Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

 

Past events in this series


Mon, 30 Jan 2023
14:15
L4

Mirror symmetry and big algebras

Tamas Hausel
(IST Austria)
Abstract

First we recall the mirror symmetry identification of the coordinate ring of certain very stable upward flows in the Hitchin system and the Kirillov algebra for the minuscule representation of the Langlands dual group via the equivariant cohomology of the cominuscule flag variety (e.g. complex Grassmannian). In turn we discuss a conjectural extension of this picture to non-very stable upward flows in terms of a big commutative subalgebra of the Kirillov algebra, which also ringifies the equivariant intersection cohomology of the corresponding affine Schubert variety.

Mon, 06 Feb 2023
14:15
L4

Constant Scalar Curvature Metrics on Algebraic Manifolds

Sean Timothy Paul
(University of Wisconsin Madison)
Abstract

According to the Yau-Tian-Donaldson conjecture, the existence of a constant scalar curvature Kähler (cscK) metric in the cohomology class of an ample line bundle $L$ on a compact complex manifold $X$ should be equivalent to an algebro-geometric "stability condition" satisfied by the pair $(X,L)$. The cscK metrics are the critical points of Mabuchi's $K$-energy functional $M$, defined on the space of Kähler potentials, and an important result of Chen-Cheng shows that cscK metrics exist iff $M$ satisfies a standard growth condition (coercivity/properness). Recently the speaker has shown that the $K$-energy is indeed proper if and only if the polarized manifold is stable. The stability condition is closely related to the classical notion of Hilbert-Mumford stability. The speaker will give a non-technical account of the many areas of mathematics that are involved in the proof. In particular, he hopes to discuss the surprising role played by arithmetic geometry ​in the spirit of Arakelov, Faltings, and Bismut-Gillet-Soule.

Mon, 27 Feb 2023
14:15
L4

TBA

Yankı Lekili
((Imperial College, London))