Organisers
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Frank Neumann, University of Leicester
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Sibylle Schroll, University of Cologne
About:
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
| Speaker |
| Questions |
Past Events:
Representation theoretic aspects of scattering diagrams
Recording not available.
Gluing relative stability conditions along pushouts
Grassmannian braiding categorified
Hilbert schemes of points on singular surfaces: combinatorics, geometry, and representation theory
Graded decorated marked surfaces: Calabi-Yau-X categories of gentle algebras
Families of Gröbner Degenerations
Euler numbers of Hilbert schemes of points on simple surface singularities and quantum dimensions of standard modules of quantum affine algebras
Geometry of the Associative Yang-Baxter equation
On Generalized Hyperpolygons
A cup-cap duality in Koszul calculus
Deformations of path algebras of quivers with relations
Homological mirror symmetry for log Calabi-Yau surfaces
Structure of Grassmannian cluster categories
Koszul duality for dg-categories and infinity-categories
Joint work with J. Holstein.
opologically trivial automorphisms of compact Kähler surfaces and manifolds
Caldero-Chapoton formulas for generalized cluster algebras from orbifolds
Contraction algebras, plumbings and flops
On d-critical birational geometry and categorical DT theories
Birationality centers, rationality problems and Cremona groups
Hodge numbers of OG10 via Ngô strings
Categorical Interactions in Algebra, Geometry and Representation Theory
Multiplicative preprojective algebras in geometry and topology
A gluing construction for Ginzburg algebras of triangulate
Uniqueness of enhancements for derived and geometric categories
Derived symplectic geometry and AKSZ topological field theories
This seminar was not recorded.
Czech Republic - Spherical Objects on Cycles of Projective Lines and Transitivity
Derived equivalence classification of Brauer graph algebras
HiDEAs to work with
Subcategories of derived categories on affine schemes and projective curves
This talk was not recorded.
Scattering amplitudes from derived categories and cluster categories
On the Landau-Ginzburg/conformal field theory correspondence
On the Landau-Ginzburg/conformal field theory correspondence
Topological Hochschild cohomology for schemes
DT invariants of some 3CY quotients
A homological stroll into the algebraic theories of racks and quandles
This seminar was not recorded.
New 3CY categories of topological surfaces
Functorially finite hearts, simple-minded systems and negative cluster categories
Derived equivalences from mutations of ice quivers with potential
Minimal models for monomial algebras
Categorical dynamical systems arising from sign-stable mutation loops
The dg Leavitt path algebra, singular Yoneda category and singularity category
Finite approximations as a tool for studying triangulated categories
Triangulations of the Möbius strip and its connections with quasi-cluster algebras
Deformation theory of Cohomological Field Theories
Perverse sheaves and schobers on Riemann surfaces
A topological characterization of the Kashiwara-Vergne groups
Higher simple-minded systems in negative Calabi-Yau categories
Dg enhancements of triangulated categories and their uniqueness
Grassmannian twists categorified
Wall-crossing structures arising from surfaces
When Aisles Meet
This talk is based on joint work with Alexandra Zvonareva, and with Thorsten Holm and Peter Jørgensen.
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).
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.
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.
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).
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.
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.