Autumn Term 2018

Please note the unusual time:
Ivan Cheltsov (University of Edinburgh). Kahler-Einstein Fano threefolds of degree 22. Friday 5th Oct, 2:00-3:00pm. Huxley 139.

Abstract: This talk is about smooth Fano threefolds of Picard rank one and anticanonical degree 22 that admit a faithful action of the multiplicative group. Donaldson conjectured that all of them must be Kahler-Einstein, see I will explain how to prove that, except possibly two explicitly described cases, all such smooth Fano threefolds are Kahler-Einstein.
This is a joint work with Costya Shramov from Moscow, see Our proof is based on a structural theorem for such threefolds obtained last year by Sasha Kuznetsov and Yuri Prokhorov, see

Oscar Randal-Williams (University of Cambridge). Metastability in the homology of mapping class groups. Friday 12th Oct, 1:30-2:30pm. Huxley 139.

Abstract: That the homology of mapping class groups of oriented surfaces stabilises with respect to the genus was discovered by Harer in the 80’s, and the range of homological degrees in which it is stable was further improved by Ivanov and Boldsen: today we know that it is 2/3 times the genus. I will explain a new type of stability result for these groups, obtained in joint work with S. Galatius and A. Kupers, which can be summarised as saying that “the failure of stability is itself stable”. More precisely, the relative homology groups which measure the failure of stability admit a new kind of stabilisation map and this is is an isomorphism in degrees up to 3/4 times the genus, and up to 4/5 times the genus with rational coefficients. I will explain this result and the strategy we use to prove it, which combines calculations of the low-dimensional homology of mapping class groups, simplicial complexes of separating arcs on surfaces, and techniques from homotopical algebra.

Victor Przyjalkowski (Steklov Mathematical Institute). Weighted complete intersections. Friday 19th Oct, 1:30-2:30pm. Huxley 139.

Abstract: We observe a classification and the main properties of one of the main class of examples of higher dimensional Fano varieties — smooth complete intersections in weighted projective spaces. We discuss their main properties and boundness results. We also discuss extremal examples from Hodge theory point of view and their relations with derived categories structures and their semiorthogonal decompositions. If time permits, we discuss mirror symmetry for the complete intersections and invariants of their Landau–Ginzburg models related to ones of the complete intersections.

Sheng Meng (Max Planck Institute for Mathematics). On the equivariant minimal model program of projective varieties admitting polarized endomorphisms. Friday 26th Oct, 1:30-2:30pm. Huxley 139.

Abstract: Let X be a normal projective variety with mild singularities admitting a polarized endomorphism f.
We will run the equivariant minimal model program relative to not just the single f but also the monoid of all surjective endomorphisms of X, up to finite-index. Several applications will be given.
This combines joint works with Paolo Cascini and De-Qi Zhang.

Mauricio Corrêa (University of Oxford). Moduli spaces of reflexive sheaves and classification of distributions on P^3. Friday 2nd Nov, 1:30-2:30pm. Huxley 139.

Abstract: We describe the moduli space of distributions in terms of Grothendieck’s Quot-scheme for the tangent bundle. In certain cases, we show that the moduli space of codimension one distributions on the projective space is an irreducible, nonsingular quasi-projective variety.
We study codimension one holomorphic distributions on the projective three-space, analyzing the properties of their singular schemes and tangent sheaves. In particular, we provide a classification of codimension one distributions of degree at most 2. We show how the connectedness of the curves in the singular sets of foliations is a integrable phenomena. This parte of the talk is a work joint with M. Jardim(Unicamp) and O. Calvo-Andrade(Cimat).
We also study foliations by curves via the investigation of their singular schemes and conormal sheaves and we provide a classification of foliations of degree at most 3 with conormal sheaves locally free. This parte of the talk is a work joint with M. Jardim(Unicamp) and S. Marchesi(Unicamp).

Raf Bocklandt (University of Amsterdam). Bridgeland and King Revisited. Friday 9th Nov, 1:30-2:30pm. Huxley 139.

Abstract: We look at King stability and Bridgeland stability in the case of mirror symmetry for surfaces and try to interprete them on both sides of the mirror construction.

Michele Bolognesi (Université de Montpellier). Categorical representability and birational geometry. Friday 16th Nov, 1:30-2:30pm. Huxley 139.

Abstract: In this talk we will first survey some ideas concerning the construction of possible birational invariants from semiorthogonal decompositions of the derived category of coherent sheaves on a given variety X. We will then introduce categorical representability, and show how in several cases it can give interesting indications on the rationality of the base variety X. In particular we will devolop the case of varieties that are fibered in intersection of quadrics. This talk originates from joint works with A.Auel and M.Bernardara.

Enrica Mazzon (Imperial College). The essential skeletons of pairs and the geometric P=W conjecture. Friday 23rd Nov, 1:30-2:30pm. Huxley 139.

Abstract: The geometric P=W conjecture is a conjectural description of the asymptotic behavior of a celebrated correspondence in non-abelian Hodge theory. In particular, it is expected that the dual boundary complex of the compactification of character varieties has the homotopy type of a sphere. In a joint work with Mirko Mauri and Matthew Stevenson, we compute the first non-trivial examples of these dual boundary complexes in the compact case. In this talk I will explain how the result is a combination of techniques from birational and non-archimedean geometry.

Marco Golla (University of Nantes). Singular symplectic curves: isotopy and symplectic fillings. Friday 30th Nov, 1:30-2:30pm. Huxley 139.

Abstract: I will be talking about symplectic curves (mostly in the projective plane) whose singularity are modelled over complex singularities. I will discuss existence and uniqueness (up to isotopy) of these curves, phrasing it in terms of symplectic fillings; the focus will be on rational curves with irreducible singularities. This is joint work with Laura Starkston (in progress).

Cristina Manolache (Imperial College). Enumerative invariants from curves with cusps. Friday 7th Dec, 1:30-2:30pm. Huxley 139.

Abstract: I will introduce moduli spaces of stable maps and stable maps from cuspidal curves and I will define virtual intersection numbers on these spaces. I will discuss how to relate these numbers. This is partially based on joint work with L Battistella, F Carocci and T Coates.

Stipsicz Andras (Alfréd Rényi Institute of Mathematics). Knot Floer homology and double branched covers. Friday 14th Dec, 1:30-2:30pm. Huxley 139.

Abstract: We will review the basic constructions of (various versions of) knot Floer homologies, show some applications and extensions of the definitions to the double branched cover, also using the covering transformation.