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INDIAN INSTITUTE OF SCIENCE EDUCATION AND RESEARCH (IISER) PUNE
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Seminars and Colloquia

Mathematics

Generalised Seiberg-Witten equations and de-generate metrics 
 
Thu, Aug 23, 2018,   03:00 PM to 04:00 PM at Madhava Hall

Dr. Varun Dilip Thakare
International Centre for Theoretical Sciences, Bengaluru

In this talk, I will discuss the Taubes-Pidstrygach generalisation of the Seiberg-Witten (SW) equations. In this generalisation, the spinor representation is replaced by a hyperKahler manifold admitting certain symmetries. Many well-known gauge theories like the Vafa-Witten equations, 5-instanton equations, the non-Abelian monopole equations etc. are special cases of this generalisation. I will show that for a family of hyperKahler manifolds, the solutions to the gen. SW can be interpreted in terms of almost-Hermitian metrics satisfying a second order PDE. Using this, I will talk about a Hitchin-Kobayashi-type correspondence for the equations on a Kahler surface. The novelty in this construction lies in the fact that the correspondence narrows down to studying the celebrated Kazdan-Warner equations. I will try to keep the talk elementary in nature, making it accessible to a wider audience.
 

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