professor Gukov obtained his PhD in 2001 from Princeton University under the supervision of Edward Witten. He then was a Long-term Prize Fellow of Clay Mathematics Institute at Harvard University and then a member at the School of Mathematics at the Institute of Advanced Study in Princeton. Since 2007 he has been a professor of theoretical physics and mathematics at California Institute of Technology. From 2010 he has been also an external scientific member at Max Planck Institute for Mathematics in Bonn. Professor Gukov has made numerous significant contributions in string theory, quantum field theory and low dimensional topology.


Abstract. Quantum physics, topology, and representation theory have a long history of working together. Therefore, it is no surprise that symmetries and their representations play an important role in describing physical phenomena and often label powerful invariants of 3-manifolds and 4-manifolds. More surprising, though, are algebraic structures labeled by topological manifolds or emergence of symmetries in quantum systems where they are not initially expected. Although instances of such 'hidden' algebraic structures are still rare and quite mysterious, they sometimes can be understood or even predicted in the framework of string theory. In this talk, intended for a broad audience, I will survey some of the recent and more intriguing examples of such relations between algebra, topology, and physics.



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