LAGOON: Longitudinal Algebra and Geometry Open ONline

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LAGOON: Longitudinal Algebra and Geometry Open ONline

 07 Apr 2022
1200 GMT



This seminar series is no longer hosted by ICMS. Check the LAGOON website for more information


  • Frank Neumann, University of Leicester
  • Sibylle Schroll, University of Cologne


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's, 12:00-13:00 (GMT).

General Seminar Programme


Past Events:

14 May 2020
Hipolito Treffinger, University of Leicester

Representation theoretic aspects of scattering diagrams

Recording not 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

04 Jun 2020
Balazs Szendroi, University of Oxford, UK

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

11 Jun 2020
Qiu Yu, Tsinghua University Beijing, China

Graded decorated marked surfaces: Calabi-Yau-X categories of gentle algebras

18 Jun 2020
Lara Bossinger, Instituto de Matemáticas UNAM Unidad, Mexico

Families of Gröbner Degenerations

25 Jun 2020
Wendy Lowen, University of Antwerp, Belgium

Linear quasi-categories as templicial modules

Joint work with Arne Mertens.

02 Jul 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

09 Jul 2020
Alexander Polishchuk, University of Oregon, USA

Geometry of the Associative Yang-Baxter equation

16 Jul 2020
Markus Reineke, Universität Bochum, Germany

Fano quiver moduli

23 Jul 2020
Laura Schaposnik, University of Illinois at Chicago, USA

On Generalized Hyperpolygons

03 Sep 2020
Andrea Solotar, Buenos Aires, Argentina

A cup-cap duality in Koszul calculus

10 Sep 2020
Zhengfang Wang, Stuttgart, Germany

Deformations of path algebras of quivers with relations

24 Sep 2020
Ailsa Keating, Cambridge, UK

Homological mirror symmetry for log Calabi-Yau surfaces

01 Oct 2020
Karin Baur, Leeds, UK and Graz, Austria

Structure of Grassmannian cluster categories

08 Oct 2020
Andrey Lazarev, Lancaster, UK

Koszul duality for dg-categories and infinity-categories

Joint work with J. Holstein.

15 Oct 2020
Fabrizio Catanese, Bayreuth, Germany

opologically trivial automorphisms of compact Kähler surfaces and manifolds

22 Oct 2020
Lang Mou, HMI Bonn, Germany

Caldero-Chapoton formulas for generalized cluster algebras from orbifolds

29 Oct 2020
Michael Wemyss, Glasgow, UK

Contraction algebras, plumbings and flops

05 Nov 2020
Yukinobu Toda, Kavli IPMU, Tokyo, Japan

On d-critical birational geometry and categorical DT theories

12 Nov 2020
Amihay Hanany, Imperial, UK

Coulomb branch

19 Nov 2020
John Greenlees, Warwick, UK

The singularity category of C^*(BG)

26 Nov 2020
Evgeny Shinder, Sheffield, UK

Birationality centers, rationality problems and Cremona groups

03 Dec 2020
Giulia Saccà, Collège de France and Columbia University, USA

Hodge numbers of OG10 via Ngô strings

10 Dec 2020
Ralph Kaufmann, Purdue, USA)

Categorical Interactions in Algebra, Geometry and Representation Theory

28 Jan 2021
Dan Kaplan, Birmingham, UK

Multiplicative preprojective algebras in geometry and topology

04 Feb 2021
Merlin Christ, Hamburg, Germany

A gluing construction for Ginzburg algebras of triangulate

11 Feb 2021
Bertrand Toën, Toulouse, France

Foliations on schemes

18 Feb 2021
Paolo Stellari, Milano, Italy

Uniqueness of enhancements for derived and geometric categories

25 Feb 2021
Claudia Scheimbauer, TU München, Germany

Derived symplectic geometry and AKSZ topological field theories

This seminar was not recorded. 

04 Mar 2021
Sebastian Opper, Prague, Czech Republic

Czech Republic - Spherical Objects on Cycles of Projective Lines and Transitivity

11 Mar 2021
Alexandra Zvonareva, Stuttgart, Germany

Derived equivalence classification of Brauer graph algebras

18 Mar 2021
Letterio Gatto, Polytechnic University of Turin

HiDEAs to work with

15 Apr 2021
Valery Lunts, Indiana, USA

Subcategories of derived categories on affine schemes and projective curves

This talk was not recorded.

22 Apr 2021
Severin Barmeier, Freiburg, Germany

Scattering amplitudes from derived categories and cluster categories

29 Apr 2021
Okke van Garderen, Glasgow, UK

On the Landau-Ginzburg/conformal field theory correspondence

06 May 2021
Ana Ros Camacho, Cardiff, UK

On the Landau-Ginzburg/conformal field theory correspondence

13 May 2021
Matt Booth, Antwerp, Belgium

Topological Hochschild cohomology for schemes

20 May 2021
Sergey Mozgovoy, Trinity College Dublin, Ireland

DT invariants of some 3CY quotients

03 Jun 2021
Markus Szymi, NTNU Trondheim, Norway

A homological stroll into the algebraic theories of racks and quandles

This seminar was not recorded.

10 Jun 2021
Fabian Haiden, Oxford, UK

New 3CY categories of topological surfaces

17 Jun 2021
David Pauksztello, Lancaster, UK

Functorially finite hearts, simple-minded systems and negative cluster categories

24 Jun 2021
Yilin Wu, Université Paris Diderot - Paris 7, France

Derived equivalences from mutations of ice quivers with potential

01 Jul 2021
Chelsea Walton, Rice, USA

Frobenius algebras galore

07 Oct 2021
Pedro Tamaroff, Leipzig, Germany

Minimal models for monomial algebras

14 Oct 2021
Shunsuke Kano, Tohoku, Japan

Categorical dynamical systems arising from sign-stable mutation loops

21 Oct 2021
Xiao-Wu Chen, Hefei, China

The dg Leavitt path algebra, singular Yoneda category and singularity category

28 Oct 2021
Amnon Neeman, ANU, Australia

Finite approximations as a tool for studying triangulated categories

04 Nov 2021
Véronique Bazier-Matte, UConn, USA

Triangulations of the Möbius strip and its connections with quasi-cluster algebras

11 Nov 2021
Bruno Vallette, Université Sorbonne Paris Nord, France)

Deformation theory of Cohomological Field Theories

18 Nov 2021
Tobias Dyckerhoff, Hamburg, Germany

Perverse sheaves and schobers on Riemann surfaces

25 Nov 2021
Marcy Robertson, Melbourne, Australia

A topological characterization of the Kashiwara-Vergne groups

09 Dec 2021
Jeremy Brightbill, Santa Barbara, USA

Higher simple-minded systems in negative Calabi-Yau categories

03 Feb 2022
Alberto Canonaco, Pavia, Italy

Dg enhancements of triangulated categories and their uniqueness

10 Feb 2022
Matt Pressland, Glasgow, UK

Grassmannian twists categorified

17 Feb 2022
Sergey Mozgovoy, Dublin, Ireland

Wall-crossing structures arising from surfaces

24 Feb 2022
Sira Gratz, Glasgow, UK

When Aisles Meet

This talk is based on joint work with Alexandra Zvonareva, and with Thorsten Holm and Peter Jørgensen.


03 Mar 2022
Eleonore Faber, Leeds, UK

Matrix factorizations of some discriminants

In this talk, we consider discriminants of complex reflection groups. We identify certain matrix factorizations, whose corresponding Cohen-Macaulay modules give a noncommutative resolution of the discriminant. We will in particular consider the family of pseudo-reflection groups G(r,p,n), for which one can explicitly determine these matrix factorizations that are indexed by partitions, using higher Specht polynomials (work in progress with Colin Ingalls, Simon May, and Marco Talarico).

10 Mar 2022
Nick Sheridan, Edinburgh, UK

The Gamma and SYZ conjectures

I will give some background on the Gamma Conjecture, which says that mirror symmetry does *not* respect integral cycles: rather, the integral cycles on a complex manifold correspond to integral cycles on the symplectic mirror, multiplied by a certain transcendental characteristic class called the Gamma class. In the second part of the talk I will explain a new geometric approach to the Gamma Conjecture, which is based on the SYZ viewpoint on mirror symmetry. We find that the appearance of zeta(k) in the asymptotics of period integrals arises from the codimension-k singular locus of the SYZ fibration. This is based on joint work with Abouzaid, Ganatra, and Iritani.

17 Mar 2022
Daniel Labardini-Fragoso, UNAM, Mexico City/ Cologne, Germany

Gentle algebras arising from surfaces with orbifold points

Some years ago, Diego Velasco and I associated a gentle algebra to each triangulation of a polygon with one orbifold point of order three, and showed that the \tau-tilting combinatorics of this gentle algebra coincides with the combinatorics of flips of triangulations.

Moreover, we showed that whenever one mutates support \tau-tilting pairs, the corresponding Caldero-Chapoton functions obey a generalized cluster exchange formula, which means that the Caldero-Chapoton algebra is isomorphic to a generalized cluster algebra of Chekhov-Shapiro.


Generalizing the aforementioned work, in ongoing collaboration Lang Mou and I associate a gentle algebra to each triangulation of any unpunctured surface with orbifold points of order three. We are able to define generalized reflection functors and DWZ-like mutations of representations. This is somewhat surprising, since the quivers we consider are allowed to have loops, and the matrix-mutation classes of their skew-symmetrizable matrices may fail to have acyclic representatives.


24 Mar 2022
Fernando Muro, Sevilla, Spain

Enhanced n-angulated categories

These categories were introduced by Geiss, Keller, and Oppermann in order to encode the behaviour of n-cluster tilting subcategories of triangulated categories. In this talk I will define differential graded enhancements for these categories, analogous to those of Bondal and Kapranov for triangulated categories. I will present an existence and uniqueness theorem for n-angulated enhancements which holds, for instance, for the additivization of an n-cluster tilting object. As a corollary, I will deduce that a triangulated category with a (higher) cluster tilting object has a unique triangulated enhancement. This is joint work with Gustavo Jasso (Lund).

31 Mar 2022
Asilata Bapat, Canberra, Australia

The sphere of spherical objects

Consider the 2-Calabi--Yau triangulated category arising from the zigzag algebra of the An quiver. The braid group acts on this category by twists in spherical objects. Given a Bridgeland stability condition, we describe how to realise the spherical objects as a dense subset of a piecewise-linear manifold. This manifold is canonically associated to the category, and the braid group acts on it piecewise-linearly. We also describe how the manifold transforms under wall-crossings of the stability condition. The talk is based on joint work with Anand Deopurkar and Anthony M. Licata.

07 Apr 2022
Pavel Safronov, Edinburgh, UK

Euler structures and noncommutative volume forms

Calabi-Yau structures on dg categories provide a noncommutative analog of symplectic structures. In this talk I will introduce a noncommutative analog of volume forms called noncommutative Euler structures. I will give some examples of these and relate noncommutative Euler structures to string topology-type operations. An application of these ideas is the proof that the Goresky--Hingston string coproduct on the homology of free loop space is not homotopy invariant. If I have time, I will also discuss how Euler structures give rise to volume forms on derived mapping stacks. This is a report on work in progress joint with Florian Naef.

Sponsors and Funders:

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