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Tuesday, February 5, 2019 - 14:30 to 15:30
Seminar Hall
Dr. Varun Thakre
International Centre for Theoretical Sciences (ICTS-TIFR), Bengaluru (India)
Generalised Seiberg-Witten equations and de-generate metrics

Abstract: Gauge theories, which have their origin in physics, have had a profound effect on mathematics and nowhere is it more strikingly evident than in dimension four. Seiberg-Witten equations and Seiberg-Witten invariants have proven to be powerful instruments for the study of smooth structures on four-manifolds.

In my talk, I will introduce the equations and talk about a generalisation of the same. Almost all the well-known gauge theories on four-manifolds can be treated as special case of this generalisation. I will then discuss some of my latest results that show an interesting pattern, in which a class of such gauge theories on four-manifolds can be thought of as statements about de-generate metrics. I will then discuss some consequences of this observation and end the talk with some research directions I plan to pursue. 

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