Name: Fukaya Categories: Coefficients, Skeleta, Stability conditions
Start: 2018-07-02T09:30:00+02:00
End: 2018-07-07T13:30:00+02:00
Location: IHES

Fukaya Categories: Coefficients, Skeleta, Stability conditions

de lundi 2 juillet 2018 (09:30) à samedi 7 juillet 2018 (13:30)

lundi 2 juillet 2018

09:30 Welcome coffee
Welcome coffee
09:30 - 10:00
Room: Marilyn and James Simons Conference Center
10:00 Introduction to Stability Program - Maxim Kontsevich (IHES)
Introduction to Stability Program
- Maxim Kontsevich (IHES)
10:00 - 11:00
Room: Marilyn and James Simons Conference Center
11:15 Coffee Break
Coffee Break
11:15 - 11:30
Room: Marilyn and James Simons Conference Center
11:30 Towards a definition of the Fukaya-Seidel category with coefficients over the complex plane - C. Simpson
Towards a definition of the Fukaya-Seidel category with coefficients over the complex plane
- C. Simpson
11:30 - 12:30
Room: Marilyn and James Simons Conference Center In this segment of our joint work in progress with Haiden, Katzarkov and Pandit, we consider a graph in the plane. We propose a definition of the A-infinity category of objects over the graph, with coefficients in a fixed appropriate DG-category, including disk corrections corresponding to the regions in the plane cut out by the graph. We can write down an explicit set of A-infinity operations, and have a heuristic comparison with Abouzaid's definition that suggests why the A-infinity axioms should hold.
12:45 Buffet-lunch
Buffet-lunch
12:45 - 14:00
Room: Marilyn and James Simons Conference Center
14:00 A note on the associativity of multiplicative structure of quantum product of divisor complement - K. Fukaya
A note on the associativity of multiplicative structure of quantum product of divisor complement
- K. Fukaya
14:00 - 15:00
Room: Marilyn and James Simons Conference Center
15:15 Coffee break
Coffee break
15:15 - 15:30
Room: Marilyn and James Simons Conference Center
15:30 Structural results in wrapped Floer theory - S. Ganatra
Structural results in wrapped Floer theory
- S. Ganatra
15:30 - 16:30
Room: Marilyn and James Simons Conference Center
mardi 3 juillet 2018

09:30 Welcome coffee
Welcome coffee
09:30 - 10:00
Room: Marilyn and James Simons Conference Center
10:00 Fukaya category based on SFT - Maxim Kontsevich (IHES)
Fukaya category based on SFT
- Maxim Kontsevich (IHES)
10:00 - 11:00
Room: Marilyn and James Simons Conference Center
11:15 Coffee break
Coffee break
11:15 - 11:30
Room: Marilyn and James Simons Conference Center
11:30 Perverse schobers, Fukaya categories with coefficients and the "algebra of the infrared" - M. Kapranov
Perverse schobers, Fukaya categories with coefficients and the "algebra of the infrared"
- M. Kapranov
11:30 - 12:30
Room: Marilyn and James Simons Conference Center
12:45 Buffet-lunch
Buffet-lunch
12:45 - 14:00
Room: Marilyn and James Simons Conference Center
14:00 HMS for SYZ singularities via immersed Lagrangians - Mohammed Abouzaid
HMS for SYZ singularities via immersed Lagrangians
- Mohammed Abouzaid
14:00 - 15:00
Room: Marilyn and James Simons Conference Center
15:15 Coffee break
Coffee break
15:15 - 15:30
Room: Marilyn and James Simons Conference Center
15:30 Non-Kahler mirror symmetry: the Hopf surface - Denis Auroux
Non-Kahler mirror symmetry: the Hopf surface
- Denis Auroux
15:30 - 16:30
Room: Marilyn and James Simons Conference Center
16:45 Enumeration of non-archimedean curves in higher dimensional log Calabi-Yau varieties - T. Yue Yu
Enumeration of non-archimedean curves in higher dimensional log Calabi-Yau varieties
- T. Yue Yu
16:45 - 17:45
Room: Marilyn and James Simons Conference Center I will discuss the enumeration of non-archimedean curves in higher dimensional affine log Calabi-Yau varieties containing an open algebraic torus, part of my joint work with S. Keel. This generalizes the previously studied two-dimensional case, and includes cluster varieties arising from representation theory. Many new ideas are developed in order to go beyond the two-dimensional case. In my talk, I will explain various properties of the moduli spaces which lead to the enumeration. Moreover, I will introduce a new notion of “skeletal curves”, curves whose skeleton lies in the essential skeleton of the ambient log Calabi-Yau variety. Such curves play a special role in the theory.
18:00 Cocktail Party
Cocktail Party
18:00 - 20:00
Room: Marilyn and James Simons Conference Center
mercredi 4 juillet 2018

09:30 Welcome coffee
Welcome coffee
09:30 - 10:00
Room: Marilyn and James Simons Conference Center
10:00 Planar case: harmonic paths in buildings - Maxim Kontsevich (IHES)
Planar case: harmonic paths in buildings
- Maxim Kontsevich (IHES)
10:00 - 11:00
Room: Marilyn and James Simons Conference Center
11:00 Coffee break
Coffee break
11:00 - 11:15
Room: Marilyn and James Simons Conference Center
11:15 Spectral networks and stability conditions: finite and tame examples - Fabian Haiden
Spectral networks and stability conditions: finite and tame examples
- Fabian Haiden
11:15 - 12:15
Room: Marilyn and James Simons Conference Center Spectral networks were introduced in theoretical physics in order to count BPS states. They are graphs with additional algebraic data drawn on a surface and minimizing a weighted total length. Heuristically, they are degenerations of higher dimensional special Lagrangian submanifolds. The main mathematical conjecture about them is that they correspond to stable objects of a stability condition on a Fukaya-type category. I will illustrate how this works in some neat examples related to Dynkin quivers and stacky projective lines. This is an ongoing joint project with L. Katzarkov, M. Kontsevich, P. Pandit, and C. Simpson.
12:30 Toward a categorical Donaldson-Uhlenbeck-Yau correspondence - Pranav Pandit
Toward a categorical Donaldson-Uhlenbeck-Yau correspondence
- Pranav Pandit
12:30 - 13:30
Room: Marilyn and James Simons Conference Center
13:30 Buffet-lunch
Buffet-lunch
13:30 - 14:30
Room: Marilyn and James Simons Conference Center
jeudi 5 juillet 2018

09:30 Welcome coffee
Welcome coffee
09:30 - 10:00
Room: Marilyn and James Simons Conference Center
10:00 Chekanov-Eliashberg dg-algebras for Weinstein domains in contact manifolds - Tobias Ekholm
Chekanov-Eliashberg dg-algebras for Weinstein domains in contact manifolds
- Tobias Ekholm
10:00 - 11:00
Room: Marilyn and James Simons Conference Center Let W be a Weinstein manifold then the product of W and the real line is naturally a contact manifold. We consider contact embeddings of a small neighborhood a W-slice in this manifold and construct the Chekanov-Eliashberg dg-algebra of such embeddings. When W is a cotangent neighborhood of a smooth Legendrian the definition agrees with the Chekanov-Eliashberg algebra of the smooth Legendrian with coefficients in chains in the based loop space. The construction gives gluing formulas for Fukaya categories.
11:15 Coffee break
Coffee break
11:15 - 11:30
Room: Marilyn and James Simons Conference Center
11:30 Axiomatics of the wrapped Fukaya category - Vivek Shende
Axiomatics of the wrapped Fukaya category
- Vivek Shende
11:30 - 12:30
Room: Marilyn and James Simons Conference Center
12:45 Buffet-lunch
Buffet-lunch
12:45 - 14:00
Room: Marilyn and James Simons Conference Center
14:00 Schobers on orbifold Riemann surfaces - Alexey Bondal
Schobers on orbifold Riemann surfaces
- Alexey Bondal
14:00 - 15:00
Room: Marilyn and James Simons Conference Center
15:15 Coffee break
Coffee break
15:15 - 15:30
Room: Marilyn and James Simons Conference Center
15:30 Enhancement for categories - Dmitry Kaledin
Enhancement for categories
- Dmitry Kaledin
15:30 - 16:30
Room: Marilyn and James Simons Conference Center
vendredi 6 juillet 2018

09:30 Welcome coffee
Welcome coffee
09:30 - 10:00
Room: Marilyn and James Simons Conference Center
10:00 Self-organized criticality and tropical geometry - Ernesto Lupercio (Cinvestav - México)
Self-organized criticality and tropical geometry
- Ernesto Lupercio (Cinvestav - México)
10:00 - 11:00
Room: Marilyn and James Simons Conference Center In this talk, I describe our joint work with Kalinin, Guzmán-Saenz, Prieto, Shkolnikov, and Kalinina involving the relation of systems in physics with Self-organized criticality (like earthquakes) and the mathematics of tropical geometry, in particular, we construct a continuous dynamical system in tropical geometry that exhibits self-organized criticality.
11:15 Coffee break
Coffee break
11:15 - 11:30
Room: Marilyn and James Simons Conference Center
11:30 On the localizing invariants of derived categories of sheaves of modules - Alexander Efimov
On the localizing invariants of derived categories of sheaves of modules
- Alexander Efimov
11:30 - 12:30
Room: Marilyn and James Simons Conference Center
12:45 Buffet-lunch
Buffet-lunch
12:45 - 14:00
Room: Marilyn and James Simons Conference Center
14:00 Deformations of Calabi-Yau categories and Poisson brackets of functions - Chris Brav
Deformations of Calabi-Yau categories and Poisson brackets of functions
- Chris Brav
14:00 - 15:00
Room: Marilyn and James Simons Conference Center We explicate two deformation problems for a smooth Calabi-Yau category C, showing in particular that the complexes underlying the Lie algebras controlling these deformation problems are shifts of negative cyclic and of cylic chains of C. Using these results, we show that the natural map from cyclic chains of C to functions on the `moduli of objects’ M_C is a map of (shifted) Lie algebras with respect to the deformation-theoretic Lie structure on cyclic chains and the Poisson bracket on functions induced by the Calabi-Yau structure on C. Our results give a chain level generalisations of classical constructions of Goldman for moduli of local systems and of Hitchin for GL(n)-Higgs bundles. This is joint work with Nick Rozenblyum.
15:15 Coffee break
Coffee break
15:15 - 15:30
Room: Marilyn and James Simons Conference Center
15:30 Toric Schobers and D-modules - Paul Horja
Toric Schobers and D-modules
- Paul Horja
15:30 - 16:30
Room: Marilyn and James Simons Conference Center
samedi 7 juillet 2018
10:00 Non-commutative curve-counting invariants - G. Dimitrov
Non-commutative curve-counting invariants
- G. Dimitrov
10:00 - 11:00
Room: Marilyn and James Simons Conference Center In a joint work with L. Katzarkov to data A,P,G,T, where A and T are triangulated categories, we attach a set whose elements are equivalence classes of fully faithful exact functors (from A to T) with property P. The equivalence relation, which will be explained in the talk, depends on G. We are interested in counting and intersection of the elements in this set. In this talk I will give more details and some examples.
11:15 TBA - A. Harder
TBA
- A. Harder
11:15 - 12:15
Room: Marilyn and James Simons Conference Center
12:30 Doubling stops and spherical swaps - Zack Sylvan
Doubling stops and spherical swaps
- Zack Sylvan
12:30 - 13:30
Room: Marilyn and James Simons Conference Center