Summer Term 2016

Cristiano Spotti (University of Cambridge). Existence of Kahler-Einstein metrics on smoothable Fano
Friday 29th Apr, 1:30-2:30pm. Huxley 130.

Abstract: In this talk I will discuss the existence of Kahler-Einstein metrics on Q-Gorenstein smoothable K-polystable Q-Fano varieties, and the relevance of such metrics for the construction of compact moduli spaces of K-polystable Fano varieties. This is joint work with S. Sun and C. Yao.

Please note the unusual time:
Giuseppe Tinaglia (King’s College). The geometry of constant mean curvature disks embedded in R3. Friday 6th May, 2-3pm. Huxley 140.

Abstract: In this talk I will survey several results on the geometry of constant mean curvature surfaces embedded in R3. Among other things I will prove radius and curvature estimates for nonzero constant mean curvature embedded disks. It then follows from the radius estimate that the only complete, simply connected surface embedded in R3 with constant mean curvature is the round sphere. This is joint work with Bill Meeks.

Michael Groechenig (Imperial College). Adèles in algebraic geometry. Friday 13th May, 1:30-2:30pm. Huxley 140.

Abstract: In the 80s Beilinson defined a canonical flasque resolution for every quasi-coherent sheaf on a Noetherian scheme. It was observed by Hübl and Yekutieli that this construction shares many formal properties with the Dolbeault resolution in complex analytic geometry. For instance there is an adelic analogue of Chern-Weil theory for characteristic classes. The first half of my talk provides an overview of the theory of adèles. In the second half we will study a naturally arising extra structure on adèles, similar to some sort of topology, which induces various incarnations of residue maps. This is joint work with O. Bräunling and J. Wolfson.

Gilberto Bini (Università di Milano). Some Examples on Calabi-Yau Threefolds and Surfaces of General Type. Friday 20th May, 1:30-2:30pm. Huxley 140.

Abstract: In this talk, we will report on various examples of Calabi-Yau varieties and, in some cases, hyperplane sections that are surfaces of general type. The results are contained in a series of papers, some of them in collaboration with Filippo F. Favale (Università degli Studi di Trento) and some of them with Matteo Penegini (Università degli Studi di Genova).

Nicholas Zufelt (Imperial College). The combinatorics of reducible Dehn surgeries. Friday 27th May, 1:30-2:30pm. Huxley 140.

Abstract: The proposed classification of reducible Dehn surgeries on knots in the three-sphere is known as the Cabling Conjecture. A large amount of progress toward the conjecture has been established which forces an arbitrary reducible surgery to coarsely resemble the cabled reducible surgery. I will discuss recent results giving rise to new progress toward this conjecture which utilizes some older, combinatorial techniques made famous in Gordon and Luecke’s proof of the Knot Complement Problem.

Ben Webster (University of Virginia). Representation theory of symplectic singularities. Friday 3rd June, 1:30-2:30pm. Huxley 140.

Abstract: Since they were introduced about 2 decades ago, symplectic singularities have shown themselves to be a remarkable branch of algebraic geometry. They are much nicer in many ways than arbitrary singularities, but still have a lot of interesting nooks and crannies. I’ll talk about these varieties from a representation theorist’s perspective. This might sound like a strange direction, but remember, any interesting symplectic structure is likely to be the classical limit of an equally interesting non-commutative structure, whose representation theory we can study. While this field is still in its infancy, it includes a lot of well-known examples like universal enveloping algebras and Cherednik algebras, and has led a lot of interesting places, including to categorified knot invariants and a conjectured duality between pairs of symplectic singularities. I’ll give a taste of these results and try to indicate some interesting future directions.

Laurentiu Maxim (University of Wisconsin). : Cohomology representations of external products of varieties and coefficients. Friday 10th June, 1:30-2:30pm. Huxley 213.

Abstract: I will explain refined generating series formulae for characters of (virtual) cohomology representations of external products of suitable coefficients on complex quasi-projective varieties. These formulae generalize previous results for symmetric and alternating powers of such coefficients, and apply also to other Schur functors. (Joint work with J. Schuermann.)

Tony Yu (Institut de Mathématiques de Jussieu). Counting open curves via closed curves. Friday 17th June, 1:30-2:30pm. Huxley 140.

Abstract: Motivated by mirror symmetry, we will study the counting of open curves in log Calabi-Yau surfaces. Although we start with a complex algebraic surface, the counting is achieved by applying methods from Berkovich geometry. The idea is to relate the counting of open curves to special types of closed curves. This gives rise to new geometric invariants inaccessible by classical methods. If time permits, I will present an explicit calculation of these invariants for a cubique surface. The results verify the Kontsevich-Soibelman wall-crossing formula for a focus-focus singularity.
No background in non-archimedean geometry is necessary to follow my talk.

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