Spring Term 2018

Mark Powell (Durham University). Stable diffeomorphism of 4-manifolds. Friday 12th Jan., 1:30-2:30pm. Huxley 139.

We say that two 4-manifolds are CP^ – stably diffeomorphic if one can add copies of the complex projective plane, with either orientations, to both manifolds until they become diffeomorphic. I will explain how to determine whether two manifold agree modulo this equivalence relation. I may also discuss the related question where stabilisation by copies of S^2 x S^2 is permitted instead.

Jorge Pereira (IMPA). Deformation of rational curves along foliations. Friday 19th Jan., 1:30-2:30pm. Huxley 139.

Abstract: Foliations on an algebraic variety X naturally determine foliations on the spaces of morphisms to X. In general, these foliations are trivial, i.e. they are nothing but foliations by points. When nontrivial they are expected to impose strong constraints on the original foliation. The talk will review situations where such expectations have been turned into results.

Alessandro Chiodo (Institut de Mathématiques de Jussieu). Mirror pairs and automorphisms. Friday 26th Jan., 1:30-2:30pm. Huxley 139.

Abstract:The first occurrences of mirror symmetry paired two Calabi–Yau threefolds X and X’ and set a relation between H^{2,1} of X and H^{1,1} of X’. We say that H*(X) “mirrors” H*(X’). In this talk we look at some pairs of Calabi-Yau orbifolds with two automorphisms x and x’ of the same order N. Within X, we consider the fixed space X_m with respect to any power x^m of x. We also consider the decomposition E_0+E_1+…+E_{N-1} of the Hodge structures of X_m as a Z/N-representation with respect to the action by x. We will present several statements involving mirrors of fixed loci and of fixed cycles. For instance, for N=m*l (with m and l proper divisors of N), the eigenspace E_l of the cohomology of X_m “mirrors” the eigenspace E_m of the cohomology of X’_l. This is work in collaboration with Kalashnikov and Veniani.

Ailsa Keating (University of Cambridge). TBA. Friday 2nd Feb., 1:30-2:30pm. Huxley 139.

Morgan Brown (University of Miami). TBA. Friday 16th Feb., 1:30-2:30pm. Huxley 139.

Sam Payne (Yale University). TBA. Friday 16th Mar., 1:30-2:30pm. Huxley 139.

Charles Favre (École Polytechnique). TBA. Friday 23rd Mar., 1:30-2:30pm. Huxley 139.

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