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On the ADHM Seiberg–Witten equations

Presented by: 
Thomas Walpuski Massachusetts Institute of Technology
Friday 18th August 2017 - 14:30 to 15:30
INI Seminar Room 1
Co-authors: Andriy Haydys (Albert-Ludwigs-Universität Freiburg), Aleksander Doan (Stony Brook University)

The ADHM Seiberg–Witten equations are a class of generalized Seiberg–Witten equations associated with the hyperkähler quotient appearing in the Atiyah, Drinfeld, Hitchin, and Manin's construction of the framed moduli space of ASD instantons on R4.  Heuristically, degenerations of solutions to the ADHM Seiberg–Wiitten equation are linked with Fueter sections of bundles of ASD instantons moduli spaces (through the Haydys correspondence).  In joint work with Andriy Haydys, we studied when and how this heuristic can be made rigorous (following work of Taubes on flat PSL(2,C)–connections.)  This work immediately leads to a number of questions.  In particular, whether a given Fueter section can be realized as a limit and whether singular Fueter sections might appear. In joint work with Aleksander Doan (partially in progress), we answer the first question and the second (assuming a conjectural improvement of the work with Haydys).  Time permitting, I will briefly discuss which role we expect the ADHM Seiberg–Witten equation to play in gauge theory on G2–manifolds.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons