• Will Donovan

Title: Perverse schobers on mirror moduli spaces

Abstract: The moduli spaces associated to the A-side and B-side of mirror symmetry carry much-studied bundles with connections, which may be related by a mirror map. I explain a categorification of such structures for certain surface and 3-fold examples, and prove homological mirror symmetry statements for these, joint with T Kuwakagi. This uses perverse sheaves of categories, as introduced by Kapranov and Schechtman. For a flopping projective line in a general 3-fold, I describe a new candidate for an associated B-side moduli space, and construct a local system of categories on it, joint with M Wemyss.

• Timothy Logvinenko

Title: Perverse schobers and orbifolds

Abstract: Perverse schobers are a recent notion introduced by Kapranov and Schechtman which is a categorification of perverse sheaves on a stratified topological space. In this talk, I will talk about a joint work with Alexei Bondal where we study perverse sheaves on an orbifold Riemann surface, their categorification to perverse schobers and related categorical structures

• Tatsuki Kuwagaki

Title: Categorification of Legendrian knots

Abstract: In the definition of perverse schobers by Kapranov--Schechtman, certain purity statement for perverse sheaves plays a key role. I will talk about a similar story in the real setting. For constructible sheaves, there exists a similar purity notion originally introduced by Kashiwara--Schapira. In particular, for R-constructible sheaves over the line/plane, one can define their categorification, which include the notions: semi-orthogonal decomposition, a pair of a category and an endofunctor, mutation, N-spherical functor, and irregular perverse schober.

• Ludmil Katrarkov

Title: Categorical curve complexes

Abstract: In this talk we will introduce new categorical construction anddiscuss possible applications to classical problems.

• Takehiko Yasuda

Title: A moduli problem in the wild McKay correspondence

Abstract: A certain moduli space appears in a conjectural generalization of the motivic McKay correspondence to positive characteristics. I will talk about construction of this moduli space. If time permits, I will discuss formulas for motivic integrals on this space, which can be regarded as motivic versions of mass formulae by Serre and Bhargava. This is a joint work with Fabio Tonini.

• Kazushi Ueda

Title: Homological mirror symmetry for Milnor fibers of invertible polynomials

Abstract: We discuss the relation between the Fukaya category of the Milnor fiber of an invertible polynomial and graded matrix factorizations of the Berglund-Hubsch transpose with one term added, using the description of the Milnor fiber as a partial compactification of a cover of a pair of pants. If the time permits, we will also discuss Sebastiani-Thom formula for the Fukaya category and permutohedral skeletons for Brieskorn-Pham singularities. This is a joint work in progress with Yanki Lekili.

• Genki Ouchi

Title: Symplectic automorphism groups of cubic fourfolds and K3 categories

Abstract: Gaberdiel, Hohenegger and Volpato (GHV) characterized automorphism groups of K3 sigma models in terms of Mukai lattice and Leech lattice. Huybrechts gave a geometric interpretation of GHV Theorem in terms of derived categories of K3 surfaces and Bridgeland stability conditions on them. In this talk, I would like to characterize symplectic automorphism groups of cubic fourfolds as automorphism groups of certain K3 sigma models using Bridgeland stability conditions on Kuznetsov’s K3 categories due to Bayer, Lahoz, Macri and Stellari.

• Yukinobu Toda

Title: Semiorthogonal decompositions under d-critical flips

Abstract: I will give semiorthogonal decompositions of derived categories of coherent sheaves in the following cases:

(1) Pandharipande-Thomas stable pair moduli spaces on CY 3-folds

(2) relative Hilbert schemes of points on K3 surfaces

(3) Thaddeus pair moduli spaces on smooth projective curves (work in progress with Naoki Koseki)

In all the cases, the SOD are constructed via d-critical flips, which are interpreted as virtual birational maps. The resulting SOD are interpreted as d-critical analogue of Bondal-Orlov, Kawamata’s D/K equivalence conjecture, and also categorifications of wall-crossing formula of Donaldson-Thomas invariants.

• Bertrand Toen

Title: The universal Hodge filtration

Abstract: In this talk I will present an object called the "universal Hodge filtration" and which is responsible for the existence of Hodge filtrations in a universal way. For this, based on ideas coming from rational and p-adic homotopy theory, I will construct the "filtered circle" (and more generaly filtered spheres), which by mapping to varieties or schemes/stacks recovers the usual Hodge filtrations on de Rham cohomology. The filtered circle exists over the ring of integers, and I will explain how this can be used in order to extend the theory of shifted symplectic structures out of the characteristic zero case.

• Yuki Hirano

Title: Derived factorization categories of non-Thom--Sebastiani-type sum of potentials

Abstract: In this talk, I will explain new Orlov-type semi-orthogonal decompositions associated to sum of potentials of certain gauged LG models that is not necessarily Thom--Sebastiani sum. I also explain that this result gives a semi-orthogonal decomposition of the homotopy category of maximally graded matrix factorizations of an invertible polynomial $f$ of chain type, and that this shows the existence of a full exceptional collection on the category whose length is equal to the Milnor number of the Berglund--H\"ubsch transpose of $f$. This is a joint work with Genki Ouchi.

• Valery Lunts

Title: 3 notions of dimension for triangulated categories

Abstract: We propose to study 3 notions of dimension for triangulated categories of the form Perf(A), where $A$ is a smooth and compact dg algebra over a field. These are the Rouquier dimension, Serre dimension and the diagonal dimension. We test some basic properties of these dimensions and compute some interesting examples. We also propose some conjectures. This is a joint work with Alexey Elagin.

• Shinobu Hosono

Title: K3 surfaces from configurations of six lines in ${\mathbb P}^2$ and mirror symmetry

Abstract: I will study a family K3 surfaces which are given as double covers of ${\mathbb P}^2$ branched along six lines in general position. Period integrals of this family satisfy the hypergeometric system E(3,6), i.e., Aomoto-Gel'fand hypergeometric system on Grassmannian G(3,6), which were studied in detail by Matsumoto, Sasaki and Yoshida in the 90's. In this talk, I will focus on the parameter space of the E(3,6) system described naturally by GIT or Baily-Borel-Satake compactification. I will find that the E(3,6) system is "locally trivialized" by corresponding GKZ systems. Based on this result, and making suitable resolutions of the compactified parameter sapce, I will obtain the desired LCSLs (large complex structure limits) where we can read off mirror symmetry by applying the generalized Frobenius method formulated in the 90's. This talk is based on a recent collaboration with B. Lian, H. Takagi.

• Alexander Kuznetsov

Title: Semiorthogonal decompositions of singular surfaces

Abstract: It is well known that any smooth projective toric surface has a full exceptional collection. I will talk about a generalization of this fact for singular surfaces. First, if the class group of Weil divisors of the surface is torsion free (for instance, this holds for all weighted projective planes), I will construct a semiorthogonal decomposition of the derived category with components equivalent to derived categories of modules over certain local finite dimensional algebras. When the class group has torsion, a similar semiorthogonal decomposition will be constructed for an appropriately twisted derived category. Many of these results extend to non-necessarily toric rational surfaces. This is a joint work with Joseph Karmazyn and Evgeny Shinder.

• Michel Van den Bergh

Title: Tilting bundles on hypertoric varieties

Abstract:

• Christopher Brav

Title: Differential forms and polyvector fields on the mother of all moduli spaces

Abstract: Given a nice dg category C, we construct differential forms and polyvector fields on $M_C$ , the 'moduli space of objects in C', using respectively negative cyclic chains of C and cyclic chains of Calabi-Yau completions of C. We discuss applications to shifted Poisson geometry. This talk is based on two different projects, one with T. Dyckherhoff and the other with N. Rozenblyum.

• Agnieszka Bodzenta

Title: Homological characterization of highest weight categories

Abstract: In my talk I will discuss highest weight categories. I will prove that a finite length abelian category is highest weight if it has two full exceptional collections of pure objects, one dual to another. I will also discuss when a restriction of an arbitrary t-structure has a highest weight heart.

• Sergey Galkin

Title: Fourth symmetric powers and twisted cubics

Abstract: I will review recent work of Pavel Popov (part of which is joint with me) that looks for relations between fourth symmetric powers of a cubic hypersurface and variety of twisted cubics on various levels: categorical, analytic, stably birational, motivic. arXiv:1810.07001 and 1810.04563.

• Hiroshi Iritani

Title: Gamma conjecture from tropical geometry

Abstract: I will explain how zeta values will appear in the asymptotics of periods near the large complex structure limit, using tropical geometry. This is based on joint work with Abouzaid, Ganatra and Sheridan.