Autumn Term 2016

János Kollár (Princeton University). Existence of Conic bundles that are not birational to numerical Calabi–Yau pairs. Friday 23rd Sep., 1:30-2:30pm. Huxley 503.

Abstract: Let X be a general conic bundle over the projective plane with branch curve of degree at least 19. We prove that there is no normal projective variety Y that is birational to X and such that some multiple of its anticanonical divisor is effective. We also give such examples for 2-dimensional conic bundles defined over a number field.

Jacob Rasmussen (Cambridge University). L-spaces, Left-orderings, and Lagrangians. Friday 14th Oct., 1:30-2:30pm. Huxley 341.

Abstract: Following Lekili, Perutz, and Auroux, we know that the Floer homology of a 3-manifold with torus boundary should be viewed as an element in the Fukaya category of the punctured torus. I’ll give a concrete description of how to do this and explain how it can be applied to study the relationship between L-spaces (3-manifolds with the simplest Heegaard Floer homology) and left orderings of their fundamental group.

Gavril Farkas (Humboldt Universität). Compact moduli of abelian differentials. Friday 21st Oct., 1:30-2:30pm. Huxley 341.

Abstract: The moduli space of holomorphic differentials (with prescribed zeros and poles) on nonsingular curves is not compact since the curve may degenerate. I will discuss a compactification of these strata in the moduli space of Deligne-Mumford stable pointed curves, which includes the space of canonical divisors as an open subset. The theory leads to geometric/combinatorial constraints on the closures of the strata of holomorphic differentials and as a consequence, one can determine the cohomology classes of the strata. This is joint work with Rahul Pandharipande.

Jenia Tevelev (University of Massachusetts at Amherst). The Craighero-Gattazzo surface is simply-connected. Friday 28th Oct., 1:30-2:30pm. Huxley 341.

Abstract: We show that the Craighero–Gattazzo surface, the minimal resolution of an explicit complex quintic surface with four elliptic singularities, is simply-connected. This was conjectured by Dolgachev and Werner, who proved that its fundamental group has a trivial profinite completion. The Craighero–Gattazzo surface is the only explicit example of a smooth simply-connected complex surface of geometric genus zero with ample canonical class. We hope that our method will find other applications: to prove a topological fact about a complex surface, we use an algebraic reduction mod p technique and deformation theory. Joint work with Julie Rana and Giancarlo Urzua.

Travis Schedler (Imperial College). TBA. Friday 4th Nov., 1:30-2:30pm. Huxley 341.

Johannes Nordstrom (University of Bath). TBA. Friday 11th Nov., 1:30-2:30pm. Huxley 341.

Arnaud Beauville (Université de Nice). TBA. Friday 25th Nov., 1:30-2:30pm. Huxley 341.

Please note the unusual location:
Alessandra Sarti (Université de Poitiers). TBA. Friday 16th Dec., 1:30-2:30pm. ICBS 300.

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