LAGOON: Longitudinal Algebra and Geometry Open ONline

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LAGOON: Longitudinal Algebra and Geometry Open ONline

 Feb 03 2022

12:00 - 13:00

Organisers:

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The LAGOON 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 and other topics.

These seminars take place on Thursday at 12:00-13:00 (GMT)

Register Here
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


03 February

Alberto Canonaco (Pavia, Italy): Dg enhancements of triangulated categories and their uniqueness

It is well known that often some intrinsic defects of triangulated categories can be avoided by enhancing them to suitable higher categorical structures, like (pretriangulated) dg categories. However, despite significant progress made in recent years, the relation between the triangulated and the dg level is not yet completely clear, and some foundational questions have received only partial answers so far. After presenting the general picture, I will report on a joint work (partly in progress) with Neeman and Stellari about uniqueness of dg enhancements.


10 February
Matt Pressland (Glasgow, UK): Grassmannian twists categorified

The Grassmannian of k-dimensional subspaces of an n-dimensional space carries a birational automorphism called the twist (or sometimes the Donaldson-Thomas transformation), defined by Berenstein-Fomin-Zelevinsky and Marsh-Scott. This automorphism respects the cluster algebra structure on the coordinate ring, being a quasi-cluster automorphism in the sense of Fraser. By work of Muller-Speyer, similar results hold for positroid strata in the Grassmannian. The cluster algebras in this picture have been categorified, by Jensen-King-Su in the case of the full Grassmannian, and by myself for more general (connected) positroid varieties. In this talk I will report on joint work with İlke Çanakçı and Alastair King, in which we describe the twist in terms of these categorifications. The key ingredient is provided by perfect matching modules, certain combinatorially defined representations for a quiver 'with faces', and I will also explain this construction.

17 February
Sergey Mozgovoy (Dublin, Ireland): Wall-crossing structures arising from surfaces
Families of Bridgeland stability conditions induce families of stability data (DT invariants), wall-crossing structures and scattering diagrams on the motivic Hall algebra. These structures can be transferred to the quantum torus if the stability conditions of the family have global dimension at most 2. I will discuss geometric stability conditions on a surface with nef anticanonical bundle. These stability conditions have global dimension 2, hence induce a family of stability data. I will also discuss the relationship of this family to the family of stability data associated to a quiver with potential, with an emphasis on the projective plane.

24 February
Sira Gratz (Glasgow, UK)

03 March
Eleonore Faber (Leeds, UK)

10 March
Nick Sheridan (Edinburgh, UK)


 

Previous Seminars

14 May 2020
Hipolito Treffinger (University of Leicester): Representation theoretic aspects of scattering diagrams

  • No recording available

 

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

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 (HMI Bonn, Germany): 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
Ralph Kaufmann (Purdue, USA): Categorical Interactions in Algebra, Geometry and Representation Theory

28 January 2021
Dan Kaplan (Birmingham, UK): Multiplicative preprojective algebras in geometry and topology


4 February
Merlin Christ (Hamburg, Germany): A gluing construction for Ginzburg algebras of triangulate

 

11 February
Bertrand Toën (Toulouse, France): Foliations on schemes

 

18 February
Paolo Stellari (Milano, Italy): Uniqueness of enhancements for derived and geometric categories


25 February
Claudia Scheimbauer (TU München, Germany): Derived symplectic geometry and AKSZ topological field theories

  • Permission to publish recording has not been given.


4 March
Sebastian Opper
, Prague, Czech Republic - Spherical Objects on Cycles of Projective Lines and Transitivity


11 March
Alexandra Zvonareva
, Stuttgart, Germany - Derived equivalence classification of Brauer graph algebras


18 March 2021
Letterio Gatto
, Polytechnic University of Turin - HiDEAs to work with

 
1 April & 8 April - Easter Break - no seminars

15 April
Valery Lunts, Indiana, USA, Subcategories of derived categories on affine schemes and projective curves
  • Talk not recorded


22 April
Severin Barmeier, Freiburg, Germany: Scattering amplitudes from derived categories and cluster categories

 
29 April
Okke van Garderen (Glasgow, UK): On the Landau-Ginzburg/conformal field theory correspondence


6 May
Ana Ros Camacho (Cardiff, UK): On the Landau-Ginzburg/conformal field theory correspondence


13 May
Matt Booth (Antwerp, Belgium): Topological Hochschild cohomology for schemes


20 May      
Sergey Mozgovoy (Trinity College Dublin, Ireland) DT invariants of some 3CY quotients


3 June
Markus Szymik (NTNU Trondheim, Norway): A homological stroll into the algebraic theories of racks and quandles

  • This talk was not recorded

10 June
Fabian Haiden (Oxford, UK) - New 3CY categories of topological surfaces


17 June
David Pauksztello (Lancaster, UK) - Functorially finite hearts, simple-minded systems and negative cluster categories


24 June
Yilin Wu - (Université Paris Diderot - Paris 7, France) Derived equivalences from mutations of ice quivers with potential


1 July
Chelsea Walton (Rice, USA): Frobenius algebras galore

 7 October
Pedro Tamaroff (Leipzig, Germany): Minimal models for monomial algebras

 
14 October
Shunsuke Kano (Tohoku, Japan): Categorical dynamical systems arising from sign-stable mutation loops


21 October

Xiao-Wu Chen (Hefei, China): The dg Leavitt path algebra, singular Yoneda category and singularity category


28 October

Amnon Neeman (ANU, Australia): Finite approximations as a tool for studying triangulated categories


4 November
Véronique Bazier-Matte (UConn, USA): Triangulations of the Möbius strip and its connections with quasi-cluster algebras


11 November
Bruno Vallette (Université Sorbonne Paris Nord, France): Deformation theory of Cohomological Field Theories


18 November
Tobias Dyckerhoff (Hamburg, Germany): Perverse sheaves and schobers on Riemann surfaces


25 November
Marcy Robertson (Melbourne, Australia): A topological characterization of the Kashiwara-Vergne groups
Click here to view the recording


9 December - 16:00 GMT
Jeremy Brightbill (Santa Barbara, USA): Higher simple-minded systems in negative Calabi-Yau categories
Click here to view the recording



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.