## LAGOON: Leicester Algebra and Geometry Open ONline

These seminars are organized by *Frank Neumann and Sibylle Schroll, University of Leicester*

This Algebra and Geometry webinar series has a strong focus on Representation Theory and Algebraic Geometry and their many interactions covering topics such as homological mirror symmetry, stability conditions, derived categories, dg-categories, Hochschild cohomology of algebras, moduli spaces and algebraic stacks, derived algebraic geometry etc.

These seminars take place on Thursday at 13:00-14:00 (BST)

To sign up to participate in these seminars, please complete this form.

Registration will close at 11.00 each Thursday.

You will be sent a link to the Zoom meeting on Thursday morning

**Forthcoming seminars:**

Future speaker details can be found here.

28 May ** Bernhard Keller ** (Université Paris Diderot - Paris 7, France) :Grassmannian braiding categorified

Abstract: Chris Fraser has discovered an action of the extended affine braid group on d strands on the Grassmannian cluster algebra of k-subspaces in n-space, where d is the least common divisor of k and n. We lift this action to the corresponding cluster category first constructed by Geiss-Leclerc-Schröer in 2008. For this, we use Jensen-King-Su's description of this category as a singularity category in the sense of Buchweitz/Orlov. We conjecture an action of the same braid group on the cluster algebra associated with an arbitrary pair of Dynkin diagrams whose Coxeter numbers are k and n. This is a report on ongoing joint work with Chris Fraser.

4 June ** Balazs Szendroi ** (University of Oxford, UK) :Hilbert schemes of points on singular surfaces: combinatorics, geometry, and representation theory

Abstract: Given a smooth algebraic surface S over the complex numbers, the Hilbert scheme of points of S is the starting point for many investigations, leading in particular to generating functions with modular behaviour and Heisenberg algebra representations. I will explain aspects of a similar story for surfaces with rational double points, with links to algebraic combinatorics and the representation theory of affine Lie algebras. I will in particular recall our 2015 conjecture concerning the generating function of the Euler characteristics of the Hilbert scheme for this singular case, and aspects of more recent work that lead to a very recent proof of the conjecture by Nakajima. Joint work with Gyenge and Nemethi, respectively Craw, Gammelgaard and Gyenge.

**Previous seminars:**

Thursday May 14

**Hipolito Treffinger **(University of Leicester)

*Representation theoretic aspects of scattering diagrams*

Thursday May 21

**Alex Takeda ** (IHES, France)

*Gluing relative stability conditions along pushouts*

A recording of this talk is available here.

Zoom is the online platform being used to deliver this seminar series.

**This seminar series is supported as part of the ICMS/INI Online Mathematical Sciences Seminars. **