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Complex and Symplectic Geometry

Monday 3rd November 2014

This is a half-day event sponsored by the London Mathematical Society to celebrate the appointment of an Assistant Professor at University of Warwick (Weiyi Zhang). There will be three talks focused on Complex geometry and Symplectic Topology. The event will be followed by a reception and dinner. If you are interested in attending this event, please REGISTER. Funds are available to UK academics for housing and travel. For further information, please contact Weiyi Zhang (weiyi dot zhang at warwick dot ac dot uk).

Organiser: Weiyi Zhang

Speakers: Nigel Hitchin (Oxford), Ivan Smith (Cambridge), Weiyi Zhang (Warwick)

Other participants:

Roberta Albuqueque, Johar Ashfaque (Liverpool), Aurelio Carlucci, Georgios Dimitroglou Rizell (Cambridge), Karim El Haloui, Jacqui Espina (UCL), Enrico Fatighenti, Diane Maclagan, David Mond, Dmitri Panov (King's), John Rawnsley, Miles Reid, Dmitriy Rumynin, Raul Sanchez Galan (UCL), Oldrich Spacil (UCL), Damiano Testa, Dmitry Tonkonog (Cambridge), Ben Wormleighton

Room B3.02, Mathematics Institute


Monday 3rd November

14:00-15:00 Nigel Hitchin (Oxford) Folded hyperkähler manifolds

15:30-16:30 Ivan Smith (Cambridge) The symplectic arc algebra

17:00-18:00 Weiyi Zhang (Warwick) J-holomorphic curves in a nef class

18:15 Dinner with wine in Mathematics Institute Common Room


Nigel Hitchin: Folded hyperkähler manifolds

The lecture will introduce folding -- a type of degeneration of symplectic forms -- in the context of hyperkähler 4-manifolds. A number of examples, in particular one generated by a hyperbolic structure on a surface, motivate this study, together with a conjecture about an infinite-dimensional Teichmuller space parametrizing geodesic structures on surfaces. A natural local boundary value problem associated to this data will be given using twistor techniques.

Ivan Smith: The symplectic arc algebra

We will consider the symplectic topology of a certain higher-dimensional cousin Y of the Milnor fibre of a Kleinian surface singularity, which arises as a Springer fibre in Lie theory and in the construction of certain symplectic link invariants. The main result is a formality theorem for certain Floer cohomology algebras in Y. This describes joint work with Mohammed Abouzaid.

Weiyi Zhang: J-holomorphic curves in a nef class

After explaining complexity of arbitrary reducible subvariety when the ambient manifold is of dimension 4, we offer an upper bound of the total genus of a J-holomorphic subvariety when the class of the subvariety is J-nef. For a spherical class, it has particularly strong consequences. It is shown that, for any tamed J, each irreducible component is a smooth rational curve. We completely classify configurations of maximal dimension. Some recent applications will be discussed. Part of the work is done jointly with Tian-Jun Li.

Aerial photograph of Maths Houses

See also:
Mathematics Research Centre
Mathematical Interdisciplinary Research at Warwick (MIR@W)
Past Events 
Past Symposia 

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Mathematics Research Centre
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University of Warwick
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