For this term, the seminars will take place in room SALC 10 (Sherfield building 5th floor, Seminar and Learning Centre room 10). The instructions below show how to reach the room:
Take the lift in Sherfield building (the one close to maths, west end of Sherfield) to the 5th floor.
Go straight ahead and slightly left, through the art gallery (follow the signs for SALC).
Exit the gallery and turn left into the Seminar and Learning Centre (SALC), go to end of corridor, turn right to room 10.
The map of the 5th floor can be useful:
Schedule
András Némethi (Budapest). Lattice cohomologies of normal surface singularities. Friday 9th January, 1:30-2:30pm. Huxley 144.
Abstract: The lattice cohomology associates with a geometric situation a bigraded Z[U] module. It has many different version. For example, we can define it for the topological type of a normal surface singularity (i.e. for a negative definite plumber 3-manifold), or to the analytic type of a normal surface singularity. This analytic setup can be generalized to higher dimensional isolated singularities and to
the curve case as well. The Euler characteristic of the topological lattice cohomology is the Seiberg-Witten invariant of the link (of the plumbed 3-manifold), the Euler characteristic of the analytic one is the geometric genus of the analytic germ. (It is also known that the topological lattice cohomology is equivalent with the Heegaard Floer theory.) In the talk I will give the construction of both topological and analytical cases, I will compare them via some examples.
Cheuk Yu Mak (Sheffield). Nilpotent slices, symplectic annular Khovanov homology and fixed point localisation. Friday 16th January, 1:30-2:30pm. Sherfield, Seminar and Learning Centre 5th floor, room 10.
Abstract: Khovanov homology is a powerful link invariant which has numerous applications. In 2006, Seidel and Smith introduced a symplectic version of Khovanov homology using Lagrangians in the generic fibre of nilpotent slices. In this talk, we will first introduce a multiplicative analogue of Seidel-Smith symplectic Khovanov homology, which we call symplectic annular Khovanov homology. Then we will explain how to use it to obtain the symplectic analogue of Stoffregen-Zhang and Lipshitz-Sarkar spectral sequences relating periodic links (resp. strongly invertible knots) to their quotients. Finally, we will end with some open questions (to the best of my knowledge). This is a joint work with Hendricks and Raghunath.
Danil Kozevnikov (Edinburgh). Lagrangian skeleta of very affine complete intersections. Friday 23rd January, 1:30-2:30pm. Sherfield, Seminar and Learning Centre 5th floor, room 10.
Abstract: In this talk, I will present some new results about skeleta of complete intersections inside (C*)^n. I will start by briefly reviewing the Batyrev-Borisov mirror construction, which uses combinatorial dualities between lattice polytopes to produce mirror pairs of Calabi-Yau complete intersections in Fano toric varieties. The main focus of the talk will be open Batyrev-Borisov complete intersections (BBCIs), which are Liouville manifolds obtained by removing the toric boundary in the Batyrev-Borisov construction. I will explain how one can use tropical geometry to compute Lagrangian skeleta of open BBCIs and decompose them into pieces mirror to certain toric varieties, which leads to a proof of homological mirror symmetry (generalising the work of Gammage-Shende and Zhou in the case of hypersurfaces).
Soheyla Feyzbakhsh (Imperial). Stability conditions on Calabi-Yau threefolds via Brill-Noether theory of curves. Friday 30th January, 1:30-2:30pm. Sherfield, Seminar and Learning Centre 5th floor, room 10.
Abstract: I will explain how classical Brill–Noether theory for vector bundles on curves, which studies the number of sections of stable vector bundles, can be used to prove the Bayer–Macrì–Toda conjecture for Calabi–Yau threefolds, which guarantees the existence of Bridgeland stability conditions on them. This is joint work with Zhiyu Liu, Naoki Koseki, and Nick Rekuski.
Graeme Wilkin (York). Loop groups, Brieskorn’s theorem and ALE spaces. Friday 6th February, 1:30-2:30pm. Sherfield, Seminar and Learning Centre 5th floor, room 10.
Abstract: Gravitational instantons are classified by the asymptotic behaviour of their metric near the boundary. In the first part of the talk I will describe joint work with Rafe Mazzeo, where we study partial compactifications of ALE gravitational instantons that have the same underlying complex manifold as the ALG gravitational instantons constructed by Hein and recently classified by Chen and Chen. In the last part of the talk I will describe work in progress to put the above construction in a more general framework and give a gauge-theoretic construction of these spaces in type A using loop groups and Brieskorn’s theorem.
Laura Pertusi (Milan). Cubic threefolds and noncommutative curves. Friday 13th February, 1:30-2:30pm. Sherfield, Seminar and Learning Centre 5th floor, room 10.
Abstract: The bounded derived category of a cubic threefold X admits a semiorthogonal decomposition formed by two exceptional line bundles and their orthogonal complement, which we denote by Ku(X). Although stability conditions are known to exist on Ku(X), the geometric structure of the associated moduli spaces of semistable objects is rather mysterious. In this talk, I will present structure results on moduli spaces and Abel-Jacobi maps, proving some interesting analogies with moduli spaces on curves, and applications to the construction of Lagrangian subvarieties in hyperkahler manifolds. This is a joint work with Chunyi Li, Yinbang Lin and Xiaolei Zhao.
Nikolas Adaloglou (Leiden). Friday 20th February, 1:30-2:30pm. Sherfield, Seminar and Learning Centre 5th floor, room 10.
Jordi Daura Serrano (Barcelona). Friday 27th February, 1:30-2:30pm. Sherfield, Seminar and Learning Centre 5th floor, room 10.
Silvia Sabatini (Cologne). Friday 6th March, 1:30-2:30pm. Sherfield, Seminar and Learning Centre 5th floor, room 10.
Davide Parise (Imperial). Friday 20th March, 1:30-2:30pm. Huxley 140.