Gauge theory and the Bogomolov-Miyaoka-Yau inequality for symplectic 4-manifolds
Paul Feehan, Rutgers University
Abstract: The Bogomolov-Miyaoka-Yau inequality for minimal compact complex surfaces of general type was proved in 1977 independently by Miyaoka, using methods of algebraic geometry, and by Yau, as an outgrowth of his proof of the Calabi conjectures. In this talk, we shall describe our program to prove the conjecture that symplectic 4-manifolds with b+>1 obey the Bogomolov-Miyaoka-Yau inequality. Our method uses Morse theory on the gauge theoretic moduli space of non-Abelian monopoles. The method aims to use the fact that there is at least one non-vanishing Seiberg-Witten invariant to produce a solution to the anti-self-dual Yang-Mills equation on a vector bundle with suitable topology over the symplectic 4-manifold. The talk is based on joint work with Tom Leness and the monographs https://arxiv.org/abs/2010.15789 (to appear in AMS Memoirs) and https://arxiv.org/abs/2206.14710.
Tea and refreshments available from 3:00-3:25 p.m. in the Assmus Conference Room (CU 212).
