12:00 - 13:00
Organisers:
- Frank Neumann, University of Leicester
- 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 12:00-13:00 (GMT).
To sign up to participate in these seminars, please complete this form.
You will be sent a link to the Zoom meeting link 24 hours in advance.
These seminars are recorded, please click here to view the playlist.
Future Seminars
28 January
Dan Kaplan (Birmingham, UK): Multiplicative preprojective algebras in geometry and topology
In 2006, Crawley-Boevey and Shaw defined the multiplicative preprojective algebra (MPA) to study certain character varieties. More recently, MPAs appeared in work of Etgü--Lekili in the study of Fukaya categories of 4-manifolds. Nice properties of the (additive) preprojective algebra are expected to hold for MPAs, but most proof techniques are not available. In joint work with Travis Schedler, we define the strong free product property, following older work of Anick. Using this property, we prove MPAs are 2-Calabi--Yau algebras for quivers containing a cycle. Moreover, using a result of Bocklandt--Galluzzi--Vaccarino, we prove the formal local structure of multiplicative quiver varieties is isomorphic to that of a (usual) quiver variety. In this talk, I'll survey these ideas and illustrate them in small examples.
4 February
Merlin Christ (Hamburg, Germany): TBA
11 February
Bertrand Toën (Toulouse, France): TBA
18 February
Paolo Stellari (Milano, Italy): TBA
1 July
Chelsea Walton (Rice, USA): TBA
Postponed Seminar
This seminar was due to take place on 21 January 2021. Resheduled date - TBA
Sebastian Opper (Prague, Czech Republic): Spherical objects on cycles of projective lines and transitivity
Polishchuk showed that spherical objects in the derived category of any cycle of projective lines yield solutions of the associative Yang-Baxter equation which raises the question whether one can classify spherical objects. He further posed the question whether the group of derived auto-equivalences of a cycle acts transitively on isomorphism classes of spherical objects. Partial solutions to both problems were given in works of Burban-Kreussler and Lekili-Polishchuk. A theorem of Burban-Drozd establishes a connection between the derived category of any cycle of projective lines with the derived category of a certain gentle algebra which can be modeled by a (toplogical) surface and which allows us to translate algebraic information in the derived category such as objects into geometric information on the surface such as curves. I will explain how the result of Burban-Drozd can be used to find a similar model for the derived category of a cycle. Afterwards we discuss how this can be exploited to classify spherical objects and establish transitivity. Further applications include a description of the group of derived auto-equivalences of a cycle and faithfulness of a certain group action as defined by Sibilla.
Previous Seminars
14 May 2020
Hipolito Treffinger (University of Leicester) - Representation theoretic aspects of scattering diagrams
21 May 2020
Alex Takeda (IHES, France) - Gluing relative stability conditions along pushouts
28 May 2020
Bernhard Keller (Université Paris Diderot - Paris 7, France) - Grassmannian braiding categorified
4 June 2020
Balazs Szendroi (University of Oxford, UK) - Hilbert schemes of points on singular surfaces: combinatorics, geometry, and representation theory
11 June, 2020
Qiu Yu (Tsinghua University Beijing, China) - Graded decorated marked surfaces: Calabi-Yau-X categories of gentle algebras
18 June 2020
Lara Bossinger (Instituto de Matemáticas UNAM Unidad, Mexico) - Families of Gröbner degenerations
25 June 2020
Wendy Lowen (University of Antwerp, Belgium) - linear quasi-categories as templicial modules (joint work with Arne Mertens)
2 July 2020
Hiraku Nakajima (Kavli IPMU, Tokyo, Japan) - Euler numbers of Hilbert schemes of points on simple surface singularities and quantum dimensions of standard modules of quantum affine algebras
9 July 2020
Alexander Polishchuk (University of Oregon, USA) - Geometry of the Associative Yang-Baxter equation
16 July 2020
Markus Reineke (Universität Bochum, Germany) - Fano quiver moduli
23 July 2020
Laura Schaposnik (University of Illinois at Chicago, USA) - On Generalized Hyperpolygons
03 September 2020
Andrea Solotar (Buenos Aires, Argentina) - A cup-cap duality in Koszul calculus
10 September 2020
Zhengfang Wang (Stuttgart, Germany) - Deformations of path algebras of quivers with relations
17 September 2020
Categorifications in Representation Theory Conference at Leicester
24 September 2020
Ailsa Keating (Cambridge, UK) - Homological mirror symmetry for log Calabi-Yau surfaces
01 October 2020
Karin Baur (Leeds, UK and Graz, Austria) - Structure of Grassmannian cluster categories
8 October 2020
Andrey Lazarev (Lancaster, UK) - Koszul duality for dg-categories and infinity-categories (joint with J. Holstein)
15 October 2020
Fabrizio Catanese (Bayreuth, Germany) - Topologically trivial automorphisms of compact Kähler surfaces and manifolds
22 October 2020
Lang Mou - Caldero-Chapoton formulas for generalized cluster algebras from orbifolds
29 October 2020
Michael Wemyss (Glasgow, UK) - Contraction algebras, plumbings and flops
5 November 2020
Yukinobu Toda (Kavli IPMU, Tokyo, Japan) - On d-critical birational geometry and categorical DT theories
12 November 2020
Amihay Hanany (Imperial, UK) - Coulomb branch
19 November 2020
John Greenlees (Warwick, UK) - The singularity category of C^*(BG)
26 November 2020
Evgeny Shinder (Sheffield, UK) - Birationality centers, rationality problems and Cremona groups
3 December 2020
Giulia Saccà (Collège de France and Columbia University, USA) - Hodge numbers of OG10 via Ngô strings
10 December 2020, 12:00 - 13:00 (GMT)
Ralph Kaufmann (Purdue, USA) - Categorical Interactions in Algebra, Geometry and Representation Theory
Zoom is the online platform being used to deliver this seminar series.
This seminar series is supported as part of the ICMS Online Mathematical Sciences Seminars.