Joint EMSG and 86th BLOC meeting

The 86th BLOC meeting is a joint meeting with the East Midlands Geometry Seminar EMSG. It will be held on 20 March 2020 at the University of Leicester. Talks will take place in Engineering Lecture Theatre 2.

Due to the current COVID-19 situation, this meeting has been CANCELLED/POSTPONED

Programme:

1:15-2:05 Karin Baur (Leeds)

"Cluster categories associated with Grasmannians"

2:15:-3:05 Ben Davison (Edinburgh)

"Refined invariants of flopping curves and finite-dimensional Jacobi algebras"

3:15-4 Coffee break

4-4:50 Elena Gal (Oxford)

"Higher Segal spaces and lax A-infinity structures"

5-5:50 Balázs Szendrői (Oxford)

"Hilbert schemes of points on singular surfaces: geometry, combinatorics and representation theory”

We will have lunch in the Graduate Kitchen at 12:00. Please let Frank Neumann fn8@leicester.ac.uk or Sibylle Schroll schroll@leicester.ac.uk know if you would like to join.

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Karin Baur (Leeds)

"Cluster categories associated with Grasmannians"

Abstract: We study the category of Cohen-Macaulay modules for a quotient of a preprojective algebra. These categories are of interest as they
categorify Scott’s cluster algebra structure on the Grassmannian. We study these extensions between modules and use this to describe
parts of the module categories. Since most of these categories are of infinite type, the general picture is far from being understood.
Joint work with Bogdanic and Garcia Elsener.

 

Ben Davison (Edinburgh)

 

"Refined invariants of flopping curves and finite-dimensional Jacobi algebras"
Abstract: Associated to a flopping curve in a 3-fold X is a finite-dimensional algebra, the contraction algebra of Donovan and Wemyss, that represents the noncommutative deformations of the structure sheaf of that curve in the category of coherent sheaves on X.  A conjecture of Brown and Wemyss states (roughly) that all finite-dimensional Jacobi algebras arise this way.  As I'll explain, this conjecture would imply the positivity of all BPS invariants for finite-dimensional Jacobi algebras - these are invariants defined in terms of noncommutative Donaldson-Thomas theory.  This is a surprising claim since it is easy to cook up negative DT invariants for infinite-dimensional Jacobi algebras.  Finally, I'll explain that this positivity does indeed hold, providing evidence for the conjecture.

 

Elena Gal (Oxford)

"Higher Segal spaces and lax A-infinity structures"

Abstract: The notion of a higher Segal object was introduces by Dyckerhoff and Kapranov as a general framework for studying higher associativity inherent in a wide range of mathematical objects. Most of the examples are related to Hall algebra type constructions, which include quantum groups. We describe a construction that assigns to a simplicial object S a datum H(S)  which is naturally interpreted as a "d-lax A-infinity algebra” precisely when S is a (d+1)-Segal object. This extends the extensively studied d=2 case.

Balazs Szendroi (Oxford)

"Hilbert schemes of points on singular surfaces: geometry, combinatorics 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.

 

BLOC is supported by an LMS Scheme 3 grant, which is used to help offset travel costs for participants, with priority given to covering travel and accommodation costs for speakers and postgraduates.

Travel information is HERE.

Reimbursement: Please check with the organisers whether your travel costs can be reimbursed. If so then please download the following form, complete it and SIGN it and send it together with your original receipts and proof of travel to:

Prof Sibylle Schroll
Department of Mathematics
University of Leicester
University Road
Leicester LE1 7RH

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