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 4/5/2018
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.

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  Shikui Chen
Stony Brook University 
Title: Design for Discovery: Generative Design of Conformal Structures using LevelSetBased Topology Optimization and Conformal Geometry Theory
In this method, a manifold (or freeform surface) is conformally mapped onto a 2D rectangular domain, where the level set functions are defined. With conformal mapping, the corresponding covariant derivatives on a manifold can be represented by the Euclidean differential operators multiplied by a scalar. Therefore, the TO problem on a freeform surface can be formulated as a 2D problem in the Euclidean space. To evolve the boundaries on a freeform surface, we propose a modified HamiltonJacobi Equation and solve it on a 2D plane following the Conformal Geometry Theory. In this way, we can fully utilize the conventional levelsetbased computational framework. Compared with other established approaches which need to project the Euclidean differential operators to the manifold, the computational difficulty of our method is highly reduced while all the advantages of conventional level set methods are well preserved. The proposed computational framework provides a solution to increasing applications involving innovative structural designs on freeform surfaces for different fields of interests. 
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
Superfast 3D imaging techniques and applications
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 
Title: Superfast 3D imaging techniques and applications
Abstract: Advances in optical imaging and machine/computer vision have provided integrated smart sensing systems for the manufacturing industry; and advanced 3D imaging could have profound impact on numerous fields, with broader applications including manufacturing, biomedical engineering, homeland security, and entertainment. Our research addresses the challenges in highspeed 3D imaging and optical information processing. For example, we have developed a system that simultaneously captures, processes and displays 3D geometries at 30 Hz with over 300,000 measurement points per frame, which was unprecedented at that time (a decade ago). Our current research focuses on achieving speed breakthroughs by developing the binary defocusing techniques and the mechanical projection method. The binary defocusing methods coincide with the inherent operation mechanism of the digitallightprocessing (DLP) technology, permitting tens of kHz 3D imaging speed at camera pixel spatial resolution; and utilizing the mechanical projection system further broaden the light spectrum usage. In this talk, I will present two platform technologies that we have developed as well as some of the applications that we have been exploring including cardiac mechanics, forensic science, as well as bioinspired robotics. 
5:156:15pm  Ronald Lok Ming Lui
CUHK 
Title: Mathematical models for restoration of turbulencedegraded images
Abstract: Turbulencedegraded image frames are distorted by both turbulent deformations and spacetimevarying blurs. To suppress these effects, a multiframe reconstruction scheme is usually considered to recover a latent image from the observed distorted image sequence. Recent approaches are commonly based on registering each frame to a reference image, by which geometric turbulent deformations can be estimated and a sharp image can be restored. A major challenge is that a fine reference image is usually unavailable, as every turbulencedegraded frame is distorted. A highquality reference image is crucial for the accurate estimation of geometric deformations and fusion of frames. Besides, it is unlikely that all frames from the image sequence are useful, and thus frame selection is necessary and highly beneficial. In this talk, we will describe several mathematical models to restore turbulencedistorted images. Extensive experimental results will also be shown to demonstrate the efficacy of different models 
]]>
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  
03282018  Andrea Montanari (Stanford)  A Mean Field View of the Landscape of TwoLayers Neural Networks
Abstract: Multilayer neural networks are among the most powerful models in machine learning and yet, the fundamental reasons for this success defy mathematical understanding. Learning a neural network requires to optimize a highly nonconvex and highdimensional objective (risk function), a problem which is usually attacked using stochastic gradient descent (SGD). Does SGD converge to a global optimum of the risk or only to a local optimum? In the first case, does this happen because local minima are absent, or because SGD somehow avoids them? In the second, why do local minima reached by SGD have good generalization properties? We consider a simple case, namely twolayers neural networks, and prove that –in a suitable scaling limit– the SGD dynamics is captured by a certain nonlinear partial differential equation. We then consider several specific examples, and show how the asymptotic description can be used to prove convergence of SGD to network with nearlyideal generalization error. This description allows to `averageout’ some of the complexities of the landscape of neural networks, and can be used to capture some important variants of SGD as well. 
03302018


04042018  Ramesh Narayan
(Harvard) 
Black Holes and Naked Singularities
Abstract: Black Hole solutions in General Relativity contain Event Horizons and 
04112018  Pablo Parrilo
(MIT) 
Graph Structure in Polynomial Systems: Chordal Networks
Abstract: The sparsity structure of a system of polynomial equations or an optimization problem can be naturally described by a graph summarizing the interactions among the decision variables. It is natural to wonder whether the structure of this graph might help in computational algebraic geometry tasks (e.g., in solving the system). In this lecture we will provide a gentle introduction to this area, focused on the key notions of chordality and treewidth, which are of great importance in related areas such as numerical linear algebra, database theory, constraint satisfaction, and graphical models. In particular, we will discuss “chordal networks”, a novel representation of structured polynomial systems that provides a computationally convenient decomposition of a polynomial ideal into simpler (triangular) polynomial sets, while maintaining its underlying graphical structure. As we will illustrate through examples from different application domains, algorithms based on chordal networks can significantly outperform existing techniques. Based on joint work with Diego Cifuentes (MIT). 
04182018  Washington Taylor
(MIT) 
On the fibration structure of known CalabiYau threefolds
Abstract: In recent years, there is increasing evidence from a variety of directions, including the physics of Ftheory and new generalized CICY constructions, that a large fraction of known CalabiYau manifolds have a genus one or elliptic fibration. In this talk I will describe recent work with YuChien Huang on a systematic analysis of the fibration structure of known toric hypersurface CalabiYau threefolds. Among other results, this analysis shows that every known CalabiYau threefold with either Hodge number exceeding 150 is genus one or elliptically fibered, and suggests that the fraction of CalabiYau threefolds that are not genus one or elliptically fibered decreases roughly exponentially with h_{11}. I will also make some comments on the connection with the structure of triple intersection numbers in CalabiYau threefolds. 
04252018  Xi Yin
(Harvard)

How we can learn what we need to know about Mtheory
Abstract: Mtheory is a quantum theory of gravity that admits an eleven dimensional Minkowskian vacuum with superPoincare symmetry and no dimensionless coupling constant. I will review what was known about Mtheory based on its relation to superstring theories, then comment on a number of open questions, and discuss how they can be addressed from holographic dualities. I will outline a strategy for extracting the Smatrix of Mtheory from correlation functions of dual superconformal field theories, and in particular use it to recover the 11D R^4 coupling of Mtheory from ABJM theory. 
05022018  
05092018 
For information on previous CMSA colloquia, click here.
]]>The following speakers are confirmed:
Schedule:
Monday, April 23
Time  Speaker  Title/Abstract 
8:30 – 9:00am  Breakfast  
9:00 – 10:00am  Fernando G.S.L Brandão
Caltech 
Title: New Directions in Quantum Algorithms: Thermalization meets Convex Optimization Abstract: I will discuss recent results on quantum algorithms for semidefinite programming, an important class of convex optimization problems with widespread applications (from resource allocation to approximating hard combinatorial problems). I will present a connection of the task of solving semidefinite programs (SDPs) to the task of quantum Gibbs sampling (which consists of computing properties of thermal states at finite temperature on a quantum computer). I will then discuss results on the time of thermalization of manybody quantum systems and show that they directly give quantum speedups for SDPs. I will also argue that the quantum algorithm for SDPs can be seen as a generalization of quantum annealing and is a good candidate for realisation on small quantum computers. 
10:00 – 10:20am  Break  
10:20 – 11:20am  Iris Cong
Harvard 
Title: Universal Quantum Computation with Gapped Boundaries
Abstract: In this talk, I will discuss topological quantum computation with gapped boundaries of twodimensional topological phases. I will first introduce the algebraic framework for topological quantum computation and gapped boundaries. Next, I will present systematic methods to encode quantum information topologically using gapped boundaries, and to perform topologically protected operations on this encoding. In particular, I will introduce a new computational primitive of topological charge measurement and present a symmetryprotected implementation of this primitive. Throughout the talk, a concrete physical example – the case of bilayer fractional quantum Hall 1/3 systems [mathematically, D(Z3)], will be discussed. For this example, we have a qutrit encoding and an abstract universal gate set. If a practical implementation is found for the required topological charge measurement, these boundaries will give rise to a direct physical realization of a universal quantum computer based on a purely Abelian topological phase. 
11:20 – 1:20pm  Lunch  
1:20 – 2:20pm  Isaac Chuang
MIT 
Title: The enduring surprises of SU(2)
Abstract: The dynamics of a qubit have long been understood to be at the heart of quantum algorithms and quantum protocols, from search to onequbit teleportation. And cascaded singlequbit operations, known as composite quantum gates, have provided powerful ways to correct systematic errors. Here, we generalize these understandings based on new results addressing the nonlinearity of single qubit dynamics: a methodology for solving the inverse mathematical problem, to find a sufficient gate sequence, given a desired response function. 
2:20 – 2:40pm  Break  
2:40 – 3:40pm  Renato Renner
ETH Zürich 
Title: Quantum information and foundations
Abstract: The black hole information paradox is a prominent example of a thought experiment which indicates that the law that quantum states evolve unitarily may not be valid universally. In this talk, I will present another informationtheoretic thought experiment, which also leads to contradictions if one takes the universal validity of unitary state evolution for granted. However, in contrast to the black hole information paradox, the experiment does not require any assumptions about gravity. 
3:40 – 4:00pm  Break  
4:00 – 5:00pm  Emil Khabiboulline Harvard 
Title: Nonlocal Interferometry with Quantum Networks
Abstract: We propose a method for optical interferometry in telescope arrays connected via networks consisting of entangled quantum mechanical nodes. In our approach, the quantum states of photons from weak distant sources, including their arrival time, are stored in quantum memories in a binary qubit encoding. These stored states are subsequently interrogated via coherent, nonlocal readout by means of entanglementassisted parity checks across the array, which effectively circumvents transmission losses between the nodes, allowing for imaging of faint sources with improved angular resolution. The state transfer to memory enables processing such as a quantum Fourier transform applied over the network. Compared with prior proposals, our scheme offers an exponential decrease in required entanglement resources, making its experimental implementation feasible with nearterm technology. 
Tuesday, April 24
Time  Speaker  Title/Abstract 
8:30 – 9:00am  Breakfast  
9:00 – 10:00am  Aram Harrow
MIT 
Title: Small quantum computers and large classical data sets
Abstract: Can we use Grover’s algorithm to quadratically speed up finding the best model fitting a data set? What about adiabatic optimization, quantum variational methods, or other more sophisticated algorithms? The answer is not obvious if we are not given the ability to query the data set in superposition. One approach is to choose a representative subset of the data and run quantum optimization algorithms on this subset. This talk will explore methods for doing so that use a classical computer either offline or in an interactive protocol together with the quantum computer. These methods allow Groverlike speedups for problems that include clustering in metric spaces and saddlepoint optimization. 
10:00 – 10:20am  Break  
10:20 – 11:20am  Adam Bene Watts
MIT 
Title : Algorithms and Bounds for XOR Games.
Abstract : The entangled value of an XOR game is the maximal win probability obtained by players who cannot communicate, but share a quantum state of possibly unbounded dimension. Studying gives us a precise tool for characterizing the power of entanglement. For any two player XOR game is easy to compute, as Tsirelson gave an efficient semidefinite program which exactly computes a game’s value. Conversely, for XOR games with three or more players computing is at least NPhard, and the best known algorithm runs with no guarantee on its convergence time. 
11:20 – 1:20pm  Lunch  
1:20 – 2:20pm  Mikhail D. Lukin
Harvard 
Title: Quantum machines based on Rydberg atom arrays 
2:20 – 2:40pm  Break  
2:40 – 3:40pm  Jacob Biamonte
Skoltech 
Title: Quantum Machine Learning Matrix Product States Abstract: Matrix product states minimize bipartite correlations to compress the classical data representing quantum states. Matrix product state algorithms and similar tools—called tensor network methods—form the backbone of modern numerical methods used to simulate manybody physics. Matrix product states have a further range of applications in machine learning. Finding matrix product states is in general a computationally challenging task, a computational task which we show quantum computers can accelerate. We present a quantum algorithm which returns a classical description of a $k$rank matrix product state approximating an eigenvector given blackbox access to a unitary matrix. Each iteration of the optimization requires $O(n\cdot k^2)$ quantum gates, yielding sufficient conditions for our quantum variational algorithm to terminate in polynomialtime. Implications include: (i) Applications of quantum random access memory are severely limited from the general restriction imposed by quantum theory in which a quantum memory itself is modified by access. Our method recursively optimizes a rank$k$ description of a quantum state: this in turn can be accessed {\it in situ} and hence our results augment the efficiency of quantum random access memory. (ii) Recently lowdepth quantum circuits for various tasks have taken center stage. We augment these studies by providing a missing theoretical backbone, both quantifying algorithms in terms of entanglement and providing lower bounds for the gatedepth needed for a computation to generate specific quantities of entanglement. (iii) Matrix product structure allows many operations to be done efficiently classically (provided one has the matrix product state to begin with). Hence, our method opens the door for hybrid quantum/classical algorithms which utilize quantum effects to determine a matrix product state and then utilizes various classical/quantum subroutines to calculate properties of matrix product states. This brings with it a host of applications in the simulation of physics and chemistry as well as in machine learning. (iv) The algorithm is general in that it works given only blackbox access to a unitary matrix. In the discussion however, we drop this restriction and cast the steps needed to perform a meaningful nearterm demonstration of this algorithm on a quantum computer, providing a lowrank approximation to eigenvectors of the quantum computers free (or closely related effective) Hamiltonian, taking a large step towards a practically useful task with lowgate counts. 
3:40 – 4:00pm  Break  
4:00 – 5:00pm  Peter Shor
MIT 
Title: Quantum information, black holes, and scrambling timeAbstract: The scrambling time of a black hole is the amount of time it takes for the black hole to evolve from a nearly unentangled state — a state where there is not much entanglement between two hemisphered to a Haarrandom state, where there is nearly maximal entanglement between the two hemispheres. Recently, the conjecture has been made that the scrambling time of a black hole is order M log M, where M is the mass of the black hole in natural units. We present an argument that implies that for this conjecture to be true, there must be nonstandard physics occuring well outside the stretched horizon of a black hole. 
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.
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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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The lectures will take place from 4:305:30pm in Science Center, Hall D.
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Photos of the event can be found on CMSA’s Blog.
Organizers:
* This event is sponsored by CMSA Harvard University.
Monday, March 27
Time  Speaker  Title 
8:30am – 9:00am  Breakfast  
9:00am – 10:00am  Kieron Burke, University of California, Irvine  Background in DFT and electronic structure calculations 
10:00am – 11:00am  Kieron Burke, University of California, Irvine 
The density functionals machines can learn 
11:00am – 12:00pm  Sadasivan Shankar, Harvard University  A few key principles for applying Machine Learning to Materials (or Complex Systems) — Scientific and Engineering Perspectives 
Tuesday, March 28
Time  Speaker  Title 
8:30am – 9:00am  Breakfast  
9:00am – 10:00am  Ryan Adams, Harvard  TBA 
10:00am – 11:00am  Gábor Csányi, University of Cambridge 
Interatomic potentials using machine learning: accuracy, transferability and chemical diversity 
11:00am – 1:00pm  Lunch Break  
1:00pm – 2:00pm  Evan Reed, Stanford University  TBA 
Wednesday, March 29
Time  Speaker  Title 
8:30am – 9:00am  Breakfast  
9:00am – 10:00am  Patrick Riley, Google  The Message Passing Neural Network framework and its application to molecular property prediction 
10:00am – 11:00am  Jörg Behler, University of Göttingen  TBA 
11:00am – 12:00pm  Ekin Doğuş Çubuk, Stanford Univers  TBA 
4:00pm  Leslie Greengard, Courant Institute  Inverse problems in acoustic scattering and cryoelectron microscopy
CMSA Colloquium 
Thursday, March 30
Time  Speaker  Title 
8:30am – 9:00am  Breakfast  
9:00am – 10:00am  Matthias Rupp, Fitz Haber Institute of the Max Planck Society  TBA 
10:00am – 11:00am  Petros Koumoutsakos, Radcliffe Institute for Advanced Study, Harvard  TBA 
11:00am – 1:00pm  Lunch Break  
1:00pm – 2:00pm  Dennis Sheberla, Harvard University  Rapid discovery of functional molecules by a highthroughput virtual screening 
Registration and additional information on the conference can be found at http://abel.harvard.edu/jdg/index.html.
Confirmed Speakers
* This event is cosponsored by Lehigh University and partially supported by the National Science Foundation.
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