The CMSA will be hosting a threeday Simons Collaboration Workshop on Homological Mirror Symmetry and Hodge Theory on April 57, 2018. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.
Please click here to register for this event. We have space for up to 30 registrants on a first come, first serve basis.
We may be able to provide some financial support for grad students and postdocs interested in this event. If you are interested in funding, please send a letter of support from your mentor to Hansol Hong at hansol84@gmail.com.
Confirmed Speakers:
 Jacob Bourjaily (Niels Bohr Institute)
 Mandy Cheung (Havard University)
 Tristan Collins (Harvard University)
 Yoosik Kim (Boston University)
 YuShen Lin (Harvard University)
 CheukYu Mak (Cambridge University)
 Yu Pan (MIT)
 Mauricio Romo (Tsinghua University)
 ShuHeng Shao (IAS)
 Zack Sylvan (Columbia University)
 Dmitry Vaintrob (IAS)
The schedule is as follows:
Thursday 4/5/2018
Time  Speaker  Title/Abstract 
12:001:30pm  Lunch  
1:302:30pm  Tristan Collins  Title: BPS Bbranes and stability
Abstract: I will give a short introduction to the deformed HermitianYangMills equation and discuss the (conjectural/motivational) relationship with stability in the sense of Bridgeland.
This talk will cover joint work with A. Jacob, D. Xie, and S.T. Yau.

2:302:45pm  Break  
2:453:45pm  Dimitry Vaintrob  Title: Operads and circle actions
Abstract: Cohomology of the topological operad FLD of framed little disks (a.k.a. the BV operad) acts on the Hochschild homology of any CalabiYau algebra. Cohomology of the related topological operad of marked nodal genus zero curves acts on a deformation of the cohomology of any symplectic manifold, and this action is responsible for all quantum product operations. It was proven by Bruno Vallette and Drummond Cole that an action of $\mathbb{Q}$homology of the operad of marked nodal curves is equivalent, in genus zero, to an action of the homology of the operad of framed little disks together with a trivialization, in a homotopytheoretic sense, of the BV operator $\Delta$. In a later paper DrummondCole showed that this result holds in a certain category of topological operads, so that in particular it is also true (on the dg level) for cohomology with coefficients in $\mathbb{Z}$ (or in an arbitrary field). In work with Alex Oancea we give a higher genus version of this result, using Segal moduli spaces of curves with parametrized boundary and their compactifications. Time permitting, I will also mention certain motivic enhancements of our result (based on more recent work) which give compatibility with Galois actions and de Rham lattices on the two sides, a result already new in genus zero. 
3:454:15pm  Break  
4:155:15pm  Mandy Cheung  Title: Counting tropical curves by quiver representation
Abstract: The work of GrossHackingKeelKontsevich tell the relation between scattering diagrams and cluster algebras. In the talk, we will describe those objects with quiver representations. After that, we will give a expression of tropical curves counting by quiver representations. This is a joint work in progress with Travis Mandel. 
Friday 4/6/2018
Time  Speaker  Title/Abstract 
9:00 – 9:30am  Breakfast  
9:3010:30 am  Zack Sylvan  
10:3011:00am  Break  
11:0012:00pm  Yu Pan  Title: Augmentations categories and exact Lagrangian cobordisms.
Abstract: To a Legendrian knot, one can associate an $A_{\infty}$ category, the augmentation category. An exact Lagrangian cobordism between two Legendrianknots gives a functor of the augmentation categories of the two knots. We study the functor and establish a long exact sequence relating the corresponding cohomologyof morphisms of the two ends. As applications, we prove that the functor between augmentation categories is injective on the level of equivalence classes of objects and find new obstructions to the existence of exact Lagrangian cobordisms in terms of linearized contact homology and ruling polynomials.

12:001:30pm  Lunch  
1:302:30pm  CheukYu Mak  Title: Tropically constructed Lagrangians in mirror quintic threefolds
Abstract: In this talk, we will explain how to construct closed Lagrangian submanifolds in mirror quintic threefolds using tropical curves and the toricdegeneration technique. As an example, we will illustrate how the corresponding Lagrangians look like for tropical curves that contribute to the Gromov–Witteninvariant of the line class of the quintic threefold. We will also show that multiplicity of a tropical curve, in this symplectic setting, will be realized as the order of the torsion the first homology group of the Lagrangian. This is a joint work with Helge Ruddat.

2:302:45pm  Break  
2:453:45pm  YuShen Lin  
3:454:15pm  Break  
4:155:15pm  Yoosik Kim  Title: Mirror construction of Grassmannians via immersed Lagrangian Floer theory
Abstract: A partial flag manifold admits a completely integrable system, socalled a GelfandCetlin system, constructed by GuilleminSternberg. The fibers of the system are almost like toric fibers. However, as the big torus action does not extend to boundary strata, nontoric Lagrangian fibers may appear at a boundary stratum. In the first part of the talk, we classify all Lagrangian fibers on partial flag manifolds of various types. After discussing it, we exhibit a construction of a mirror of some low dimensional Grassmannians using StromingerYauZaslow mirror symmetry. To incorporate nontoric Lagrangian fibers, which are sometimes nonzero objects in the Fukaya category, we produce immersed Lagrangians arising from smoothing faces containing a face having nontoric Lagrangian. We then glue deformation spaces of Lagrangians to obtain the Rietsch mirror. This talk is based on joint work with Yunhyung Cho and YongGeun Oh, and ongoing joint work with Hansol Hong and SiuCheong Lau. 
Saturday 4/7/2018
Time  Speaker  Title/Abstract 
8:309:00am  Breakfast  
9:0010:00am  Jacob Bourjaily 
Title: Stratifying OnShell Cluster Varieties
Abstract: There exists a deep correspondence between a class of physically important functions—called “onshell functions”—and certain (cluster variety) subspaces of Grassmannian manifolds, endowed with a volume form that is left invariant under cluster coordinate transformations. These are called “onshell varieties” (which may or may not include all cluster varieties). It is easy to prove that the number of onshell varieties is finite, from which it follows that the same is true for onshell functions. This is powerful and surprising for physics, because these onshell functions encode complete information about perturbative quantum field theory.
In this talk, I describe the details of this correspondence and how it is constructed and give the broad physics motivations for obtaining a more systematic understanding of onshell cluster varieties. I outline a general, bruteforce strategy for classifying these spaces; and describe the results found by applying this strategy to the case of Gr(3,6).

10:0010:15am  Break  
10:1511:15am  ShuHeng Shao  Title: Vertex Operator Algebra, WallCrossing Invariants, and Physics
Abstract: Motivated by fourdimensional conformal field theory with N=2 supersymmetry, we discuss an interesting relation between vertex operator algebras (VOAs) and KontsevichSoibelman wallcrossing. We discuss a conjectured formula for the vacuum character of this VOA from the associated KontsevichSoibelman wallcrossing invariant of the fourdimensional field theory. We further generalize this proposal to include extended supersymmetric objects, known as line defects and surface defects, into the fourdimensional field theory. Each such defect gives rise to a module of the associated VOA and we propose a formula for the character of this module. 
11:1511:30am  Break  
11:3012:30pm  Mauricio Romo  Title: Aspects of Btwisted (2,2) and (0,2) hybrid models
Abstract: I will talk about properties and definition of certain sphere correlators for elements on the chiral ring of Btwisted hybrid models for the case they posses (2,2) and (0,2) supersymmetry. I will review these models and their Bchiral ring. I will present some interesting analytic properties of these correlators and some sufficient criteria for the absence of instanton corrections in the (0,2) case.
