Cheol-Hyun Cho

- Title: Gluing localized homological mirror functors 

- Abstract: Using formal deformation theory of a reference Lagrangian submanifold L, we can define a localized mirror functor from Fukaya category to the matrix factorization category of the potential function of L. It is called localized since the functor is non-trivial only for Lagrangians having non-trivial Floer homology with the chosen reference L. Given two different reference Lagrangian submanifolds, we explain how to glue two localized mirror functors to obtain a global functor. As an example, we discuss the case of punctured Riemann surfaces. This is a joint work in progress with Hansol Hong and Siu-Cheong Lau 

Chris Elliott

- Title: Singular Support Conditions for Coherent Sheaves Coming From Vacua

- Abstract: The notion of the singular support of a coherent sheaf was introduced by Arinkin and Gaitsgory in order to properly formulate the categorical geometric Langlands conjecture. In this talk I'll explain a natural physical origin for these singular support conditions as support conditions in the moduli space of vacua of the B-model. In particular we'll see how the singular support condition for geometric Langlands comes from applying this idea to Kapustin and Witten's family of gauge theories and discuss some conjectures related to a novel factorization structure on the geometric Langlands categories. This is joint work with Philsang Yoo.

John Francis

- Title: Factorization homology and the cobordism hypothesis

- Abstract: Factorization homology offers a multiplicative analogue of ordinary homology. Ordinary homology "integrates" an abelian group or chain complex over the moduli space of open subspaces of an n-manifold X. The result takes disjoint unions of manifolds to direct sums of chain complexes. The alpha version of factorization homology "integrates" an n-disk algebra over the Ran space-the space of finite subsets of X, topologized so that points can collide. Ran spaces have been studied in diverse works from Borsuk-Ulam and Bott, to Beilinson-Drinfeld, Gaitsgory-Lurie and others. The alpha form of factorization homology is the sheaf homology of Ran(X) with coefficients defined by an n-disk algebra A. Factorization homology simultaneously generalizes singular homology and Hochschild homology. I'll discuss applications of this alpha form of factorization homology in the study of mapping spaces in algebraic topology, bundles on algebraic curves, and perturbative quantum field theory.

I'll also describe a beta form of factorization homology, where one replaces Ran(X) with a moduli space of stratifications of X, designed to overcome certain strict limitations of the alpha form. One can "integrate" an n-category over over the moduli space of vari-framed stratifications. One such application, in work-in-progress with David Ayala, is to proving the Cobordism Hypothesis, after Baez-Dolan, Costello, Hopkins-Lurie, and Lurie. This asserts that for a suitable target C, there is an equivalence TQFT(C) = obj(C) between C-valued framed topological field theories and objects of C.

Gregory Ginot

- Title: Introduction to derived geometry and brane actions.

- Abstract: The series of lectures is meant as an introduction for objects and techniques useful for the rest of the conference. The first talk will give a short introduction to derived geometry while the second talk will focus on (infty)-operads and in particular the En structure carried in correspondence by mapping stacks with source a sphere which can be seen as partial instance of TFT.

Rune Haugseng

- Title: The AKSZ construction in derived algebraic geometry as an extended TQFT

- Abstract: The AKSZ construction, as implemented by Pantev-To?n-Vaqui?-Vezzosi in the context of derived algebraic geometry, gives a symplectic structure on the derived stack of maps from an oriented compact manifold to a symplectic derived stack. I  will describe how this gives rise to a family of extended topological field theories valued in higher categories of symplectic derived stacks, with the higher morphisms given by a notion of higher Lagrangian correspondences. This is joint work in progress with Damien Calaque and Claudia Scheimbauer.

Etienne Mann

- Title : Quantum D modules and mirror symmetry 

- Abstract: In this talk, we will present how a quantum D module is a generalization of Hodge structure. One can construct these structures from different fields of mathematics so that they are very useful to express mirror symmetry. We will also make the link with Givental's cone.

Byungdo Park

- Title: A classification of equivariant gerbe connections

- Abstract: U(1)-banded gerbes are geometric objects representing degree 3 integral cohomology classes of the base space, just as U(1)-bundles represent elements of one lower degree cohomology group via the first Chern class. It has been used frequently for both mathematical and physical problems; for example in twisted K-theory and D-brane charge classifications, Wess-Zumino-Witten terms, string structures, and more recently topological insulators. I would like to talk about a joint work with Corbett Redden on an equivalence between the 2-groupoid of U(1)-bundle gerbe connections on a differential quotient stack defined via simplicial sheaves and the 2-groupoid of equivariant bundle gerbe connections. Differential geometry and topology of bundle gerbes as well as an introduction to differential cohomology will be discussed.

Marco Robalo

- Title: Derived Algebraic Geometry, Matrix Factorisations and Vanishing Cycles

- Abstract: In this lectures we will start with a review the classical theory of matrix factorisation categories and explain how their 2-periodic structures can be obtained via derived algebraic geometry. This follows from results of A. Preygel in zero characteristic, and joint work with B. Toen, G. Vezzosi and A. Blanc over general basis. We will review Orlov’s equivalence between matrix factorisations and categories of singularities and to conclude I will report a result obtained in collaboration with A.Blanc, B. Toen, and G. Vezzosi, establishing a link between the l-adic realization of the dg-categories of singularities and l-adic vanishing cycles.

Vivek Shende

- Title: Localization of the Fukaya category, microlocal sheaves, and mirror symmetry.

- Abstract: I’ll discuss why the wrapped Fukaya category of an exact symplectic manifold localizes to a cosheaf of categories on the skeleton; how to compute the resulting cosheaf, and the consequences for mirror symmetry.

Hiro Lee Tanaka

- Title: Morse theory and a stack of Broken Lines

- Abstract: In my two hours, I'll talk about efforts to rephrase Morse theory as a deformation problem. This requires some discussion of stacks and sheaves on stacks. If time allows, I'll also talk about how this relates to Lagrangian Floer theory--the end goal is to give an enrichment of Fukaya categories over spectra, while still staying true to the basic geometry of Fukaya categories. This is joint work with Jacob Lurie.