Paul Feehan (Rutgers University). Morse theory on moduli spaces of pairs and the Bogomolov-Miyaoka-Yau inequality. Friday 3rd May, 1:30-2:30pm. Huxley 140 (NOTE this is a different room to last term).

Abstract: We describe an approach to Bialynicki-Birula theory for holomorphic C^∗ actions on complex analytic spaces and Morse-Bott theory for Hamiltonian functions for the induced circle actions. A key principle is that positivity of a suitably defined “virtual Morse-Bott index” at a critical point of the Hamiltonian function implies that the critical point cannot be a local minimum even when it is a singular point in the moduli space. Inspired by Hitchin’s 1987 study of the moduli space of Higgs monopoles over Riemann surfaces, we apply our method in the context of the moduli space of non-Abelian monopoles or, equivalently, stable holomorphic pairs over a closed, complex, Kaehler surface. We use the Hirzebruch-Riemann-Roch Theorem to compute virtual Morse-Bott indices of all critical strata (Seiberg-Witten moduli subspaces) and show that these indices are positive in a setting motivated by a conjecture that all closed, smooth four-manifolds of Seiberg-Witten simple type (including symplectic four-manifolds) obey the Bogomolov-Miyaoka-Yau inequality..

Paul Norbury (University of Melbourne). tbc. Friday 10th May, 1:30-2:30pm. Huxley 140.

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tbc (tbc). tbc. Friday 17th May, 1:30-2:30pm. Huxley 140.

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Abigail Ward (University of Cambridge). tbc. Friday 24th May, 1:30-2:30pm. Huxley 140.

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tbc (tbc). tbc. Friday 31st May, 1:30-2:30pm. Huxley 140.

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Iacopo Brivio (Harvard University). tbc. Friday 7th June, 1:30-2:30pm. Huxley 140.

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Yuji Odaka (Kyoto University). tbc. Friday 14th June, 1:30-2:30pm. Huxley 341 (NOTE this is not the usual room).

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Ana Caraiani (Imperial College London). tbc. Friday 21st June, 1:30-2:30pm. Huxley 140.

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tbc (tbc). tbc. Friday 28th June, 1:30-2:30pm. Huxley 140.

Abstract: tbc.