Saturday 8th April
2.00pm Registration in Mathematics Institute Common Room
2.30-4.00 Welcome and problem session (chaired by Colin Rourke) Mathematics Institute Lecture Room 2
Sunday 9th April
11.00am Ramble to Kenilworth Castle followed by pub lunch at the Clarendon Arms
2.00pm onwards: Tour of castle (price is 3.50 or 2.60 for students) (A mini-bus will be available to ferry participants back to the University after lunch or the tour)
Monday 10th April
Registration in Mathematics Institute Room 30
Monday 10th - Saturday 15th inclusive
Talks in Mathematics Institute Lecture Room 2
Slot 1: 10.00am-11.00am, Slot 2: 11.30am-12.30pm,
Slot 3: 2.00pm-3.00pm, Slot 4: 3.30pm-4.30pm
Coffee available 9.45-11.15am and tea 3-4.15pm
No talks on Wednesday afternoon (outing).
Workshop finishes Saturday 12.30 (after the morning talks)
Tuesday 11th
6.30pm Workshop buffet : Mathematics Institute Common Room
Wednesday 12th
2.00pm Outing to Baddesly Clinton (National Trust country house)
TALKS
Monday 10th April
Slot 1: Jack Morava (John Hopkins) "Topological gravity in dimensions two and four"
Slot 2: Simon Donaldson (Imperial College London) "Lefschetz fibrations and Taubes' Theorem on the canonical class"
Slot 3: Reiko Miyaoka (Sophia University, Tokyo) "Stability and other topics on minimal surfaces"
Slot 4: Roger Bielawski (Edinburgh) "Cluster decomposition of monopole metrics".
Tuesday 11th April
Slot 1: Jaques Hurtubise (Montreal, Canada) "Calogero-Moser systems and Hitchin systems"
Slot 2: Nigel Ray (Manchester) "Toric actions in Topology"
Slot 3: Paul Sutcliffe (Kent) "Skyrmions Fullerenes and rational maps"
Slot 4: Sadok Kallel (Lille, France) "On the Topology of Families of Curves in Projective Space"
Wednesday 12th April
Slot 1: Jennifer Schultens (Emory and Bonn) title TBA
Slot 2: Shaun Martin (Stonybrook) "Hamiltonian symplectic manifolds and wall-crossing formulas"
Thursday 13th April
Slot 1: Alexei Kovalev "Twisted connected sums and special holonomy in dimension 7"
Slot 2: A.S. Dzhumadil'daev (Kazakstan and Oxford) "Cohomologies, identities and hidden deformations of right-symmetric algebras"
Slot 3: Colin Rourke (Warwick) "The desingularisation of smooth maps"
Slot 4: TBA
Friday 14th April
Slot 1: Vicente Munoz (Madrid) "Donaldson invariants and modular forms"
Slot 2: Tamas Hausel (UC Berkeley) "L^2 cohomology and Schwarzschild instantons"
Slot 3: Balazs Szendroi (Warwick) "Mirror symmetry and the Torelli problem"
Slot 4: TBA
Saturday 15th April
Slots 1 and 2 : Daryl Cooper (UC Santa Barbara) "The End of the Orbifold Theorem ?"
Selected abstracts
Daryl Cooper Title: The End of the Orbifold Theorem ?
We will discuss the completion of the proof of Thurston's Orbifold theorem. The case of finite orbifold group when there are vertices in the singular locus presents special difficulties analogous to the difficulties in studying 3-manifolds with finite fundamental group. Our proof in this case involves a detailed study of spherical Seifert fibered orbifolds. (Joint with Kerckhoff and Hodgson)
Homework problem: which Seifert fibered 3-manifolds admit more than one Seifert fibering ?
Jack Morava Title: Topological gravity in dimensions two and four
A (two-)category with manifolds as objects and cobordisms as maps [and diffeomorphisms as two-morphisms] becomes a very interesting topological category when its morphism categories are replaced by their classifying spaces: the result is a hybrid of Segal's category and Wheeler's superspace. The physicists' theories of topological gravity are just monoidal representations of such categories: Kontsevich-Witten theory is the `standard' example in two dimensions, but classical Abel-Jacobi theory also fits naturally in this framework. Floer-Donaldson theory yields a more complicated, and interesting, example.
A.S. Dzhumadil'daev (Almaty) Cohomologies, identities and hidden deformations of right-symmetric algebras.
Right-symmetric algebras are defined by identity $a\circ(b\circ c)-(a\circ b)\circ c=a\circ(c\circ b)-(a\circ c)\circ b.$ Example: Centerless Virasoro algebra under half commutator $a\partial \circ b\partial =b\partial(a)\partial$ is right-symmetric. Cohomology theory for right-symmetric algebras are developed. Hopf algebraic structure of universal eneveloping algebras of right-symmetric algebras are studied. Deformations of right-symmetric Witt algebra are decsribed. In particular, hidden deformations of Virasoro algebra are studied. Minimal polynomial identities for right-symmetric Witt algebras are found.
Colin Rourke The desingularisation of smooth maps
This is joint work with Brian Sanderson. We give short new proofs of results of Eliashberg, Gromov and Spring which allow a smooth map or projection to be desingularised (leaving only Morse-type singularities) by a smooth C^0-small isotopy. The new proofs are constructive and give information about the finishing map or embedding not obtainable from the original proofs.
