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:
The schedule is as follows:
Thursday 4/4/2018
Time  Speaker  Title/Abstract 
12:001:30pm  Lunch  
1:302:30pm  Tristan Collins  
2:302:45pm  Break  
2:453:45pm  Dimitry Vaintrob  
3:454:15pm  Break  
4:155:15pm  Mandy Cheung 
Friday 4/5/2018
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 
Saturday 4/6/2018
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  
11:1511:30am  Break  
11:3012:30pm  Mauricio Romo 
The organizing committee consists of Yang Wang (HKUST), Ronald Lui (CUHK), David Gu (Stony Brook), and ShingTung Yau (Harvard).
Please click here to register for the event.
Confirmed Speakers:
This event is supported by the CMSA and the NSF.
Schedule:
Saturday, March 24
Time………….  Speaker  Title/Abstract 
9:009:30am  Breakfast & opening speech  
9:3010:30am  Stephen Wong
Houston Methodist/Weill Cornell Medicine 
Title: Applications of deep learning in pathologic image diagnosis and high content screening 
10:3011:00am  Break  
11:0012:00pm  Lakshminarayanan Mahadevan
Harvard University 
Title: Programming Shape 
12:001:30pm  Lunch  
1:302:30pm  Monica Hurdal
Florida State University 
Title: Geometry, Computation, and Modeling the Folding Patterns of the Human Brain
Abstract: The folding patterns of each brain are unique. There is much controversy in the biological community as to how the folding patterns of the brain develop and if the folding patterns can be used to identify and diagnose disease. In this presentation, I will discuss some of the mathematical and modeling approaches my research group is using to investigate these topics. Conformal mapping, topology, and Turing patterns are some of the methods we are using to characterize and model the folding patterns of the human brain in development, health, and disease. 
2:302:45pm  Break  
2:453:45pm  Allen Tannenbaum
Stony Brook University 
Title: Optimal Mass Transport for MatrixValued Densities: A Quantum Mechanical Approach
Abstract: Optimal mass transport is a rich area of research with applications to numerous disciplines including econometrics, fluid dynamics, automatic control, transportation, statistical physics, shape optimization, expert systems, image processing, and meteorology. In this talk, we describe a noncommutative counterpart of optimal transport where density matrices (i.e., Hermitian matrices that are positivedefinite and have unit trace) replace probability distributions, and where “transport” corresponds to a flow on the space of such matrices that minimizes a corresponding action integral. We employ generalizations of the seminal approach of Benamou and Brenier. In particular, we utilize ideas from quantum mechanics in a Benamou–Brenier framework. Our version of noncommutative optimal mass transport allows us to define geodesics on the space of positivedensities. Applications are given to diffusion tensor MR data. This is joint work with Yongxin Chen and Tryphon Georgiou. 
3:454:15pm  Break  
4:155:15pm  David Gu
Stony Brook University 
Title: A Geometric View to Generative Models
Abstract: In this work, we show the intrinsic relations between optimal transportation and convex geometry, especially the variational approach to solve Alexandrov problem: constructing a convex polytope with prescribed face normals and volumes. This leads to a geometric interpretation to generative models, and leads to a novel framework for generative models. By using the optimal transportation view of GAN model, we show that the discriminator computes the Kantorovich potential, the generator calculates the transportation map. For a large class of transportation costs, the Kantorovich potential can give the optimal transportation map by a closeform formula. Therefore, it is sufficient to solely optimize the discriminator. This shows the adversarial competition can be avoided, and the computational architecture can be simplified. Preliminary experimental results show the geometric method outperforms WGAN for approximating probability measures with multiple clusters in low dimensional space. 
5:156:15pm 
Sunday, March 25
Time………….  Speaker………..  Title/Abstract 
9:009:30am  Breakfast  
9:3010:30am  Hongkai Zhao
University of California, Irvine 
Title: A scaling law for the intrinsic complexity of high frequency wave fields, random fields and random matrices
Abstract: We characterize the intrinsic complexity of a set S in a metric space W by the least dimension N of a linear space V ⊂ W that can approximate S to an error. We show a scaling law for N for high frequency wave fields in term of the wavelength, for random fields in term of the correlation length, and for a set of random vectors in term of the dimension. 
10:3011:00am  Break  
11:0012:00pm  Guowei Wei
Michigan State University 
Title: Is it time for a great chemistry between mathematics and biology?
Abstract: In the history of science, mathematics has been a great partner of natural science, except for biology. The Hodgkin–Huxley model and Turing model indicate the union between mathematics and biology in the old days. However, in 1960s, biology became microscopic, i.e., molecular, while mathematics became abstract. They have been on two divergent paths since then. Modern biology, including molecular biology, structural biology, cell biology, evolutionary biology, biochemistry, biophysics, genetics, etc. are intimidating to mathematicians, while advanced mathematics, such as algebra, topology, geometry, graph theory, and analysis are equally frightening to biologists. Fortunately, biology assumed an omics dimension around the dawn of the millennium. The exponential growth of biological data has paved the way for biology to undertake a historic transition from being qualitative, phenomenological and descriptive to being quantitative, analytical and predictive. Such a transition offers both unprecedented opportunities and formidable challenges for mathematicians, just as quantum physics did a century ago. I will discuss how deep learning and mathematics, including algebraic topology, differential geometry, graph theory, and partial differential equation, lead my team to be a top performer in recent two D3R Grand Challenges, a worldwide competition series in computeraided drug design and discovery. It is time for mathematics to embrace modern biology. 
12:001:30pm  Lunch  
1:302:30pm  Laurent Demanet
MIT 
Title: 1930s Analysis for 2010s Signal Processing: Recent Progress on the Superresolution Question
Abstract: The ability to access signal features below the diffraction limit of an imaging system is a delicate nonlinear phenomenon called superresolution. The main theoretical question in this area is still mostly open: it concerns the precise balance of noise, bandwidth, and signal structure that enables superresolved recovery. When structure is understood as sparsity on a grid, we show that there is a precise scaling law that extends ShannonNyquist theory, and which governs the asymptotic performance of a class of simple “subspacebased” algorithms. This law is universal in the minimax sense that no statistical estimator can outperform it significantly. By contrast, compressed sensing is in many cases suboptimal for the same task. Joint work with Nam Nguyen. 
2:302:45pm  Break  
2:453:45pm  Yue Lu
Harvard University 
Title: Understanding Nonconvex Statistical Estimation via Sharp Asymptotic Methods: Phase Transitions, Scaling Limits, and Mapping Optimization Landscapes
Abstract: We are in the age of ubiquitous collection and processing of data of all kinds on unprecedented scales. Extracting meaningful information from the massive datasets being compiled by our society presents challenges and opportunities to signal and information processing research. For many modern statistical estimation problems, the new highdimensional settings allow one to apply powerful asymptotic methods from probability theory and statistical physics to obtain precise characterizations that would otherwise be too complicated in moderate dimensions. I will present three vignettes of our work on exploiting such blessings of dimensionality to understand nonconvex statistical estimation via sharp asymptotic methods. In particular, I will show (1) the exact characterization of a widelyused spectral method for nonconvex signal recoveries; (2) how to use scaling and meanfield limits to analyze nonconvex optimization algorithms for highdimensional inference and learning; and (3) how to precisely characterize the optimization landscape of a highdimensional binary regression problem by exactly counting and mapping local minima. In all these problems, asymptotic methods not only clarify some of the fascinating phenomena that emerge with highdimensional data, they also lead to optimal designs that significantly outperform commonly used heuristic choices. 
3:454:15pm  Break  
4:155:15pm  Jianfeng Cai
HKUST 
Title: NonConvex Methods for LowRank Matrix Reconstruction
Abstract: We present a framework of nonconvex methods for reconstructing a low rank matrix from its limited information, which arises from numerous practical applications in machine learning, imaging, signal processing, computer vision, etc. Our framework uses the geometry of the Riemannian manifold of all rankr matrices. The methods will be applied to several concrete example problems such as matrix completion, phase retrieval, and robust principle component analysis. We will also provide theoretical guarantee of our methods for the convergence to the correct lowrank matrix. 
5:156:15pm  Lixin Shen
Syracuse University 
Title: Overcomplete Tensor Decomposition via Convex Optimization Abstract: Tensors provide natural representations for massive multimode datasets and tensor methods also form the backbone of many machine learning, signal processing, and statistical algorithms. The utility of tensors is mainly due to the ability to identify overcomplete, nonorthogonal factors from tensor data, which is known as tensor decomposition. I will talk about our recent theories and computational methods for guaranteed overcomplete, nonorthogonal tensor decomposition using convex optimization. By viewing tensor decomposition as a problem of measure estimation from moments, we developed the theory for guaranteed decomposition under three assumptions: (i) Incoherence; (ii) Bounded spectral norm; and (iii) Gram isometry. Under these three assumptions, one can retrieve tensor decomposition by solving a convex, infinitedimensional analog of l1 minimization on the space of measures. The optimal value of this optimization defines the tensor nuclear norm that can be used to regularize tensor inverse problems, including tensor completion, denoising, and robust tensor principal component analysis. Remarkably, all the three assumptions are satisfied with high probability if the rankone tensor factors are uniformly distributed on the unit spheres, implying exact decomposition for tensors with random factors. I will also present and numerically test two computational methods based respectively on BurerMonteiro lowrank factorization 
Monday, March 26
Time………….  Speaker……..  Title/Abstract 
9:009:30am  Breakfast  
9:3010:30am  Jun Zhang
University of Michigan, Ann Arbor 
Title: Geometry of Maximum Entropy Inference
Abstract: We revisit classic framework of maximum entropy inference. It is wellknown that the MaxEnt solution is the exponential family, which can be characterized by the duallyflat Hessian geometry. Here, we provide a generalization to the classic formulation by using a general form of entropy function, which leads to the deformedexponential family as its solution. The resulting geometry may still be Hessian, but there is an extra degree of freedom in specifying the underlying geometry. Our framework can cover various generalized entropy functions, such as Tsallis entropy, Renyi entropy, phientropy, and crossentropy functions widely used in machine learning and information sciences. It is an elementary application of concepts from Information Geometry. 
10:3011:00am  Break  
11:0012:00pm  Eric Miller
Tufts University 
Title: A Totally Tubular Talk
Abstract: The objective of this talk is to provide an overview of work over the past decade or so within my group at Tufts related to the quantification of tubular structures arising in a variety of medical imaging applications. We describe methods for detailed segmentation of dense neuronal networks from electron microscopy data as well as the identification of the bare connectivity structure of the murine cerebral microvasculature network given farfromideal fluorescence microcopy data sets. Beyond mapping, we have addressed problems of anomaly detection when considering the localization of intracranial aneurysms and developed graphbased methods as the basis for capturing differences in cerebral vascular networks across subjects. Though the problems and the data types are quite diverse, the mathematical and algorithmic methods share a number of commonalities. With the exception of the anomaly detection work, the neuronal segmentation, vascular network connectivity analysis, and network registration methods are all cast as binary integer programming problems. Though not in this class of solutions, the anomaly detection problem makes use of a geometric feature associated with curves, the writhe number, but applied to tubular surfaces and thus seems appropriate given the subject matter of this workshop. 
12:001:30pm  Lunch  
1:302:30pm  Jerome Darbon
Brown University 
Title: On convex finitedimensional variational methods in imaging sciences, and HamiltonJacobi equations
Abstract: We consider standard finitedimensional variational models used in signal/image processing that consist in minimizing an energy involving a data fidelity term and a regularization term. We propose new remarks from a theoretical perspective which give a precise description on how the solutions of the optimization problem depend on the amount of smoothing effects and the data itself. The dependence of the minimal values of the energy is shown to be ruled by HamiltonJacobi equations, while the minimizers u(x,t) for the observed images x and smoothing parameters t are given by u(x,t)=x – \nabla H(\nabla E(x,t)) where E(x,t)is the minimal value of the energy and H is a Hamiltonian related to the data fidelity term. Various vanishing smoothing parameter results are derived illustrating the role played by the prior in such limits. Finally, we briefly present an efficient numerical numerical method for solving certain HamiltonJacobi equations in high dimension and some applications in optimal control. 
2:302:45pm  Break  
2:453:45pm  Rongjie Lai
RPI 
Title: Understanding ManifoldStructure Data via Geometric Modeling and Learning.
Abstract: Analyzing and inferring the underlying global intrinsic structures of data from its local information are critical in many fields. In practice, coherent structures of data allow us to model data as low dimensional manifolds, represented as point clouds, in a possible high dimensional space. Different from image and signal processing which handle functions on flat domains with welldeveloped tools for processing and learning, manifoldstructured data sets are far more challenging due to their complicated geometry. For example, the same geometric object can take very different coordinate representations due to the variety of embeddings, transformations or representations (imagine the same human body shape can have different poses as its nearly isometric embedding ambiguities). These ambiguities form an infinite dimensional isometric group and make higherlevel tasks in manifoldstructured data analysis and understanding even more challenging. To overcome these ambiguities, I will first discuss modeling based methods. This approach uses geometric PDEs to adapt the intrinsic manifolds structure of data and extracts various invariant descriptors to characterize and understand data through solutions of differential equations on manifolds. Inspired by recent developments of deep learning, I will also discuss our recent work of a new way of defining convolution on manifolds and demonstrate its potential to conduct geometric deep learning on manifolds. This geometric way of defining convolution provides a natural combination of modeling and learning on manifolds. It enables further applications of comparing, classifying and understanding manifoldstructured data by combing with recent advances in machine learning theory. If time permits, I will also discuss extensions of these methods to understand manifoldstructured data represented as incomplete interpoint distance information by combining with lowrank matrix completion theory. 
3:454:15pm  Break  
4:155:15pm  Song Zhang
Purdue University 

5:156:15pm  Ronald Lok Ming Lui
CUHK 
]]>
The schedule below will be updated as speakers are confirmed.
Date…………  Speaker  Title 
02092018 *Friday  Fan Chung
(UCSD) 
Sequences: random, structured or something in between
There are many fundamental problems concerning sequences that arise in many areas of mathematics and computation. Typical problems include finding or avoiding patterns; testing or validating various `randomlike’ behavior; analyzing or comparing different statistics, etc. In this talk, we will examine various notions of regularity or irregularity for sequences and mention numerous open problems. 
02142018  Zhengwei Liu
(Harvard Physics) 
A new program on quantum subgroups
Abstract: Quantum subgroups have been studied since the 1980s. The A, D, E classification of subgroups of quantum SU(2) is a quantum analogue of the McKay correspondence. It turns out to be related to various areas in mathematics and physics. Inspired by the quantum McKay correspondence, we introduce a new program that our group at Harvard is developing. 
02212018  Don Rubin
(Harvard) 
Essential concepts of causal inference — a remarkable history
Abstract: I believe that a deep understanding of cause and effect, and how to estimate causal effects from data, complete with the associated mathematical notation and expressions, only evolved in the twentieth century. The crucial idea of randomized experiments was apparently first proposed in 1925 in the context of agricultural field trails but quickly moved to be applied also in studies of animal breeding and then in industrial manufacturing. The conceptual understanding seemed to be tied to ideas that were developing in quantum mechanics. The key ideas of randomized experiments evidently were not applied to studies of human beings until the 1950s, when such experiments began to be used in controlled medical trials, and then in social science — in education and economics. Humans are more complex than plants and animals, however, and with such trials came the attendant complexities of noncompliance with assigned treatment and the occurrence of “Hawthorne” and placebo effects. The formal application of the insights from earlier simpler experimental settings to more complex ones dealing with people, started in the 1970s and continue to this day, and include the bridging of classical mathematical ideas of experimentation, including fractional replication and geometrical formulations from the early twentieth century, with modern ideas that rely on powerful computing to implement aspects of design and analysis. 
02262018 *Monday  Tom Hou
(Caltech) 
Computerassisted analysis of singularity formation of a regularized 3D Euler equation
Abstract: Whether the 3D incompressible Euler equation can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This question is closely related to the Clay Millennium Problem on 3D NavierStokes Equations. In a recent joint work with Dr. Guo Luo, we provided convincing numerical evidence that the 3D Euler equation develops finite time singularities. Inspired by this finding, we have recently developed an integrated analysis and computation strategy to analyze the finite time singularity of a regularized 3D Euler equation. We first transform the regularized 3D Euler equation into an equivalent dynamic rescaling formulation. We then study the stability of an approximate selfsimilar solution. By designing an appropriate functional space and decomposing the solution into a low frequency part and a high frequency part, we prove nonlinear stability of the dynamic rescaling equation around the approximate selfsimilar solution, which implies the existence of the finite time blowup of the regularized 3D Euler equation. This is a joint work with Jiajie Chen, De Huang, and Dr. Pengfei Liu. 
03072018  Richard Kenyon
(Brown) 
Harmonic functions and the chromatic polynomial
Abstract: When we solve the Dirichlet problem on a graph, we look for a harmonic function with fixed boundary values. Associated to such a harmonic function is the Dirichlet energy on each edge. One can reverse the problem, and ask if, for some choice of conductances on the edges, one can find a harmonic function attaining any given tuple of edge energies. We show how the number of solutions to this problem is related to the chromatic polynomial, and also discuss some geometric applications. This talk is based on joint work with Aaron Abrams and Wayne Lam. 
03142018  
03212018  Ramesh Narayan
(Harvard) 
Black Holes and Naked Singularities 
03282018  Andrea Montanari (Stanford)  
03302018
*Friday* 3:004:15pm 

04042018  
04112018  
04182018  Washington Taylor
(MIT) 

04252018  
05022018  
05092018 
For information on previous CMSA colloquia, click here.
]]>During the Spring 2018 Semester Artan Sheshmani (QGM/CMSA) will be teaching a CMSA special lecture series on Quantum Cohomology, Nakajima Vareties and Quantum groups. The lectures will be held Tuesdays and Thursdays beginning January 25th, from 1:00 to 3:00pm in room G10, CMSA Building.
You can watch Prof. Sheshmani describe the series here.
The Syllabus is as follows:
Date………..  Topic  Video/Audio 
1252018  GromovWitten invariants
Definition, examples via algebraic geometry I 
Video / Audio / Combined

1292018  GromovWitten invariants
Definition, examples via algebraic geometry II 

212018  GromovWitten invariants
Virtual Fundamental Class I (definition) 
Video / Audio / Combined

262018  No Lecture  
282018  No Lecture  
2132018  GromovWitten invariants
Virtual Fundamental Class II (computation in some cases) 

2152018  Computing GW invariants
Three level GW classes Genus zero invariants of the projective plane 

2202018  Quantum Cohomology
Small Quantum Cohomology (Definition and Properties) I 

2222018  Quantum Cohomology
Small Quantum Cohomology (Definition and Properties) II 

2272018  Quantum Cohomology
Big Quantum Cohomology I 

312018  Quantum Cohomology
Big Quantum Cohomology II GW potential WDVV equation 

362018  GW invariants via Quantum Cohomology
The Quintic threefold case The P^2 case 

382018  GW invariants via Quantum Cohomology
Dubrovin (quantum) connection 

3132018  Nakajima varieties
Algebraic and symplectic reduction 

3152018  Nakajima varieties
Nakajima Quiver varieties 

3202018  Nakajima varieties
Quasi maps to Nakajima varieties 

3222018  Quantum cohomology of Nakajima varieties
Stable envelops and Rmatrices I 

3272018  Quantum cohomology of Nakajima varieties
Stable envelops and Rmatrices II 

3292018  Quantum cohomology of Nakajima varieties
Stable envelops and Rmatrices III 

432018  Quantum cohomology of Nakajima varieties
Yangians I 

452018  Quantum cohomology of Nakajima varieties
Yangians II 

4102018  No Lecture  
4122018  No Lecture  
4172018  Quantum cohomology of Nakajima varieties
Quantum multiplication 

4192018  Quantum cohomology of Nakajima varieties
Shift and Quantum operators 

4242018  Quantum cohomology of Nakajima varieties
Quantum multiplication by divisors 

4262018  Quantum cohomology of Nakajima varieties
Quantum cohomology of cotangent bundle of Grassmannians I, II 

512018  Final Remarks 
]]>
The following speakers are confirmed:
Jointly organized by Harvard University, Massachusetts Institute of Technology, and Microsoft Research New England, the Charles River Lectures on Probability and Related Topics is a oneday event for the benefit of the greater Boston area mathematics community.
The 2017 lectures will take place 9:15am – 5:30pm on Monday, October 2 at Harvard University in the Harvard Science Center.
***************************************************
**************************************************
Please note that registration has closed.
In Harvard Science Center Hall C:
8:45 am – 9:15 am: Coffee/light breakfast
9:15 am – 10:15 am: Ofer Zeitouni
Title:
Abstract:
10:20 am – 11:20 am: Andrea Montanari
Title:
Abstract:
11:20 am – 11:45 am: Break
11:45 am – 12:45 pm: Paul Bourgade
Title:
Abstract:
1:00 pm – 2:30 pm: Lunch
In Harvard Science Center Hall E:
2:45 pm – 3:45 pm: Roman Vershynin
Title: Deviations of random matrices and applications
Abstract: Uniform laws of large numbers provide theoretical foundations for statistical learning theory. This lecture will focus on quantitative uniform laws of large numbers for random matrices. A range of illustrations will be given in high dimensional geometry and data science.
3:45 pm – 4:15 pm: Break
4:15 pm – 5:15 pm: Massimiliano Gubinelli
Title:
Abstract:
Alexei Borodin, Henry Cohn, Vadim Gorin, Elchanan Mossel, Philippe Rigollet, Scott Sheffield, and H.T. Yau
]]>Please click here to register for this event. We have space for up to 30 registrants on a first come, first serve basis.
Confirmed Participants:
Wednesday, January 10
Time  Speaker  Title/Abstract 
9:3010:30am  Tony Pantev  Homological Mirror Symmetry and the mirror map for del Pezzo surfaces
Abstract: I will discuss the general mirror symmetry question for 
10:30 – 11:00am  Break  
11:00 – 12:00pm  YoungHoon Kiem  Knorrer periodicity in curve counting
Abstract: The derived Knorrer periodicity compares the derived category of coherent sheaves on a projective hypersurface with that of matrix factorizations of its defining equation. I’d like to talk about a parallel development in curve counting, including ChangLi’s pfield invariant, ChangLiLi’s algebraic theory of (narrow) FJRW invariant and PolishchukVaintrob’s cohomological field theory, from the viewpoint of cosection localization. 
12:00 – 1:45pm  Lunch  
1:45 – 2:45pm  Kaoru Ono  Antisymplectic involutions and twisted sectors in Langranian Floer theory
Abstract: After explaining some results in Lagrangian Floer theory in the presence of an antisymplectic involution, I will present a definition of twisted sectors, which is suitable for Lagrangian Floer theory in orbifold setting. The first part is based on joint works with K. Fukaya, Y.G. Oh and H. Ohta and the second is based on a joint work (in progress) with B. Chen and B.L. Wang. 
2:45 – 3:15pm  Tea  
3:15 – 4:15pm  Radu Laza  Some remarks on degenerations of Ktrivial varieties
Abstract A fundamental result for K3 surfaces is the KulikovPerssonPinkham theorem on degenerations of K3 surfaces. In this talk, I will explore higher di mensional analogues of it and potential applications. Specifically, as a consequence of the minimal model program, Fujino has a obtained a weak analogue of the KPP Theorem for Ktrivial varieties. I will then discuss some relationships between the dual complex of the central fiber and the monodromy of the degenerations. I will then explain some consequences of this for Hyperkaehler manifolds and CalabiYau 3folds. 
Thursday, January 11
Time  Speaker  Title/Abstract 
9:3010:30am  Yan Soibelman 
RiemannHilbert correspondence in dimension one, Fukaya categories and periodic monopoles Abstract: By RHcorrespondence in dimension one I understand not only the classical one for holonomic Dmodules on curves, but also its versions for qdifference and elliptic difference equations. The unifying geometry for all versions is the one of partially compactified symplectic surfaces. Then the RHcorrespondence relates the category of holonomic coherent sheaves on the quantized symplectic surface with an appropriate partially wrapped Fukaya category of that surface. The nonabelian Hogde theory in dimension one deals with twistor families of the parabolic versions of the above categories. In the case of qdifference equations the role of harmonic objects is played by doubly periodic monopoles, while in the case of elliptic difference equations it is played by triply periodic monopoles. Talk is based on the joint project with Maxim Kontsevich.

10:30 – 11:00am  Break  
11:00 – 12:00pm  CheolHyun Cho  Gluing localized mirror functors.
Abstract: Given a Lagrangian submanifold L, we can consider a formal deformation theory of $L$ which is developed by FukayaOhOhtaOno. This provides a local mirror (with respect to L), given by the Lagrangian Floer potential function on the formal MaurerCartan space of L. Then, we can canonically construct a localized mirror functor from Fukaya category to the matrix factorization category. Given two different Lagrangian submanifolds, we explain how to glue these local mirrors to obtain a global mirror model, and also how to glue their localized mirror functors to obtain a global version of homological mirror functor. This is a joint work in progress with Hansol Hong and SiuCheong Lau. 
12:00 – 1:45pm  Lunch  
1:45 – 2:45pm  Mohammed Abouzaid  
2:45 – 3:15pm  Tea  
3:15 – 4:15pm  SiuCheong Lau  Immersed Lagrangians and wallcrossing
Abstract: We find the Floertheoretical gluing between local moduli of Lagrangian immersions, and use it to study wallcrossing for local CalabiYau manifolds. It is a joint work with Cho and Hong. In a joint work with Hong and Kim, we apply the technique to recover the Lie theoretical mirror of Gr(2,n). 
Friday, January 12
Time  Speaker  Title/Abstract 
9:3010:30am  Eric Zaslow  Framing Duality
Abstract: A symmetric quiver with g nodes is described by a symmetric adjacency matrix of size g. The same data defines a “framing” of a certain genusg Legendrian surface in the fivesphere, and the invariants of the quiver conjecturally relate to the open GromovWitten (GW) invariants of a nonexact Lagrangian filling of the surface. (Physically, both data count the same BPS states but from different perspectives.) Further, cluster theory can be exploited to conjecturally obtain all open GW invariants of Lagrangian fillings of a wider class of Legendrian surfaces described by cubic planar graphs.
In this talk, I will describe these observations, which build on prior work of others and are explored in joint works with David Treumann and Linhui Shen. 
10:30 – 11:00am  Break  
11:00 – 12:00pm  Si Li  CalabiYau geometry, KodairaSpencer gravity and integrable hierarchy
Abstract: We discuss some physical and geometric aspects of KodairaSpencer gravity (BCOV theory) on CalabiYau geometry and explain how quantum master equation leads to integrable hierarchies 
12:00 – 1:45pm  Lunch  
1:45 – 2:45pm  Sergueï Barannikov  Quantum master equation on cyclic cochains and categorical higher genus GromovWitten invariants
The construction of cohomology classes in the compactified moduli spaces of curves based on the quantum master equation on cyclic cochains will be reviewed. For the simplest category consisting of one object with only the identity morphism it produces the generating function for products of the psiclasses. The talk is based on the speaker’s works “Modular operads and BatalinVilkovisky geometry” (MPIM Bonn preprint 200648 (04/2006)) and “Noncommutative Batalin–Vilkovisky geometry and matrix integrals” (preprint Hal00102085 (09/2006)). 
2:45 – 3:15pm  Tea  
3:15 – 4:15pm  Thomas Lam  Mirror symmetry for flag varieties via the Langlands program
Abstract: I will talk about a mirror theorem for minuscule flag 
4:15 – 4:30pm  Break  
4:30 – 5:30pm  Colleen Robles

Generalizing the SatakeBailyBorel compactification.
Abstract: The SatakeBailyBorel (SBB) compactification is an projective algebraic completion of a locally Hermitian symmetric space. This construction, along with Borel’s Extension Theorem, provides the conduit to apply Hodge theory to study the moduli spaces (and their compactifications) of principally polarized abelian varieties and K3 surfaces. Most period domains are not Hermitian, and so one would like to generalize SBB in the hopes of similarly applying Hodge theory to study the moduli spaces (and their compactifications) of more general classes of algebraic varieties. In this talk I will present one such generalization. This work joint work with M. Green, P. Griffiths and R. Laza. 
Saturday, January 13
Time  Speaker  Title/Abstract 
9:3010:30am  Chenglong Yu  Higher HasseWitt matrices and period integrals
Abstract: I shall explain a program to relate the arithmetic of CalabiYau hypersurfaces in toric varieties or flag varieties, to their period integrals at the large complex structure limit. In particular, we prove a recent conjecture of Vlasenko regarding higher HasseWitt matrices. This work follows Katz’s description of Frobenius action in terms of local expansions. It is joint work with Huang, Lian and Yau.

10:30 – 11:00am  Break  
11:00 – 12:00pm  Kazushi Ueda  Moduli of K3 surfaces as moduli of Ainfinity structures
Abstract: We give a description of the moduli space of K3 surfaces polarized 
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