Introduction to Stability Program

• Maxim Kontsevich (IHES)

Room: Marilyn and James Simons Conference Center

Towards a definition of the Fukaya-Seidel category with coefficients over the complex plane

• C. Simpson

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.

A note on the associativity of multiplicative structure of quantum product of divisor complement

• K. Fukaya

Room: Marilyn and James Simons Conference Center

Structural results in wrapped Floer theory

• S. Ganatra

Room: Marilyn and James Simons Conference Center

Fukaya category based on SFT

• Maxim Kontsevich (IHES)

Room: Marilyn and James Simons Conference Center

Perverse schobers, Fukaya categories with coefficients and the "algebra of the infrared"

• M. Kapranov

Room: Marilyn and James Simons Conference Center

HMS for SYZ singularities via immersed Lagrangians

• Mohammed Abouzaid

Room: Marilyn and James Simons Conference Center

Non-Kahler mirror symmetry: the Hopf surface

• Denis Auroux

Room: Marilyn and James Simons Conference Center

Enumeration of non-archimedean curves in higher dimensional log Calabi-Yau varieties

• T. Yue Yu

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.

Planar case: harmonic paths in buildings

• Maxim Kontsevich (IHES)

Room: Marilyn and James Simons Conference Center

Spectral networks and stability conditions: finite and tame examples

• Fabian Haiden

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.

Toward a categorical Donaldson-Uhlenbeck-Yau correspondence

• Pranav Pandit

Room: Marilyn and James Simons Conference Center

Chekanov-Eliashberg dg-algebras for Weinstein domains in contact manifolds

• Tobias Ekholm

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.

Axiomatics of the wrapped Fukaya category

• Vivek Shende

Room: Marilyn and James Simons Conference Center

Schobers on orbifold Riemann surfaces

• Alexey Bondal

Room: Marilyn and James Simons Conference Center

Enhancement for categories

• Dmitry Kaledin

Room: Marilyn and James Simons Conference Center

Self-organized criticality and tropical geometry

• Ernesto Lupercio (Cinvestav - México)

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.

On the localizing invariants of derived categories of sheaves of modules

• Alexander Efimov

Room: Marilyn and James Simons Conference Center

Deformations of Calabi-Yau categories and Poisson brackets of functions

• Chris Brav

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.

Toric Schobers and D-modules

• Paul Horja

Room: Marilyn and James Simons Conference Center

Non-commutative curve-counting invariants

• G. Dimitrov

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.

TBA

• A. Harder

Room: Marilyn and James Simons Conference Center

Doubling stops and spherical swaps

• Zack Sylvan

Room: Marilyn and James Simons Conference Center