The CMSA Colloquium will take place every Wednesday from 4:305:30pm in CMSA Building, 20 Garden Street, G10.
Date  Speaker  Title/Abstract 
9/26/2018  XiaoGang Wen (MIT)  Title: A classification of low dimensional topological orders and fully extended TQFTs
Abstract: In this talk, I will review the recent progress on classification of gapped phases of quantum matter (ie topological orders) in 1,2, and 3 spatial dimensions for boson systems. In 1dimension, there is no nontrivial topological orders. In 2dimensions, the topological orders are classified by modular tensor category theory. In 3dimensions, the topological orders are classified by a simple class of braided fusion 2categories. The classification of topological orders may correspond to a classification of fully extended unitary TQFTs. 
10/03/2018  Richard Schoen (Stanford)  Title: Perspectives on the scalar curvature
Abstract: This will be a general talk concerning the role that the scalar curvature plays in Riemannian geometry and general relativity. We will describe recent work on extending the known results to all dimensions, and other issues which are being actively studied. 
10/10/2018  Justin Solomon (MIT)  Title: Correspondence and Optimal Transport for Geometric Data Processing
Abstract: Correspondence problems involving matching of two or more geometric domains find application across disciplines, from machine learning to computer vision. A basic theoretical framework involving correspondence along geometric domains is optimal transport (OT). Dating back to early economic applications, the OT problem has received renewed interest thanks to its applicability to problems in machine learning, computer graphics, geometry, and other disciplines. The main barrier to wide adoption of OT as a modeling tool is the expense of optimization in OT problems. In this talk, I will summarize efforts in my group to make largescale transport tractable over a variety of domains and in a variety of application scenarios, helping transition OT from theory to practice. In addition, I will show how OT can be used as a unit in algorithms for solving a variety of problems involving the processing of geometricallystructured data. 
10/17/2018  Jeremy England (MIT)  Title: Wisdom of the Jumble
Abstract: There are certain, specific behaviors that are particularly distinctive of life. For example, living things selfreplicate, harvest energy from challenging environmental sources, and translate experiences of past and present into actions that accurately anticipate the predictable parts of their future. What all of these activities have in common from a physics standpoint is that they generally take place under conditions where the pronounced flow of heat sharpens the arrow of time. We have therefore sought to use thermodynamics to understand the emergence and persistence of lifelike phenomena in a wide range of messy systems made of many interacting components. In this talk I will discuss some of the recent insights we have gleaned from studying emergent finetuning in disordered collections of matter exposed to complexly patterned environments. I will also point towards future possible applications in the design of new, more lifelike ways of computing that have the potential to either be cheaper or more powerful than existing means. 
10/31/2018  Moon Duchin (Tufts)  Title: Exploring the (massive) space of graph partitions
Abstract: The problem of electoral redistricting can be set up as a search of the space of partitions of a graph (representing the units of a state or other jurisdiction) subject to constraints (state and federal rules about the properties of districts). I’ll survey the problem and some approaches to studying it, with an emphasis on the deep mathematical questions it raises, from combinatorial enumeration to discrete differential geometry to dynamics. 
11/14/2018  Dusa McDuff (Columbia)  Title: The virtual fundamental class in symplectic geometry
Abstract: Essential to many constructions and applications of symplectic geometry is the ability to count Jholomorphic curves. The moduli spaces of such curves have well understood compactifications, and if cut out transversally are oriented manifolds of dimension equal to the index of the problem, so that they a fundamental class that can be used to count curves. In the general case, when the defining equation is not transverse, there are various different approaches to constructing a representative for this class, We will discuss and compare different approaches to such a construction e.g. using polyfolds or various kinds of finite dimensional reduction. Most of this is joint work with Katrin Wehrheim. 
11/19/2018  Xiaoqin Wang (Johns Hopkins)  Title: Computational Principles of Auditory Cortex
Abstract: Auditory cortex is located at the top of a hierarchical processing pathway in the brain that encodes acoustic information. This brain region is crucial for speech and music perception and vocal production. Auditory cortex has long been considered a difficult brain region to study and remained one of less understood sensory cortices. Studies have shown that neural computation in auditory cortex is highly nonlinear. In contrast to other sensory systems, the auditory system has a longer pathway between sensory receptors and the cerebral cortex. This unique organization reflects the needs of the auditory system to process timevarying and spectrally overlapping acoustic signals entering the ears from all spatial directions at any given time. Unlike visual or somatosensory cortices, auditory cortex must also process and differentiate sounds that are externally generated or selfproduced (during speaking). Neural representations of acoustic information in auditory cortex are shaped by auditory feedback and vocal control signals during speaking. Our laboratory has developed a unique and highly vocal nonhuman primate model (the common marmoset) and quantitative tools to study neural mechanisms underlying audition and vocal communication. 
11/28/2018  Robert Haslhofer (University of Toronto)  Title: Recent progress on mean curvature flow
Abstract: A family of surfaces moves by mean curvature flow if the velocity at each point is given by the mean curvature vector. Mean curvature flow is the most natural evolution in extrinsic geometry and shares many features with Hamilton’s Ricci flow from intrinsic geometry. In the first half of the talk, I will give an overview of the well developed theory in the mean convex case, i.e. when the mean curvature vector everywhere on the surface points inwards. Mean convex mean curvature flow can be continued through all singularities either via surgery or as level set solution, with a precise structure theory for the singular set. In the second half of the talk, I will report on recent progress in the general case without any curvature assumptions. Namely, I will describe our solution of the mean convex neighborhood conjecture and the nonfattening conjecture, as well as a general classification result for all possible blowup limits near spherical or cylindrical singularities. In particular, assuming Ilmanen’s multiplicity one conjecture, we conclude that for embedded twospheres the mean curvature flow through singularities is wellposed. This is joint work with Kyeongsu Choi and Or Hershkovits. 
12/5/2018  Robert McCann (University of Toronto)  Title: Displacement convexity of Boltzmann’s entropy characterizes positive energy in general relativity
Abstract: Einstein’s theory of gravity is based on assuming that the fluxes of a energy and momentum in a physical system are proportional to a certain variant of the Ricci curvature tensor on a smooth 3+1 dimensional spacetime. The fact that gravity is attractive rather than repulsive is encoded in the positivity properties which this tensor is assumed to satisfy. Hawking and Penrose (1971) used this positivity of energy to give conditions under which smooth spacetimes must develop singularities. By lifting fractional powers of the Lorentz distance between points on a globally hyperbolic spacetime to probability measures on spacetime events, we show that the strong energy condition of Hawking and Penrose is equivalent to convexity of the BoltzmannShannon entropy along the resulting geodesics of probability measures. This new characterization of the strong energy condition on globally hyperbolic manifolds also makes sense in (nonsmooth) metric measure settings, where it has the potential to provide a framework for developing a theory of gravity which admits certain singularities and can be continued beyond them. It provides a Lorentzian analog of Lott, Villani and Sturm’s metricmeasure theory of lower Ricci bounds, and hints at new connections linking gravity to the second law of thermodynamics. Preprint available at http://www.math.toronto.edu/mccann/papers/GRO.pdf 
12/12/2018  Zhiwei Yun (MIT)  Title: Shtukas: what and why
Abstract: This talk is of expository nature. Drinfeld introduced the notion of Shtukas and the moduli space of them. I will review how Shtukas compare to more familiar objects in geometry, how they are used in the Langlands program, and what remains to be done about them. 
1/30/2019  Richard Freeman (Harvard)  Title: Innovation in Cell Phones in the US and China: Who Improves Technology Faster?
Abstract: Cell phones are the archetypical modern consumer innovation, spreading around the world at an incredible pace, extensively used for connecting people with the Internet and diverse apps. Consumers report spending from 25 hours a day at their cell phones, with 44% of Americans saying “couldn’t go a day without their mobile devices.” Cell phone manufacturers introduce new models regularly, embodying additional features while other firms produce new applications that increase demand for the phones. Using newly developed data on the prices, attributes, and sales of different models in the US and China, this paper estimates the magnitude of technological change in the phones in the 2000s. It explores the problems of analyzing a product with many interactive attributes in the standard hedonic price regression model and uses Principal Components Regression to reduce dimensionality. The main finding is that technology improved the value of cell phones at comparable rates in the US and China, despite different market structures and different evaluations of some attributes and brands. The study concludes with a discussion of ways to evaluate the economic surplus created by the cell phones and their contribution to economic wellbeing. 
2/7/2019
*Thursday* 
Ulrich Mueller (Princeton)  Title: Inference for the Mean
Abstract: Consider inference about the mean of a population with finite variance, based on an i.i.d. sample. The usual tstatistic yields correct inference in large samples, but heavy tails induce poor small sample behavior. This paper combines extreme value theory for the smallest and largest observations with a normal approximation for the tstatistic of a truncated sample to obtain more accurate inference. This alternative approximation is shown to provide a refinement over the standard normal approximation to the full sample tstatistic under more than two but less than three moments, while the bootstrap does not. Small sample simulations suggest substantial size improvements over the bootstrap. 
2/13/2019  Christian Santangelo (UMass Amherst)  Title: 4D printing with folding forms
Abstract: 4D printing is the name given to a set of advanced manufacturing techniques for designing flat materials that, upon application of a stimulus, fold and deform into a target threedimensional shapes. The successful design of such structures requires an understanding of geometry as it applies to the mechanics of thin, elastic sheets. Thus, 4D printing provides a playground for both the development of new theoretical tools as well as old tools applied to new problems and experimental challenges in soft materials. I will describe our group’s efforts to understand and design structures that can fold from an initially flat sheet to target threedimensional shapes. After reviewing the stateoftheart in the theory of 4D printing, I will describe recent results on the folding and misfolding of flat structures and highlight the challenges remaining to be overcome. 
2/20/2019  Michael Woodford (Columbia)  Title: Optimally Imprecise Memory and Biased Forecasts
Abstract: We propose a model of optimal decision making subject to a memory constraint. The constraint is a limit on the complexity of memory measured using Shannon’s mutual information, as in models of rational inattention; the structure of the imprecise memory is optimized (for a given decision problem and noisy environment) subject to this constraint. We characterize the form of the optimally imprecise memory, and show that the model implies that both forecasts and actions will exhibit idiosyncratic random variation; that beliefs will fluctuate forever around the rationalexpectations (perfectmemory) beliefs with a variance that does not fall to zero; and that more recent news will be given disproportionate weight. The model provides a simple explanation for a number of features of observed forecast bias in laboratory and field settings. [authors: Rava Azeredo da Silveira (ENS) and Michael Woodford (Columbia)] 
2/27/2019
2:30pm 
Ian Martin (LSE)  Title: Sentiment and Speculation in a Market with Heterogeneous Beliefs
Abstract: We present a dynamic model featuring riskaverse investors with heterogeneous beliefs. Individual investors have stable beliefs and risk aversion, but agents who were correct in hindsight become relatively wealthy; their beliefs are overrepresented in market sentiment, so “the market” is bullish following good news and bearish following bad news. Extreme states are far more important than in a homogeneous economy. Investors understand that sentiment drives volatility up, and demand high risk premia in compensation. Moderate investors supply liquidity: they trade against market sentiment in the hope of capturing a variance risk premium created by the presence of extremists. [with Dimitris Papadimitriou] 
3/6/2019
2:30pm 
Philippe Sosoe (Cornell)  Title: A sharp transition for Gibbs measures associated to the nonlinear Schrödinger equation
Abstract: In 1987, Lebowitz, Rose and Speer (LRS) showed how to construct formally invariant measures for the nonlinear Schrödinger equation on the torus. This seminal contribution spurred a large amount of activity in the area of partial differential equations with random initial data. In this talk, I will explain LRS’s result, and discuss a sharp transition in the construction of the Gibbstype invariant measures considered by these authors. (Joint work with Tadahiro Oh and Leonardo Tolomeo) 
3/13/2019
5:15pm 
Greg Galloway (University of Miami)  Title: On the geometry and topology of initial data sets in General Relativity
Abstract: A theme of long standing interest (to the speaker!) concerns the relationship between the topology of spacetime and the occurrence of singularities (causal geodesic incompleteness). Many results concerning this center around the notion of topological censorship, which has to do with the idea that the region outside all black holes (and white holes) should be simple. The aim of the results to be presented is to provide support for topological censorship at the pure initial data level, thereby circumventing difficult issues of global evolution. The proofs rely on the recently developed theory of marginally outer trapped surfaces, which are natural spacetime analogues of minimal surfaces in Riemannian geometry. The talk will begin with a brief overview of general relativity and topological censorship. The talk is based primarily on joint work with various collaborators: Lars Andersson, Mattias Dahl, Michael Eichmair and Dan Pollack. 
3/20/2019  Sonia Jaffe (Microsoft)  Title: Quality Externalities on Platforms: The Case of Airbnb
Abstract: We explore quality externalities on platforms: when buyers have limited information, a seller’s quality affects whether her buyers return to the platform, thereby impacting other sellers’ future business. We propose an intuitive measure of this externality, applicable across a range of platforms. Guest Return Propensity (GRP) is the aggregate propensity of a seller’s customers to return to the platform. We validate this metric using Airbnb data: matching customers to listings with a one standard deviation higher GRP causes them to take 17% more subsequent trips. By directing buyers to higherGRP sellers, platforms may be able to increase overall seller surplus. (Joint work with Peter Coles, Steven Levitt, and Igor Popov.) 
3/27/2019
5:15pm 
Tatyana Sharpee (Salk Institute for Biological Studies)  Title: Hyperbolic geometry of the olfactory space.
Abstract: The sense of smell can be used to avoid poisons or estimate a food’s nutrition content because biochemical reactions create many byproducts. Thus, the presence of certain bacteria in the food becomes associated with the emission of certain volatile compounds. This perspective suggests that it would be convenient for the nervous system encode odors based on statistics of their cooccurrence within natural mixtures rather than based on the chemical structure per se. I will discuss how this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate distance between species computed along dendograms, and more generally between points within hierarchical treelike networks. We find that these coordinates, which were generated purely based on the statistics of odors in the natural environment, provide a contiguous map of human odor pleasantness. Further, a separate analysis of human perceptual descriptions of smells indicates that these also generate a three dimensional hyperbolic representation of odors. This match in geometries between natural odor statistics and human perception can help to minimize distortions that would otherwise arise when mapping odors to perception. We identify three axes in the perceptual space that are aligned with odor pleasantness, its molecular boiling point and acidity. Because the perceptual space is curved, one can predict odor pleasantness by knowing the coordinates along the molecular boiling point and acidity axes. 
4/3/2019
2:30pm 
Sarah Moshary (Chicago Booth)  Title: Deregulation through Direct Democracy: Lessons from Liquor
Abstract: This paper examines the merits of state control versus private provision of spirits retail, using the 2012 deregulation of liquor sales in Washington state as an event study. We document effects along a number of dimensions: prices, product variety, convenience, substitution to other goods, state revenue, and consumption externalities. We estimate a demand system to evaluate the net effect of privatization on consumer welfare. Our findings suggest that deregulation harmed the median Washingtonian, even though residents voted in favor of deregulation by a 16% margin. Further, we find that vote shares for the deregulation initiative do not reflect welfare gains at the ZIP code level. We discuss implications of our findings for the efficacy of direct democracy as a policy tool. 
4/10/2019
2:30pm 
Pietro Veronesi (Chicago Booth)  Title: Inequality Aversion, Populism, and the Backlash Against Globalization
Abstract: Motivated by the recent rise of populism in western democracies, we develop a model in which a populist backlash emerges endogenously in a growing economy. In the model, voters dislike inequality, especially the high consumption of “elites.” Economic growth exacerbates inequality due to heterogeneity in risk aversion. In response to rising inequality, richcountry voters optimally elect a populist promising to end globalization. Countries with more inequality, higher financial development, and current account deficits are more vulnerable to populism, both in the model and in the data. Evidence on who voted for Brexit and Trump in 2016 also supports the model. 
4/17/2019  YiZhuang You (UCSD)  Title: Machine Learning Physics: From Quantum Mechanics to Holographic Geometry
Abstract: Inspired by the “third wave” of artificial intelligence (AI), machine learning has found rapid applications in various topics of physics research. Perhaps one of the most ambitious goals of machine learning physics is to develop novel approaches that ultimately allows AI to discover new concepts and governing equations of physics from experimental observations. In this talk, I will present our progress in applying machine learning technique to reveal the quantum wave function of BoseEinstein condensate (BEC) and the holographic geometry of conformal field theories. In the first part, we apply machine translation to learn the mapping between potential and density profiles of BEC and show how the concept of quantum wave function can emerge in the latent space of the translator and how the Schrodinger equation is formulated as a recurrent neural network. In the second part, we design a generative model to learn the field theory configuration of the XY model and show how the machine can identify the holographic bulk degrees of freedom and use them to probe the emergent holographic geometry. . [1] C. Wang, H. Zhai, Y.Z. You. Uncover the Black Box of Machine Learning Applied to Quantum Problem by an Introspective Learning Architecture https://arxiv.org/abs/1901.11103 [2] H.Y. Hu, S.H. Li, L. Wang, Y.Z. You. Machine Learning Holographic Mapping by Neural Network Renormalization Group https://arxiv.org/abs/1903.00804 [3] Y.Z. You, Z. Yang, X.L. Qi. Machine Learning Spatial Geometry from Entanglement Features https://arxiv.org/abs/1709.01223 
4/24/2019  Shengwu Li (Harvard) 
Title: Credible Mechanisms
Abstract: Consider an extensiveform mechanism, run by an auctioneer who communicates sequentially and privately with agents. Suppose the auctioneer can deviate from the rules provided that no single agent detects the deviation. A mechanism is credible if it is incentivecompatible for the auctioneer to follow the rules. We study the optimal auctions in which only winners pay, under symmetric independent private values. The firstprice auction is the unique credible static mechanism. The ascending auction is the unique credible strategyproof mechanism.

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 
Date  Name  Title/Abstract 
012517  Sam Gershman, Harvard Center for Brain Science, Department of Psychology 
Title: Spectral graph theory of cognitive maps Abstract: The concept of a “cognitive map” has played an important role in neuroscience and psychology. A cognitive map is a representation of the environment that supports navigation and decision making. A longstanding question concerns the precise computational nature of this map. I offer a new mathematical foundation for the cognitive map, based on ideas at the intersection of spectral graph theory and reinforcement learning. Empirical data from neural recordings and behavioral experiments supports this theory. 
020117  Sean Eddy, Harvard Department of Molecular and Cellular Biology  Title: Biological sequence homology searches: the future of deciphering the past
Abstract: Computational recognition of distant common ancestry of biological sequences is a key to studying ancient events in molecular evolution.The better our sequence analysis methods are, the deeper in evolutionary time we can see. A major aim in the field is to improve the resolution of homology recognition methods by building increasingly realistic, complex, parameterrich models. I will describe current and future research in homology search algorithms based on probabilistic inference methods, using hidden Markov models(HMMs) and stochastic contextfree grammars (SCFGs). We make these methods available in the HMMER and Infernal software from my laboratory, in collaboration with database teams at the EuropeanBioinformatics Institute in the UK. 
020817  Matthew Headrick, Brandeis University  Title: Quantum entanglement, classical gravity, and convex programming: New connections
Abstract: In recent years, developments from the study of black holes and quantum gravity have revealed a surprising connection between quantum entanglement and classical general relativity. The theory of convex programming, applied in the differentialgeometry setting, turns out to be useful for understanding what’s behind this correspondence. We will describe these developments, giving the necessary background in quantum information theory and convex programming along the way. 
021517  Masahito Yamazaki, IMPU  Title: Geometry of 3manifolds and Complex ChernSimons Theory
Abstract: The geometry of 3manifolds has been a fascinating subject in mathematics. In this talk I discuss a “quantization” of 3manifold geometry, in the language of complex ChernSimons theory. This ChernSimons theory in turn is related to the physics of 30dimensional supersymmetric field theories through the socalled 3d/3d correspondence, whose origin can be traced back to a mysterious theory on the M5branes. Along the way I will also comment on the connection with a number of related topics, such as knot theory, hyperbolic geometry, quantum dilogarithm and cluster algebras. 
022217  Steven Rayan, University of Saskatchewan 
Title: Higgs bundles and the Hitchin system Abstract: I will give an informal introduction to the Hitchin system, an object lying at the crossroads of geometry and physics. As a moduli space, the Hitchin system parametrizes semistable Higgs bundles on a Riemann surface up to equivalence. From this point of view, the Hitchin map and spectral curves emerge. We’ll use these to form an impression of what the moduli space “looks like”. I will also outline the appearances of the Hitchin system in dynamics, hyperkaehler geometry, and mirror symmetry. 
030117  Jun Liu, Harvard University  Title: Expansion of biological pathways by integrative Genomics
Abstract: The number of publicly available gene expression datasets has been growing dramatically. Various methods had been proposed to predict gene coexpression by integrating the publicly available datasets. These methods assume that the genes in the query gene set are homogeneously correlated and consider no genespecific correlation tendencies, no background intraexperimental correlations, and no quality variations of different experiments. We propose a twostep algorithm called CLIC (CLustering by Inferred Coexpression) based on a coherent Bayesian model to overcome these limitations. CLIC first employs a Bayesian partition model with feature selection to partition the gene set into disjoint coexpression modules (CEMs), simultaneously assigning posterior probability of selection to each dataset. In the second step, CLIC expands each CEM by scanning the whole reference genome for candidate genes that were not in the input gene set but coexpressed with the genes in this CEM. CLIC is capable of integrating over thousands of gene expression datasets to achieve much higher coexpression prediction accuracy compared to traditional coexpression methods. Application of CLIC to ~1000 annotated human pathways and ~6000 poorly characterized human genes reveals new components of some wellstudied pathways and provides strong functional predictions for some poorly characterized genes. We validated the predicted association between protein C7orf55 and ATP synthase assembly using CRISPR knockout assays. Based on the joint work with Yang Li and the Vamsi Mootha lab. 
030817  Gabor Lippner, Northeastern University  Title: Evolution of cooperation in structured populations
Abstract: Understanding how the underlying structure affects the evolution of a population is a basic, but difficult, problem in the evolutionary dynamics. Evolutionary game theory, in particular, models the interactions between individuals as games, where different traits correspond to different strategies. It is one of the basic approaches to explain the emergence of cooperative behavior in Darwinian evolution. In this talk I will present new results about the model where the population is represented by an interaction network. We study the likelihood of a random mutation spreading through the entire population. The main question is to understand how the network influences this likelihood. After introducing the model, I will explain how the problem is connected to the study of meeting times of random walks on graphs, and based on this connection, outline a general method to analyze the model on general networks.

031517  Spring Break: No session  
032217  Gunther Uhlmann, University of Washington 
Abstract: We will consider the inverse problem of determining the sound speed or index of refraction of a medium by measuring the travel times of
waves going through the medium. This problem arises in global seismology in an attempt to determine the inner structure of the Earth by measuring travel times of earthquakes. It has also applications in optics and medical imaging among others.
The problem can be recast as a geometric problem: Can one determine a Riemannian metric of a Riemannian manifold with boundary by measuring the distance function between boundary points? This is the boundary rigidity problem. We will also consider the problem of determining the metric from the scattering relation, the socalled lens rigidity problem. The linearization of these problems involve the integration of a tensor along geodesics, similar to the Xray transform.
We will also describe some recent results, joint with Plamen Stefanov and Andras Vasy, on the partial data case, where you are making measurements on a subset of the boundary. No previous knowledge of Riemannian geometry will be assumed.

032917  Leslie Greengard, Courant Institute  Title: Inverse problems in acoustic scattering and cryoelectron microscopy
Abstract: A variety of problems in image reconstruction give rise to largescale, nonlinear and nonconvex optimization problems. We will show how recursive linearization combined with suitable fast solvers are bringing such problems within practical reach, with an emphasis on acoustic scattering and protein structure determination via cryoelectron microscopy. NOTE: This talk will begin at 4:00pm 
040517  Gongjie Li, Harvard University  Title: Unveiling the Origin of Planetary Systems by Dynamical and Statistical Approaches
Abstract: The unexpected diversity of observed extrasolar planetary systems has posed new challenges to our classical understanding of planetary formation. A lot of these challenges can be addressed by a deeper understanding of the dynamics in planetary systems, which will also allow us to construct more accurate planetary formation theories consistent with observations. In this talk, I will first explain the origin of counter orbiting planets using a new dynamical mechanism I discovered, which also has wide implications in other astrophysical systems, such as the enhancement of tidal disruption rates near supermassive black hole binaries. In addition, I will discuss the architectural properties of circumbinary planetary systems from selection biases using statistical methods, and infer the origin of such systems. 
041217  Shlomo Razamat, Israel Institute of Technology  Title: Complicated fourdimensional physics and simple mathematics
Abstract: We will discuss SCFTs in four dimensions obtained from compactifications of six dimensional models. We will discuss the relation of the partition functions, specifically the supersymmetric index, of the SCFTs to certain special functions, and argue that the partition functions are expected to be naturally expressed in terms of eigenfunctions of generalizations of RuijsenaarsSchneider models. We will discuss how the physics of the compactifications implies various precise mathematical identities involving the special functions, most of which are yet to be proven. 
041917  Cumrun Vafa, Harvard University  Title: String Swampland
Abstract: In this talk I review the idea behind identification of the string swampland. In particular I discuss the weak gravity conjecture as one such criterion and explain a nogo theorem for nonsupersymmetric AdS/CFT holography. 
042717  Mehran Kardar, MIT  Title: Levitation by Casimir forces in and out of equilibrium
Abstract: Equilibrium fluctuationinduced forces are abundant in nature, ranging from quantum electrodynamic (QED) Casimir and van der Waals forces, to their thermal analogs in fluctuating soft matter. Repulsive Casimir forces have been proposed for a variety of shapes and materials. A generalization of Earnshaw’s theorem constrains the possibility of levitation by Casimir forces in equilibrium. The scattering formalism, which forms the basis of this proof, can be used to study fluctuationinduced forces for different materials, diverse geometries, both in and out of equilibrium. Conformal field theory methods suggest that critical (thermal) Casimir forces are not subject to a corresponding constraint. Note: This talk will begin at 3:00pm 
050217  Simona Cocco, Laboratoire de Physique Statistique de l’ENS  Title: Reverse modeling of protein sequence data: from graphical models to structural and functional predictions
Body: A fundamental yet largely open problem in biology and medicine is to understand the relationship between the aminoacid sequence of a protein and its structure and function. Protein databases such as Pfam, which collect, align, and classify protein sequences into families containing Note: This talk will begin at 4:00pm 
050317  XueMei Li, University of Warwick  Title: Perturbation to conservation law and stochastic averaging
Abstract: A deterministic or random system with a conservation law is often used to Note: This talk will be held in the Science Center, Room 507 
051017  
051717  Kwok Wai Chan, Chinese University of Hong Kong  Title: Scattering diagrams from asymptotic analysis on MaurerCartan equations
Abstract: In 2005, a program was set forth by Fukaya aiming at investigating SYZ mirror symmetry by asymptotic analysis on MaurerCartan equations. In this talk, I will explain some results which implement part of Fukaya’s program. More precisely, I will show how semiclassical limits of MaurerCartan solutions give rise naturally to consistent scattering diagrams, which are known to encode GromovWitten data on the mirror side and have played an important role in the works of KontsevichSoibelman and GrossSiebert on the reconstruction problem in mirror symmetry. This talk is based on joint work with Conan Leung and Ziming Ma, which was substantially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CUHK14302015). 
052417  NO COLLOQUIUM  
053117  Peter Michor, University of Vienna  Title: Geometry of shape spaces and diffeomorphism groups and some of their uses
Abstract: This talk is devoted to shape spaces, Riemannian metrics on them, their geodesics and distance functions, and some of their uses, mainly in computational anatomy. The simplest Riemannian metrics have vanishing geodesic distance, so one has to use, for example, higher order Sobolev metrics on shape spaces. These have curvature, which complicates statistics on these spaces. 
Date  Name  Title 
090916 
Bong Lian, Brandeis 
Title: RiemannHilbert Problem and Period Integrals Abstract: Period integrals of an algebraic manifolds are certain special functions that describe, among other things, deformations of the variety. They were originally studied by Euler, Gauss and Riemann, who were interested in analytic continuation of these objects. In this lecture, we will discuss a number of longstanding problems on period integrals in connection with mirror symmetry and CalabiYau geometry. We will see how the theory of Dmodules have led us to solutions and insights into some of these problems. 
091416  SzeMan Ngai, Georgia Southern University  Title: The multifractal formalism and spectral asymptotics of selfsimilar measures with overlaps
Abstract: Selfsimilar measures form a fundamental class of fractal measures, and is much less understood if they have overlaps. The multifractal formalism, if valid, allows us to compute the Hausdorff dimension of the multifractal components of the measure through its Lqspectrum. The asymptotic behavior of the eigenvalue counting function for the associated Laplacians is closely related to the multifractal structure of the measure. Throughout this talk, the infinite Bernoulli convolution associated with the golden ratio will be used as a basic example to describe some of the results. 
092116  Prof. L. Mahadevan, Harvard SEAS  Title: “Morphogenesis: Biology, Physics and Mathematics”
Abstract: A century since the publication of Darcy Thompson’s classic “On growth and form,” his vision has finally begun to permeate into the fabric of modern biology. Within this backdrop, I will discuss some simple questions inspired by the onset of form in biology wherein mathematical models and computations, in close connection with experiments allow us to begin unraveling the physical basis for morphogenesis in the context of examples such as tendrils, leaves, guts, and brains. I will also try and indicate how these problems enrich their roots, creating new questions in mathematics, physics, and biology. 
092816  Hong Liu, MIT  Title: A new theory of fluctuating hydrodynamics
Despite its long and glorious history, hydrodynamics has so far been formulated mostly at the level of equations of motion, which is inadequate for capturing fluctuations. In a fluid, however, fluctuations occur spontaneously and continuously, at both the quantum and statistical levels, the understanding of which is important for a wide variety of physical problems. Another unsatisfactory aspect of the current formulation of hydrodynamics is that the equations of motion are constrained by various phenomenological conditions on the solutions, which need to be imposed by hand. One of such constraints is the local second law of thermodynamics, which plays a crucial role, yet whose physical origin has been obscure. We present a new theory of fluctuating hydrodynamics which incorporates fluctuations systematically and reproduces all the phenomenological constraints from an underlying Z_2 symmetry. In particular, the local second law of thermodynamics is derived. The theory also predicts new constraints which can be considered as nonlinear generalizations of Onsager relations. When truncated to Gaussian noises, the theory recovers various nonlinear stochastic equations. Curiously, to describe thermal fluctuations of a classical fluid consistently one needs to introduce anticommuting variables and the theory exhibits an emergent supersymmetry. 
100516 
Alexander Logunov, TelAviv University 
Title: Zeroes of harmonic functions and Laplace eigenfunctions
Abs: Nadirashvili conjectured that for any nonconstant harmonic function in R^3 its zero set has infinite area. This question was motivated by the Yau conjecture on zero sets of Laplace eigenfunctions. Both conjectures can be treated as an attempt to control the zero set of a solution of elliptic PDE in terms of growth of the solution. For holomorhpic functions such kind of control is possible only from one side: there is a plenty of holomorphic functions that have no zeros. While for a realvalued harmonic function on a plane the length of the zero set can be estimated (locally) from above and below by the frequency, which is a characteristic of growth of the harmonic function. We will discuss the notion of frequency, its properties and applications to zero sets in the higher dimensional case, where the understanding is far from being complete. 
101216  Conan Nai Chung Leung, CUHK 
Title: Coisotropic Abranes and their SYZ transform Abstract: “Kapustin introduced coisotropic Abranes as the natural boundary condition for strings in Amodel, generalizing Lagrangian branes and argued that they are indeed needed to for homological mirror symmetry. I will explain in the semiflat case that the Nahm transformation along SYZ fibration will transform fiberwise YangMills holomorphic bundles to coisotropic Abranes. This explains SYZ mirror symmetry away from the large complex structure limit.” 
101916  Vaughan Jones, UC Berkeley  Title: Are the Thompson groups any good as a model for Diff(S^1)?
Abstract. The Thompson groups are by definition groups of piecewise linear 
102616 
Henry Cohn, Microsoft 
Sums of squares, correlation functions, and exceptional geometric structures Some exceptional structures such as the icosahedron or E_8 root system have remarkable optimality properties in settings such as packing, energy minimization, or coding. How can we understand and prove their optimality? In this talk, I’ll interweave this story with two other developments in recent mathematics (without assuming familiarity with either): how semidefinite optimization and sums of squares have expanded the scope of optimization, and how representation theory has shed light on higher correlation functions for particle systems. 
110216 
Christian Borgs, Microsoft 
Title: Graphon processes and limits of sparse graph sequences Abstract: The theory of graph limits for dense graphs is by now well established, with graphons describing both the limit of a sequence of deterministic graphs, and a model for socalled exchangeable random graphs. Here a graphon is a function defined over a “feature space’’ equipped with some probability measure, the measure describing the distribution of features for the nodes, and the graphon describing the probability that two nodes with given features form a connection. While there are rich models of sparse random graphs based on graphons, they require an additional parameter, the edge density, whose dependence on the size of the graph has either to be postulated as an additional function, or considered as an empirical observed quantity not described by the model. In this talk I describe a new model, where the underlying probability space is replaced by a sigmafinite measure space, leading to both a new random model for exchangeable graphs, and a new notion of graph limits. The new model naturally produces a graph valued stochastic process indexed by a continuous time parameter, a “graphon process”, and describes graphs which typically have degree distributions with long tails, as observed in large networks in real life. 
110916
TIME CHANGE: 4PM 
Norden E. Huang, National Central University, (Taiwan) 
Title: On HoloHilbert Spectral Analysis
Traditionally, spectral analysis is defined as transform the time domain data to frequency domain. It is achieved through integral transforms based on additive expansions of a priori determined basis, under linear and stationary assumptions. For nonlinear processes, the data can have both amplitude and frequency modulations generated by intrawave and interwave interactions involving both additive and nonlinear multiplicative processes. Under such conditions, the additive expansion could not fully represent the physical processes resulting from multiplicative interactions. Unfortunately, all existing spectral analysis methods are based on additive expansions, based either on a priori or adaptive bases. While the adaptive Hilbert spectral analysis could accommodate the intrawave nonlinearity, the interwave nonlinear multiplicative mechanisms that include crossscale coupling and phase lock modulations are left untreated. To resolve the multiplicative processes, we propose a full informational spectral representation: The HoloHilbert Spectral Analysis (HHSA), which would accommodate all the processes: additive and multiplicative, intramode and intermode, stationary and nonstationary, linear and nonlinear interactions, through additional dimensions in the spectrum to account for both the variations in frequency and amplitude modulations (FM and AM) simultaneously. Applications to waveturbulence interactions and other data will be presented to demonstrate the usefulness of this new spectral representation. 
111616  Tristan Collins, Harvard University
TIME CHANGE: 3:30PM 
Title: Restricted volumes and finite time singularities of the KahlerRicci flow Abstract: I will discuss the relationship between restricted volumes, as defined algebraically or analytically, and the finite time singularities of the KahlerRicci flow. This is joint work with Valentino Tosatti. 
112216 TUESDAY
TIME CHANGE: 45PM 
Xiangfeng Gu, Stonybrook 
Title: Differential Geometric Methods for Engineering Applications Abstract: With the development of virtual reality and augmented reality, many challenging problems raised in engineering fields. Most of them are with geometric nature, and can be explored by modern geometric means. In this talk, we introduce our approaches to solve several such kind of problems: including geometric compression, shape classification, surface registration, cancer detection, facial expression tracking and so on, based on surface Ricci flow and optimal mass transportation. 
113016
TIME CHANGE: 4:20PM 
Sharad Ramanathan, Harvard MCB & SEAS 
Title: Finding coordinate systems to monitor the development of mammalian embryos 
120716 
Valentino Tosatti, Northwestern 
Title: Metric limits of hyperkahler manifolds Abstract: I will discuss a proof of a conjecture of KontsevichSoibelman and GrossWilson about the behavior of unitdiameter Ricciflat Kahler metrics on hyperkahler manifolds (fibered by holomorphic Lagrangian tori) near a large complex structure limit. The collapsed GromovHausdorff limit is a special Kahler metric on a halfdimensional complex projective space, away from a singular set of Hausdorff codimension at least 2. The resulting picture is also compatible with the StromingerYauZaslow mirror symmetry. This is joint work with Yuguang Zhang. 
121416 