Dave Morrison (UCSB). Degenerations of K3 surfaces, gravitational instantons, and M-theory. Friday 13th Jan., 1:30-2:30pm. Huxley 213.
Abstract: The detailed study of degenerations of K3 surfaces as complex manifolds goes back more than forty years and is fairly complete. Much less is known about the analogous problem in differential geometry of finding Gromov–Hausdorff limits for sequences of Ricci-flat metrics on the K3 manifold. I will review recent work of H.-J. Hein and G. Chen–X. Chen on gravitational instantons with curvature decay, and descirbe applications to the K3 degeneration problem. M-theory suggests an additional geometric structure to add, and I will give a conjectural sketch of how that structure should clarify the limiting behavior.
Michel van Garrel (KIAS). From local to relative Gromov-Witten invariants via log geometry. Friday 20th Jan., 1:30-2:30pm. Huxley 341.
Abstract: Let X be a smooth projective variety and let L be a line bundle corresponding to a smooth ample divisor D. In this joint work with Graber and Ruddat, we show that the genus zero local Gromov-Witten invariants of L are maximally tangent relative Gromov-Witten invariants of the pair (X,D). This generalizes an old formula of Takahashi. The key technical ingredient is the theory of log stable maps by Gross and Siebert.
Dan Pomerleano (Imperial College). Two, infinity and beyond . Friday 27th Jan., 1:30-2:30pm. Huxley 341.
Abstract: I will sketch a proof that every nondegenerate contact form on a closed connected three-manifold, such that the associated contact structure has torsion ﬁrst Chern class, has either two or inﬁnitely many simple Reeb orbits. Key ingredients in the proof are the isomorphism between embedded contact homology and Seiberg-Witten Floer cohomology as proven by Taubes, an identity recovering the contact volume from the lengths of certain Reeb orbit sets, and the theory of global surfaces of section as developed by Hofer-Wysocki-Zehnder. This is joint work with Daniel Cristofaro-Gardiner and Michael Hutchings.
Jason Lotay (University College London). TBA. Friday 3rd Feb., 1:30-2:30pm. Huxley 341.
Zsolt Patakfalvi (École polytechnique fédérale de Lausanne). TBA. Friday 10th Feb., 1:30-2:30pm. Huxley 341.
Thibaut Delcroix (École normale supérieure – Paris). TBA. Friday 17th Feb., 1:30-2:30pm. Huxley 341.
Alexandru Dimca (Université de Nice). TBA. Friday 24th Feb., 1:30-2:30pm. Huxley 341.
Jean-Pierre Demailly (Université de Grenoble). TBA. Friday 3rd Mar., 1:30-2:30pm. Huxley 341.
Florin Ambro (Institute of Mathematics of the Romanian Academy). Curves with ordinary singularities. Friday 10th Mar., 1:30-2:30pm. Huxley 341.
Abstract: I will discuss the classification of projective curves with ordinary singularities (simplest kind),
in a way parallel to the classification of projective curves with no singularities.