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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20191002T163000
DTEND;TZID=America/New_York:20191002T173000
DTSTAMP:20260516T060354
CREATED:20240212T101431Z
LAST-MODIFIED:20240530T194159Z
UID:10001965-1570033800-1570037400@cmsa.fas.harvard.edu
SUMMARY:Cohomologies on almost complex manifolds and their applications 
DESCRIPTION:Speaker: Spiro Karigiannis (University of Waterloo)\n\n\nTitle: Cohomologies on almost complex manifolds and their applications\n\nAbstract: We define three cohomologies on an almost complex manifold (M\, J)\, defined using the Nijenhuis-Lie derivations induced from the almost complex structure J and its Nijenhuis tensor N\, regarded as vector-valued forms on M. One of these can be applied to distinguish non-isomorphic non-integrable almost complex structures on M. Another one\, the J-cohomology\, is familiar in the integrable case but we extend its definition and applicability to the case of non-integrable almost complex structures. The J-cohomology encodes whether a complex manifold satisfies the “del-delbar-lemma”\, and more generally in the non-integrable case the J-cohomology encodes whether (M\, J) satisfies a generalization of this lemma. We also mention some other potential cohomologies on almost complex manifolds\, related to an interesting question involving the Nijenhuis tensor. This is joint work with Ki Fung Chan and Chi Cheuk Tsang.
URL:https://cmsa.fas.harvard.edu/event/10-2-2019-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.02.19-791x1024-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190925T163000
DTEND;TZID=America/New_York:20190925T173000
DTSTAMP:20260516T060354
CREATED:20240212T104035Z
LAST-MODIFIED:20240514T175737Z
UID:10001999-1569429000-1569432600@cmsa.fas.harvard.edu
SUMMARY:Double affine Hecke algebras
DESCRIPTION:Speaker: Pavel Etingof (MIT)\n\nTitle:  Double affine Hecke algebras\n\nAbstract: Double affine Hecke algebras (DAHAs) were introduced by I. Cherednik in the early 1990s to prove Macdonald’s conjectures. A DAHA is the quotient of the group algebra of the elliptic braid group attached to a root system by Hecke relations. DAHAs and their degenerations are now central objects of representation theory. They also have numerous connections to many other fields — integrable systems\, quantum groups\, knot theory\, algebraic geometry\, combinatorics\, and others. In my talk\, I will discuss the basic properties of double affine Hecke algebras and touch upon some applications.\n\n\n\n  \n 
URL:https://cmsa.fas.harvard.edu/event/9-25-2019-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-09.25.19-791x1024-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190918T163000
DTEND;TZID=America/New_York:20190918T173000
DTSTAMP:20260516T060354
CREATED:20240212T102253Z
LAST-MODIFIED:20240514T175908Z
UID:10001976-1568824200-1568827800@cmsa.fas.harvard.edu
SUMMARY:A taste of noncommutative convex algebraic geometry
DESCRIPTION:Speaker: Bill Helton (UC San Diego)\n\nTitle:  A taste of noncommutative convex algebraic geometry\n\nAbstract: The last decade has seen the development of a substantial noncommutative (in a free algebra) real and complex algebraic geometry. The aim of the subject is to develop a systematic theory of equations and inequalities for (noncommutative) polynomials or rational functions of matrix variables. Such issues occur in linear systems engineering problems\, in free probability (random matrices)\, and in quantum information theory. In many ways the noncommutative (NC) theory is much cleaner than classical (real) algebraic geometry. For example\,\n\n◦ A NC polynomial\, whose value is positive semidefinite whenever you plug matrices into it\, is a sum of squares of NC polynomials.\n◦ A convex NC semialgebraic set has a linear matrix inequality representation.\n◦ The natural Nullstellensatz are falling into place.\n\n The goal of the talk is to give a taste of a few basic results and some idea of how these noncommutative problems occur in engineering. The subject is just beginning and so is accessible without much background. Much of the work is joint with Igor Klep who is also visiting CMSA for the Fall of 2019.
URL:https://cmsa.fas.harvard.edu/event/9-18-2019-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-09.12.19-791x1024-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190424T163000
DTEND;TZID=America/New_York:20190424T173000
DTSTAMP:20260516T060355
CREATED:20240212T103852Z
LAST-MODIFIED:20240514T180043Z
UID:10001998-1556123400-1556127000@cmsa.fas.harvard.edu
SUMMARY:Credible Mechanisms
DESCRIPTION:Speaker: Shengwu Li (Harvard)\n\n\nTitle: Credible Mechanisms\n\nAbstract: Consider an extensive-form 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 incentive-compatible for the auctioneer to follow the rules. We study the optimal auctions in which only winners pay\, under symmetric independent private values. The first-price auction is the unique credible static mechanism. The ascending auction is the unique credible strategy-proof mechanism.
URL:https://cmsa.fas.harvard.edu/event/4-24-2019-colloquium/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-042419.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190417T163000
DTEND;TZID=America/New_York:20190417T173000
DTSTAMP:20260516T060355
CREATED:20240212T095021Z
LAST-MODIFIED:20240514T180443Z
UID:10001936-1555518600-1555522200@cmsa.fas.harvard.edu
SUMMARY:Machine Learning Physics: From Quantum Mechanics to Holographic Geometry
DESCRIPTION:Speaker: Yi–Zhuang You (UCSD)\n\n\n\nTitle: Machine Learning Physics: From Quantum Mechanics to Holographic Geometry\n\n\n\nAbstract: 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 Bose-Einstein 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.\n\n\n[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\n[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\n[3] Y.-Z. You\, Z. Yang\, X.-L. Qi. Machine Learning Spatial Geometry from Entanglement Features https://arxiv.org/abs/1709.01223
URL:https://cmsa.fas.harvard.edu/event/4-17-2019-colloquium/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-041719-5.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190410T143000
DTEND;TZID=America/New_York:20190410T153000
DTSTAMP:20260516T060355
CREATED:20240212T112326Z
LAST-MODIFIED:20240514T181503Z
UID:10002069-1554906600-1554910200@cmsa.fas.harvard.edu
SUMMARY:Inequality Aversion\, Populism\, and the Backlash Against Globalization
DESCRIPTION:Speaker: Pietro Veronesi (University of Chicago) \nTitle: Inequality Aversion\, Populism\, and the Backlash Against Globalization \nAbstract: 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\, rich-country 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.
URL:https://cmsa.fas.harvard.edu/event/4-10-2019-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-041019-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190403T143000
DTEND;TZID=America/New_York:20190403T153000
DTSTAMP:20260516T060355
CREATED:20240212T112705Z
LAST-MODIFIED:20240514T181644Z
UID:10002077-1554301800-1554305400@cmsa.fas.harvard.edu
SUMMARY:Deregulation through Direct Democracy: Lessons from Liquor
DESCRIPTION:Speaker:  Sarah Moshary (University of Chicago) \nTitle:  Deregulation through Direct Democracy: Lessons from Liquor \nAbstract:  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.
URL:https://cmsa.fas.harvard.edu/event/4-3-2019-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-040319.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190327T171500
DTEND;TZID=America/New_York:20190327T181500
DTSTAMP:20260516T060355
CREATED:20240212T110407Z
LAST-MODIFIED:20240514T181829Z
UID:10002031-1553706900-1553710500@cmsa.fas.harvard.edu
SUMMARY:Hyperbolic geometry of the olfactory space
DESCRIPTION:Speaker: Tatyana Sharpee (Salk Institute for Biological Studies) \nTitle: Hyperbolic geometry of the olfactory space \nAbstract: The sense of smell can be used to avoid poisons or estimate a food’s nutrition content because biochemical reactions create many by-products. 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 co-occurrence 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 tree-like 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. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/3-27-2019-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-032719.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190320T163000
DTEND;TZID=America/New_York:20190320T173000
DTSTAMP:20260516T060355
CREATED:20240212T105115Z
LAST-MODIFIED:20240507T204308Z
UID:10002015-1553099400-1553103000@cmsa.fas.harvard.edu
SUMMARY:Quality Externalities on Platforms: The Case of Airbnb
DESCRIPTION:Speaker:  Sonia Jaffe  (Microsoft) \nTitle: Quality Externalities on Platforms: The Case of Airbnb \nAbstract:  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 higher-GRP sellers\, platforms may be able to increase overall seller surplus. (Joint work with Peter Coles\, Steven Levitt\, and Igor Popov.)
URL:https://cmsa.fas.harvard.edu/event/3-20-2019-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=application/pdf:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-032019.pdf
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190313T171500
DTEND;TZID=America/New_York:20190313T181500
DTSTAMP:20260516T060355
CREATED:20240212T105402Z
LAST-MODIFIED:20240514T182140Z
UID:10002017-1552497300-1552500900@cmsa.fas.harvard.edu
SUMMARY:On the geometry and topology of initial data sets in General Relativity
DESCRIPTION:Speaker: Greg Galloway (University of Miami) \nTitle: On the geometry and topology of initial data sets in General Relativity \nAbstract: 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.
URL:https://cmsa.fas.harvard.edu/event/2-13-2019-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-031319-791x1024-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190228T143000
DTEND;TZID=America/New_York:20190228T150000
DTSTAMP:20260516T060355
CREATED:20240212T104226Z
LAST-MODIFIED:20240514T182343Z
UID:10002002-1551364200-1551366000@cmsa.fas.harvard.edu
SUMMARY:A sharp transition for Gibbs measures associated to the nonlinear Schrödinger equation
DESCRIPTION:Speaker: Philippe Sosoe (Cornell) \nTitle: A sharp transition for Gibbs measures associated to the nonlinear Schrödinger equation \nAbstract: 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 Gibbs-type invariant measures considered by these authors. (Joint work with Tadahiro Oh and Leonardo Tolomeo)
URL:https://cmsa.fas.harvard.edu/event/3-6-2019-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-030619-791x1024-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190227T143000
DTEND;TZID=America/New_York:20190227T153000
DTSTAMP:20260516T060355
CREATED:20240212T102330Z
LAST-MODIFIED:20240514T182606Z
UID:10001978-1551277800-1551281400@cmsa.fas.harvard.edu
SUMMARY:Sentiment and Speculation in a Market with Heterogeneous Beliefs
DESCRIPTION:Speaker: Ian Martin (LSE) \nTitle: Sentiment and Speculation in a Market with Heterogeneous Beliefs \nAbstract: We present a dynamic model featuring risk-averse 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. [Joint work with Dimitris Papadimitriou] \n  \n 
URL:https://cmsa.fas.harvard.edu/event/2-27-2019-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-022719-e1550767365109.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190220T163000
DTEND;TZID=America/New_York:20190220T173000
DTSTAMP:20260516T060355
CREATED:20240212T114533Z
LAST-MODIFIED:20240514T182813Z
UID:10002102-1550680200-1550683800@cmsa.fas.harvard.edu
SUMMARY:Optimally Imprecise Memory and Biased Forecasts
DESCRIPTION:Speaker: Michael Woodford (Columbia) \nTitle: Optimally Imprecise Memory and Biased Forecasts \nAbstract: 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 rational-expectations (perfect-memory) 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. [Joint work with Rava Azeredo da Silveira and Yeji Sung
URL:https://cmsa.fas.harvard.edu/event/2-20-2019-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-022019-791x1024-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190207T163000
DTEND;TZID=America/New_York:20190207T173000
DTSTAMP:20260516T060355
CREATED:20240212T101329Z
LAST-MODIFIED:20240514T182948Z
UID:10001963-1549557000-1549560600@cmsa.fas.harvard.edu
SUMMARY:Inference for the Mean
DESCRIPTION:Speaker: Ulrich Mueller (Princeton) \nTitle: Inference for the Mean \nAbstract: Consider inference about the mean of a population with finite variance\, based on an i.i.d. sample. The usual t-statistic 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 t-statistic 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 t-statistic under more than two but less than three moments\, while the bootstrap does not. Small sample simulations suggest substantial size improvements over the bootstrap.
URL:https://cmsa.fas.harvard.edu/event/2-7-2019-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-020719.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190119T163000
DTEND;TZID=America/New_York:20190119T163000
DTSTAMP:20260516T060355
CREATED:20240212T100703Z
LAST-MODIFIED:20240514T183205Z
UID:10001956-1547915400-1547915400@cmsa.fas.harvard.edu
SUMMARY:Innovation in Cell Phones in the US and China: Who Improves Technology Faster?
DESCRIPTION:Speaker: Richard B. Freeman (Harvard University and NBER) \nTitle: Innovation in Cell Phones in the US and China: Who Improves Technology Faster? \nAbstract: 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 2-5 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 well-being.
URL:https://cmsa.fas.harvard.edu/event/1-30-2019-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Screen-Shot-2019-01-29-at-9.16.13-AM.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20181205T163000
DTEND;TZID=America/New_York:20181205T173000
DTSTAMP:20260516T060355
CREATED:20240213T072513Z
LAST-MODIFIED:20240514T183912Z
UID:10002179-1544027400-1544031000@cmsa.fas.harvard.edu
SUMMARY:Displacement convexity of Boltzmann's entropy characterizes positive energy in general relativity
DESCRIPTION:Speaker: Robert McCann (University of Toronto) \nTitle: Displacement convexity of Boltzmann’s entropy characterizes positive energy in general relativity \nAbstract: 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 Boltzmann-Shannon entropy along the resulting geodesics of probability measures. This new characterization of the strong energy condition on globally hyperbolic manifolds also makes sense in (non-smooth) 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 metric-measure 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 \n 
URL:https://cmsa.fas.harvard.edu/event/12-05-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-120518.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20181128T163000
DTEND;TZID=America/New_York:20181128T173000
DTSTAMP:20260516T060355
CREATED:20240213T072819Z
LAST-MODIFIED:20240514T184301Z
UID:10002180-1543422600-1543426200@cmsa.fas.harvard.edu
SUMMARY:Recent progress on mean curvature flow
DESCRIPTION:Speaker: Robert Haslhofer (University of Toronto) \nTitle: Recent progress on mean curvature flow \nAbstract: 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 two-spheres the mean curvature flow through singularities is well-posed. This is joint work with Kyeongsu Choi and Or Hershkovits.
URL:https://cmsa.fas.harvard.edu/event/11-28-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-112818-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20181119T150000
DTEND;TZID=America/New_York:20181119T160000
DTSTAMP:20260516T060355
CREATED:20240213T071141Z
LAST-MODIFIED:20240514T184752Z
UID:10002165-1542639600-1542643200@cmsa.fas.harvard.edu
SUMMARY:Computational Principles of Auditory Cortex
DESCRIPTION:Speaker: Xiaoqin Wang (Johns Hopkins University) \nTitle: Computational Principles of Auditory Cortex \nAbstract: 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 time-varying 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 self-produced (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 non-human primate model (the common marmoset) and quantitative tools to study neural mechanisms underlying audition and vocal communication.
URL:https://cmsa.fas.harvard.edu/event/11-19-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-111918.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20181114T160000
DTEND;TZID=America/New_York:20181114T170000
DTSTAMP:20260516T060355
CREATED:20240213T071016Z
LAST-MODIFIED:20240514T184520Z
UID:10002163-1542211200-1542214800@cmsa.fas.harvard.edu
SUMMARY:The virtual fundamental class in symplectic geometry
DESCRIPTION:Speaker: Dusa McDuff (Columbia University)  \nTitle: The virtual fundamental class in symplectic geometry \nAbstract: Essential to many constructions and applications of symplectic geometry is the ability to count J-holomorphic 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. \n 
URL:https://cmsa.fas.harvard.edu/event/11-14-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-111418.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20181031T163000
DTEND;TZID=America/New_York:20181031T173000
DTSTAMP:20260516T060355
CREATED:20240213T072029Z
LAST-MODIFIED:20240514T184941Z
UID:10002176-1541003400-1541007000@cmsa.fas.harvard.edu
SUMMARY:Exploring the (massive) space of graph partitions
DESCRIPTION:Speaker: Moon Duchin (Tufts) \nTitle: Exploring the (massive) space of graph partitions \nAbstract: 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. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/colloquium-10-31-2018/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/2018_10_29_11_55_54.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180413T163000
DTEND;TZID=America/New_York:20180413T173000
DTSTAMP:20260516T060355
CREATED:20240213T065558Z
LAST-MODIFIED:20240514T185400Z
UID:10002143-1523637000-1523640600@cmsa.fas.harvard.edu
SUMMARY:On the fibration structure of known Calabi-Yau threefolds
DESCRIPTION:Speaker: Washington Tayor (MIT) \nTitle: On the fibration structure of known Calabi-Yau threefolds \nAbstract: In recent years\, there is increasing evidence from a variety of directions\, including the physics of F-theory and new generalized CICY constructions\, that a large fraction of known Calabi-Yau manifolds have a genus one or elliptic fibration. In this talk I will describe recent work with Yu-Chien Huang on a systematic analysis of the fibration structure of known toric hypersurface Calabi-Yau threefolds. Among other results\, this analysis shows that every known Calabi-Yau threefold with either Hodge number exceeding 150 is genus one or elliptically fibered\, and suggests that the fraction of Calabi-Yau 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 Calabi-Yau threefolds.
URL:https://cmsa.fas.harvard.edu/event/4-18-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/2018_04_13_11_01_32-e1523633302205.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180411T163000
DTEND;TZID=America/New_York:20180411T173000
DTSTAMP:20260516T060355
CREATED:20240213T065052Z
LAST-MODIFIED:20240515T144439Z
UID:10002134-1523464200-1523467800@cmsa.fas.harvard.edu
SUMMARY:Graph Structure in Polynomial Systems: Chordal Networks
DESCRIPTION:Speaker: Pablo Parillo (MIT) \nTitle: Graph Structure in Polynomial Systems: Chordal Networks \nAbstract: 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).
URL:https://cmsa.fas.harvard.edu/event/4-11-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/2018_04_10_09_58_15-e1523369654177.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180404T163000
DTEND;TZID=America/New_York:20180404T163000
DTSTAMP:20260516T060355
CREATED:20240213T064751Z
LAST-MODIFIED:20240515T174223Z
UID:10002129-1522859400-1522859400@cmsa.fas.harvard.edu
SUMMARY:Black Holes and Naked Singularities
DESCRIPTION:Speaker: Ramesh Narayan\, Department of Astronomy\, Harvard University \nTitle: Black Holes and Naked Singularities \nAbstract: Black Hole solutions in General Relativity contain Event Horizons and Singularities. Astrophysicists have discovered two populations of black hole candidates in the Universe: stellar-mass objects with masses in the range 5 to 30 solar masses\, and supermassive objects with masses in the range million to several billion solar masses. There is considerable evidence that these objects have Event Horizons. It thus appears that astronomical black hole candidates are true Black Holes. Direct evidence for Singularities is much harder to obtain since\, at least in the case of Black Holes\, the Singularities are hidden inside the Event Horizon. However\, General Relativity also permits Naked Singularities which are visible to external observers. Toy Naked Singularity models have been constructed\, and some observational features of accretion flows in these spacetimes have been worked out.
URL:https://cmsa.fas.harvard.edu/event/4-4-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-040418-e1522340269661.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180328T163000
DTEND;TZID=America/New_York:20180328T173000
DTSTAMP:20260516T060355
CREATED:20240213T064501Z
LAST-MODIFIED:20240515T174531Z
UID:10002125-1522254600-1522258200@cmsa.fas.harvard.edu
SUMMARY:A Mean Field View of the Landscape of Two-Layers Neural Networks
DESCRIPTION:Speaker: Andrea Montanari (Stanford) \nTitle: A Mean Field View of the Landscape of Two-Layers Neural Networks \nAbstract: Multi-layer 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 non-convex and high-dimensional 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 two-layers neural networks\, and prove that –in a suitable scaling limit– the SGD dynamics is captured by a certain non-linear 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 nearly-ideal generalization error. This description allows to ‘average-out’ some of the complexities of the landscape of neural networks\, and can be used to capture some important variants of SGD as well. [Based on joint work with Song Mei and Phan-Minh Nguyen]
URL:https://cmsa.fas.harvard.edu/event/3-28-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-032818-e1521831836462-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180307T163000
DTEND;TZID=America/New_York:20180307T173000
DTSTAMP:20260516T060355
CREATED:20240213T063843Z
LAST-MODIFIED:20240515T175119Z
UID:10002121-1520440200-1520443800@cmsa.fas.harvard.edu
SUMMARY:Harmonic functions and the chromatic polynomial
DESCRIPTION:Speaker: Richard Kenyon\, Brown \nTitle: Harmonic functions and the chromatic polynomial
URL:https://cmsa.fas.harvard.edu/event/2-7-2018-colloquium/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-030718-e1520356183643.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180226T163000
DTEND;TZID=America/New_York:20180226T173000
DTSTAMP:20260516T060355
CREATED:20240213T063608Z
LAST-MODIFIED:20240515T175404Z
UID:10002119-1519662600-1519666200@cmsa.fas.harvard.edu
SUMMARY:Computer-assisted analysis of singularity formation of a regularized 3D Euler equation
DESCRIPTION:Speaker: Tom Hou\, Caltech \nTitle: Computer-assisted analysis of singularity formation of a regularized 3D Euler equation \n 
URL:https://cmsa.fas.harvard.edu/event/2-26-2018-colloquium/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-022618-e1519319166314.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180221T163000
DTEND;TZID=America/New_York:20180221T173000
DTSTAMP:20260516T060355
CREATED:20240213T063335Z
LAST-MODIFIED:20240515T175648Z
UID:10002115-1519230600-1519234200@cmsa.fas.harvard.edu
SUMMARY:Essential concepts of Causal inference—a remarkable history
DESCRIPTION:Speaker: Don Rubin (Harvard Statistics) \nTitle: Essential concepts of Causal inference—a remarkable history \nAbstract: 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 non-compliance 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. \n 
URL:https://cmsa.fas.harvard.edu/event/2-21-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-022118-e1518810758992.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180214T163000
DTEND;TZID=America/New_York:20180214T173000
DTSTAMP:20260516T060355
CREATED:20240213T063118Z
LAST-MODIFIED:20240515T180124Z
UID:10002113-1518625800-1518629400@cmsa.fas.harvard.edu
SUMMARY:A new program on quantum subgroups
DESCRIPTION:Speaker: Zhengwei Liu (Harvard Physics) \nTitle: A new program on quantum subgroups \nAbstract: 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. \n 
URL:https://cmsa.fas.harvard.edu/event/02-14-2018-colloqium/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-021418-e1518126484875.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180208T170000
DTEND;TZID=America/New_York:20180208T180000
DTSTAMP:20260516T060355
CREATED:20240213T062806Z
LAST-MODIFIED:20240515T181311Z
UID:10002110-1518109200-1518112800@cmsa.fas.harvard.edu
SUMMARY:Sequences: random\, structured or something in between
DESCRIPTION:Speaker: Fan Chung (University of California\, San Diego) \nTitle: Sequences: random\, structured or something in between \nAbstract: 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 ‘random-like’ 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. \n 
URL:https://cmsa.fas.harvard.edu/event/02-08-2018-colloquium/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-020818-e1518025233926.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180113T152500
DTEND;TZID=America/New_York:20180113T152500
DTSTAMP:20260516T060355
CREATED:20240213T062547Z
LAST-MODIFIED:20240213T062547Z
UID:10002108-1515857100-1515857100@cmsa.fas.harvard.edu
SUMMARY:2020-2021 Colloquium\, Wednesdays
DESCRIPTION:During the Spring 2021 semester\, and until further notice\, all seminars will take place virtually.\nThe 2020-2021 Colloquium will take place every Wednesday from 9:00 to 10:00am ET virtually\, using zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars\, as well as the weekly CMSA Colloquium series. Please email the seminar organizers to obtain a link. This year’s colloquium will be organized by Wei Gu and Sergiy Verstyuk. The schedule below will be updated as speakers are confirmed. \nTo learn how to attend\, please fill out this form. \nInformation on previous colloquia can be found here.\n \nSpring 2021:\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n\n\n1/27/2021\nEvelyn Tang (Max Planck Institute for Dynamics and Self-Organization) \nSlides\n\nVideo\nTitle: Topology protects chiral edge currents in stochastic systems \nAbstract: Living systems can exhibit time-scales much longer than those of the underlying components\, as well as collective dynamical behavior. How such global behavior is subserved by stochastic constituents remains unclear. I will present two-dimensional stochastic networks that consist of out-of-equilibrium cycles at the molecular scale and support chiral edge currents in configuration space. I will discuss the topological properties of these networks and their uniquely non-Hermitian features such as exceptional points and vorticity. As these emergent edge currents are associated to macroscopic timescales and length scales\, simply tuning a small number of parameters enables varied dynamical phenomena including a global clock\, stochastic growth and shrinkage\, and synchronization.\n\n\n2/3/2021\nAndré Luiz de Gouvêa (Northwestern) \nVideo\nTitle: The Brave Nu World \nAbstract: Neutrinos are the least understood of the fundamental particles that make up the so-called Standard Model of Particle Physics. Measuring neutrino properties and identifying how they inform our understanding of nature at the smallest distant scales is among the highest priorities of particle physics research today. I will discuss our current understanding of neutrinos\, concentrating on the observation of neutrino oscillations and neutrino masses\, along with all the open questions that came of these discoveries from the end of the 20th century.\n\n\n2/10/2021\nMykhaylo Shkolnikov (Princeton) \nVideo\nTitle: Probabilistic approach to free boundary problems and applications \nAbstract: We will discuss a recently developed probabilistic approach to (singular) free boundary problems\, such as the supercooled Stefan problem. The approach is based on a new notion of solution\, referred to as probabilistic\, which arises naturally in the context of large system limits of interacting particle systems. In the talk\, I will give an example of how such interacting particle systems arise in applications (e.g.\, finance)\, then obtain a solution of a free boundary problem in the large system limit\, and discuss how this solution can be analyzed mathematically (thereby answering natural questions about the systemic risk in financial systems and neural synchronization in the brain). The talk is based on recent and ongoing joint works with Sergey Nadtochiy\, Francois Delarue\, Jiacheng Zhang and Xiling Zhang\n\n\n2/17/2021\n9:00 – 10:00PM ET\nC. Seshadhri (UC Santa Cruz) \nVideo\nTitle: Studying the (in)effectiveness of low dimensional graph embeddings \nAbstract: Low dimensional graph embeddings are a fundamental and popular tool used for machine learning on graphs. Given a graph\, the basic idea is to produce a low-dimensional vector for each vertex\, such that “similarity” in geometric space corresponds to “proximity” in the graph. These vectors can then be used as features in a plethora of machine learning tasks\, such as link prediction\, community labeling\, recommendations\, etc. Despite many results emerging in this area over the past few years\, there is less study on the core premise of these embeddings. Can such low-dimensional embeddings effectively capture the structure of real-world (such as social) networks? Contrary to common wisdom\, we mathematically prove and empirically demonstrate that popular low-dimensional graph embeddings do not capture salient properties of real-world networks. We mathematically prove that common low-dimensional embeddings cannot generate graphs with both low average degree and large clustering coefficients\, which have been widely established to be empirically true for real-world networks. Empirically\, we observe that the embeddings generated by popular methods fail to recreate the triangle structure of real-world networks\, and do not perform well on certain community labeling tasks. (Joint work with Ashish Goel\, Caleb Levy\, Aneesh Sharma\, and Andrew Stolman.)\n\n\n2/24/2021\nDavid Ben-Zvi (U Texas) \nVideo\nTitle: Electric-Magnetic Duality for Periods and L-functions \nAbstract: I will describe joint work with Yiannis Sakellaridis and Akshay Venkatesh\, in which ideas originating in quantum field theory are applied to a problem in number theory.\nA fundamental aspect of the Langlands correspondence — the relative Langlands program — studies the representation of L-functions of Galois representations as integrals of automorphic forms. However\, the data that naturally index the period integrals (spherical varieties for G) and the L-functions (representations of the dual group G^) don’t seem to line up.\nWe present an approach to this problem via the Kapustin-Witten interpretation of the [geometric] Langlands correspondence as electric-magnetic duality for 4-dimensional supersymmetric Yang-Mills theory. Namely\, we rewrite the relative Langlands program as duality in the presence of supersymmetric boundary conditions. As a result the partial correspondence between periods and L-functions is embedded in a natural duality between Hamiltonian actions of the dual groups.\n\n\n3/3/2021 \n9:00pm ET\nOmer Tamuz (Caltech)\nTitle: Monotone Additive Statistics \nAbstract: How should a random quantity be summarized by a single number? We study mappings from random variables to real numbers\, focussing on those with the following two properties: (1) monotonicity with respect to first-order stochastic dominance\, and (2) additivity for sums of independent random variables. This problem turns out to be connected to the following question: Under what conditions on the random variables X and Y does there exist an independent Z so that X + Z first-order stochastically dominates Y + Z? \n(Joint work with Tobias Fritz\, Xiaosheng Mu\, Luciano Pomatto and Philipp Strack.)\n\n\n3/10/2021 \n9:00pm ET\nPiotr Indyk (MIT)\nTitle: Learning-Based Sampling and Streaming \nAbstract: Classical algorithms typically provide “one size fits all” performance\, and do not leverage properties or patterns in their inputs. A recent line of work aims to address this issue by developing algorithms that use machine learning predictions to improve their performance. In this talk I will present two examples of this type\, in the context of streaming and sampling algorithms. In particular\, I will show how to use machine learning predictions to improve the performance of (a) low-memory streaming algorithms for frequency estimation (ICLR’19)\, and (b) sampling algorithms for estimating the support size of a distribution (ICLR’21). Both algorithms use an ML-based predictor that\, given a data item\, estimates the number of times the item occurs in the input data set. (The talk will cover material from papers co-authored with T Eden\, CY Hsu\, D Katabi\, S Narayanan\, R Rubinfeld\, S Silwal\, T Wagner and A Vakilian.\n\n\n3/17/2021\n9:00pm ET\nChiu-Chu Melissa Liu (Columbia)\nTitle: Topological Recursion and Crepant Transformation Conjecture \nAbstract: The Crepant Transformation Conjecture (CTC)\, first proposed by Yongbin Ruan and later refined/generalized by others\, relates Gromov-Witten (GW) invariants of K-equivalent smooth varieties or smooth Deligne-Mumford stacks. We will outline a proof of all-genus open and closed CTC for symplectic toric Calabi-Yau 3-orbifolds based on joint work with Bohan Fang\, Song Yu\, and Zhengyu Zong. Our proof relies on the Remodeling Conjecture (proposed by Bouchard-Klemm-Marino-Pasquetti and proved in full generality by Fang\, Zong and the speaker) relating open and closed GW invariants of a symplectic toric Calabi-Yau 3-orbifold to invariants of its mirror curve defined by Chekhov-Eynard-Orantin Topological Recursion.\n\n\n3/24/2021\nWeinan E (Princeton) \nVideo\nTitle: Machine Learning and PDEs \nAbstract: I will discuss two topics:\n(1) Machine learning-based algorithms and “regularity” theory for very high dimensional PDEs;\n(2) Formulating machine learning as PDE (more precisely\, integral-differental equation) problems.\n\n\n3/31/2021\nThore Graepel (DeepMind/UCL) \nVideo\nTitle: From AlphaGo to MuZero – Mastering Atari\, Go\, Chess and Shogi by Planning with a Learned Model \nAbstract: Constructing agents with planning capabilities has long been one of the main challenges in the pursuit of artificial intelligence. Tree-based planning methods have enjoyed huge success in challenging domains\, such as chess and Go\, where a perfect simulator is available. However\, in real-world problems the dynamics governing the environment are often complex and unknown. In this work we present the MuZero algorithm which\, by combining a tree-based search with a learned model\, achieves superhuman performance in a range of challenging and visually complex domains\, without any knowledge of their underlying dynamics. MuZero learns a model that\, when applied iteratively\, predicts the quantities most directly relevant to planning: the reward\, the action-selection policy\, and the value function. When evaluated on 57 different Atari games – the canonical video game environment for testing AI techniques\, in which model-based planning approaches have historically struggled – our new algorithm achieved a new state of the art. When evaluated on Go\, chess and shogi\, without any knowledge of the game rules\, MuZero matched the superhuman performance of the AlphaZero algorithm that was supplied with the game rules.\n\n\n4/7/2021\nKui Ren (Columbia)\nTitle: Inversion via Optimization: Revisiting the Classical Least-Squares Formulation of Inverse Problems \nAbstract: The classical least-squares formulation of inverse problems has provided a successful framework for the computational solutions of those problems. In recent years\, modifications and alternatives have been proposed to overcome some of the disadvantages of this classical formulation in dealing with new applications. This talk intends to provide an (likely biased) overview of the recent development in constructing new least-squares formulations for model and data-driven solutions of inverse problems.\n\n\n4/14/2021\nSiu-Cheong Lau (Boston U)\nTitle: An algebro-geometric formulation of computing machines \nAbstract: Neural network in machine learning has obvious similarity with quiver representation theory.  The main gap between the two subjects is that network functions produced from two isomorphic quiver representations are not equal\, due to the presence of non-linear activation functions which are not equivariant under the automorphism group.  This violates the important math/physics principle that isomorphic objects should produce the same results.  In this talk\, I will introduce a general formulation using moduli spaces of framed modules of (noncommutative) algebra and fix this gap.  Metrics over the moduli space are crucial.  I will also explain uniformization between spherical\, Euclidean and hyperbolic moduli.\n\n\n4/21/2021\nVasco Carvalho (Cambridge)\nTitle: The Economy as a Complex Production Network\nAbstract: A modern economy is an intricately linked web of specialized production units\, each relying on the flow of inputs from their suppliers to produce their own output\, which in turn is routed towards other downstream units. From this production network vantage point we: (i) present the theoretical foundations for the role of such input linkages as a shock propagation channel and as a mechanism for transforming micro-level shocks into macroeconomic\, economy-wide fluctuations (ii) selectively survey both empirical and simulation-based studies that attempt to ascertain the relevance and quantitative bite of this argument and (time permitting) (iii) discuss a range of domains where this networked production view is currently being extended to.\n\n\n4/28/2021 \n9:00 – 10:00pm ET\nShamit Kachru (Stanford) \nSlides\nTitle: K3 Metrics from String Theory \nAbstract: Calabi-Yau manifolds have played a central role in important developments in string theory and mathematical physics.  Famously\, they admit Ricci flat metrics — but the proof of that fact is not constructive\, and the metrics remain mysterious.  K3 is perhaps the simplest non-trivial compact Calabi-Yau space.  In this talk\, I describe two different methods of constructing (smooth\, Ricci flat) K3 metrics\, and a string theory duality which relates them.  The duality re-sums infinite towers of disc instanton corrections via a purely classical infinite-dimensional hyperkahler quotient construction\, which can be practically implemented.\n\n\n\n\n\nFall 2020:\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n\n\n9/23/2020\nDavid Kazhdan (Hebrew University)\nTitle: On Applications of Algebraic Combinatorics to Algebraic Geometry \nAbstract: I present a derivation of a number of  results on morphisms of a high Schmidt’s rank from a result in Algebraic Combinatorics. In particular will explain the flatness of such morphisms and show their fibers have rational singularities.\n\n\n10/7/2020 \n10:00am\nMariangela Lisanti (Princeton University) \nVideo\nTitle: Mapping the Milky Way’s Dark Matter Halo with Gaia \nAbstract: The Gaia mission is in the process of mapping nearly 1% of the Milky Way’s stars—-nearly a billion in total.  This data set is unprecedented and provides a unique view into the formation history of our Galaxy and its associated dark matter halo.  I will review results based on the most recent Gaia data release\, demonstrating how the evolution of the Galaxy can be deciphered from the stellar remnants of massive satellite galaxies that merged with the Milky Way early on.  This analysis is an inherently “big data” problem\, and I will discuss how we are leveraging machine learning techniques to advance our understanding of the Galaxy’s evolution.  Our results indicate that the local dark matter is not in equilibrium\, as typically assumed\, and instead exhibits distinctive dynamics tied to the disruption of satellite galaxies.  The updated dark matter map built from the Gaia data has ramifications for direct detection experiments\, which search for the interactions of these particles in terrestrial targets.\n\n\n10/14/2020\nGil Kalai (Hebrew University and IDC Herzliya) \nVideo\nTitle: Statistical\, mathematical\, and computational aspects of noisy intermediate-scale quantum computers \nAbstract: Noisy intermediate-scale quantum (NISQ) Computers hold the key for important theoretical and experimental questions regarding quantum computers. In the lecture I will describe some questions about mathematics\, statistics and computational complexity which arose in my study of NISQ systems and are related to\na) My general argument “against” quantum computers\,\nb) My analysis (with Yosi Rinott and Tomer Shoham) of the Google 2019 “quantum supremacy” experiment.\nRelevant papers:\nYosef Rinott\, Tomer Shoham and Gil Kalai\, Statistical aspects of the quantum supremacy demonstration\, https://gilkalai.files.\nwordpress.com/2019/11/stat-quantum2.pdf\nGil Kalai\, The Argument against Quantum Computers\, the Quantum Laws of Nature\, and Google’s Supremacy Claims\, https://gilkalai.files.\nwordpress.com/2020/08/laws-blog2.pdf\nGil Kalai\, Three puzzles on mathematics\, computations\, and games\, https://gilkalai.files.\nwordpress.com/2019/09/main-pr.pdf\n\n\n10/21/2020\nMarta Lewicka (University of Pittsburgh) \nVideo\nTitle: Quantitative immersability of Riemann metrics and the infinite hierarchy of prestrained shell models \nAbstract: We propose results that relate the following two contexts:\n(i) Given a Riemann metric G on a thin plate\, we study the question of what is its closest isometric immersion\, with respect to the distance measured by energies E^h which are modifications of the classical nonlinear three-dimensional elasticity.\n(ii) We perform the full scaling analysis of E^h\, in the context of dimension reduction as the plate’s thickness h goes to 0\, and derive the Gamma-limits of h^{-2n}E^h for all n. We show the energy quantization\, in the sense that the even powers 2n of h are the only possible ones (all of them are also attained).\nFor each n\, we identify conditions for the validity of the corresponding scaling\, in terms of the vanishing of Riemann curvatures of G up to appropriate orders\, and in terms of the matched isometry expansions. Problems that we discuss arise from the description of elastic materials displaying heterogeneous incompatibilities of strains that may be associated with growth\, swelling\, shrinkage\, plasticity\, etc. Our results display the interaction of calculus of variations\,\ngeometry and mechanics of materials in the prediction of patterns and shape formation.\n\n\n10/28/2020\nJonathan Heckman (University of Pennsylvania) \nVideo\nTitle: Top Down Approach to Quantum Fields \nAbstract: Quantum Field theory (QFT) is the common language of particle physicists\, cosmologists\, and condensed matter physicists. Even so\, many fundamental aspects of QFT remain poorly understood. I discuss some of the recent progress made in understanding QFT using the geometry of extra dimensions predicted by string theory\, highlighting in particular the special role of seemingly “exotic”  higher-dimensional supersymmetric QFTs with no length scales known as six-dimensional superconformal field theories (6D SCFTs). We have recently classified all examples of such 6D SCFTs\, and are now using this to extra observables from strongly correlated systems in theories with more than four spacetime dimensions\, as well as in spacetimes with four or fewer spacetime dimensions. Along the way\, I will also highlight the remarkable interplay between physical and mathematical structures in the study of such systems\n\n\n11/4/2020\n9:00pm ET\nSurya Ganguli (Stanford) \nVideo\nTitle: Weaving together machine learning\, theoretical physics\, and neuroscience through mathematics \nAbstract: An exciting area of intellectual activity in this century may well revolve around a synthesis of machine learning\, theoretical physics\, and neuroscience.  The unification of these fields will likely enable us to exploit the power of complex systems analysis\, developed in theoretical physics and applied mathematics\, to elucidate the design principles governing neural systems\, both biological and artificial\, and deploy these principles to develop better algorithms in machine learning.  We will give several vignettes in this direction\, including:  (1) determining the best optimization problem to solve in order to perform regression in high dimensions;  (2) finding exact solutions to the dynamics of generalization error in deep linear networks; (3) developing interpretable machine learning to derive and understand state of the art models of the retina; (4) analyzing and explaining the origins of hexagonal firing patterns in recurrent neural networks trained to path-integrate; (5) delineating fundamental theoretical limits on the energy\, speed and accuracy with which non-equilibrium sensors can detect signals\nSelected References:\nM. Advani and S. Ganguli\, Statistical mechanics of optimal convex inference in high dimensions\, Physical Review X\, 6\, 031034\, 2016.\nM. Advani and S. Ganguli\, An equivalence between high dimensional Bayes optimal inference and M-estimation\, NeurIPS\, 2016.\nA.K. Lampinen and S. Ganguli\, An analytic theory of generalization dynamics and transfer learning in deep linear networks\, International Conference on Learning Representations (ICLR)\, 2019.\nH. Tanaka\, A. Nayebi\, N. Maheswaranathan\, L.M. McIntosh\, S. Baccus\, S. Ganguli\, From deep learning to mechanistic understanding in neuroscience: the structure of retinal prediction\, NeurIPS 2019.\nS. Deny\, J. Lindsey\, S. Ganguli\, S. Ocko\, The emergence of multiple retinal cell types through efficient coding of natural movies\, Neural Information Processing Systems (NeurIPS) 2018.\nB. Sorscher\, G. Mel\, S. Ganguli\, S. Ocko\, A unified theory for the origin of grid cells through the lens of pattern formation\, NeurIPS 2019.\nY. Bahri\, J. Kadmon\, J. Pennington\, S. Schoenholz\, J. Sohl-Dickstein\, and S. Ganguli\, Statistical mechanics of deep learning\, Annual Reviews of Condensed Matter Physics\, 2020.\nS.E. Harvey\, S. Lahiri\, and S. Ganguli\, A universal energy accuracy tradeoff in nonequilibrium cellular sensing\, https://arxiv.org/abs/2002.10567\n\n\n11/11/2020\nKevin Buzzard (Imperial College London) \nVideo\nTitle: Teaching proofs to computers \nAbstract: A mathematical proof is a sequence of logical statements in a precise language\, obeying some well-defined rules. In that sense it is very much like a computer program. Various computer tools have appeared over the last 50 years which take advantage of this analogy by turning the mathematical puzzle of constructing a proof of a theorem into a computer game. The newest tools are now capable of understanding some parts of modern research mathematics. In spite of this\, these tools are not used in mathematics departments\, perhaps because they are not yet capable of telling mathematicians *something new*.\nI will give an overview of the Lean theorem prover\, showing what it can currently do. I will also talk about one of our goals: using Lean to make practical tools which will be helpful for future researchers in pure mathematics.\n\n\n11/18/2020\nJose A. Scheinkman (Columbia) \nVideo\nTitle: Re-pricing avalanches \nAbstract: Monthly aggregate price changes exhibit chronic fluctuations but the aggregate shocks that drive these fluctuations are often elusive.  Macroeconomic models often add stochastic macro-level shocks such as technology shocks or monetary policy shocks to produce these aggregate fluctuations. In this paper\, we show that a state-dependent  pricing model with a large but finite number of firms is capable of generating large fluctuations in the number of firms that adjust prices in response to an idiosyncratic shock to a firm’s cost of price adjustment.  These fluctuations\, in turn\, cause fluctuations  in aggregate price changes even in the absence of aggregate shocks. (Joint work with Makoto Nirei.)\n\n\n11/25/2020 \n10:45am\nEric J. Heller (Harvard) \nVideo\nTitle: Branched Flow \nAbstract: In classical and quantum  phase space flow\, there exists a regime of great physical relevance that is belatedly but rapidly generating a new field. In  evolution under smooth\, random\, weakly deflecting  but persistent perturbations\, a remarkable regime develops\, called branched flow. Lying between the first cusp catastrophes at the outset\, leading to fully chaotic  statistical flow much later\, lies the visually beautiful regime of branched flow.  It applies to tsunami wave propagation\, freak wave formation\, light propagation\, cosmic microwaves arriving from pulsars\, electron flow in metals and devices\, sound propagation in the atmosphere and oceans\, the large scale structure of the universe\, and much more. The mathematical structure of this flow is only partially understood\, involving exponential instability coexisting with “accidental” stability. The flow is qualitatively universal\, but this has not been quantified.  Many questions arise\, including the scale(s) of the random medium\,  and the time evolution of manifolds and “fuzzy” manifolds in phase space.  The classical-quantum (ray-wave)  correspondence in this flow is only partially understood.  This talk will be an introduction to the phenomenon\, both visual and mathematical\, emphasizing unanswered questions\n\n\n12/2/2020\nDouglas Arnold (U of Minnesota) \nVideo\nTitle: Preserving geometry in numerical discretization \nAbstract: An important design principle for numerical methods for differential equations is that the discretizations preserve key geometric\, topological\, and algebraic structures of the original differential system.  For ordinary differential equations\, such geometric integrators were developed at the end of the last century\, enabling stunning computations in celestial mechanics and other applications that would have been impossible without them.  Since then\, structure-preserving discretizations have been developed for partial differential equations.  One of the prime examples has been the finite element exterior calculus or FEEC\, in which the structures to preserve are related to Hilbert complexes underlying the PDEs\, the de Rham complex being a canonical example.  FEEC has led to highly successful new numerical methods for problems in fluid mechanics\, electromagnetism\, and other applications which relate to the de Rham complex.  More recently\, new tools have been developed which extend the applications of FEEC far beyond the de Rham complex\, leading to progress in discretizations of problems from solid mechanics\, materials science\, and general relativity.\n\n\n12/9/2020\nManuel Blum and Lenore Blum (Carnegie Mellon) \nVideo\nTitle: What can Theoretical Computer Science Contribute to the Discussion of Consciousness? \nAbstract: The quest to understand consciousness\, once the purview of philosophers and theologians\, is now actively pursued by scientists of many stripes. We study consciousness from the perspective of theoretical computer science. This is done by formalizing the Global Workspace Theory (GWT) originated by cognitive neuroscientist Bernard Baars and further developed by him\, Stanislas Dehaene\, and others. We give a precise formal definition of a Conscious Turing Machine (CTM)\, also called Conscious AI\, in the spirit of Alan Turing’s simple yet powerful definition of a computer. We are not looking for a complex model of the brain nor of cognition but for a simple model of (the admittedly complex concept of) consciousness.\nAfter formally defining CTM\, we give a formal definition of consciousness in CTM. We then suggest why the CTM has the feeling of consciousness. The reasonableness of the definitions and explanations can be judged by how well they agree with commonly accepted intuitive concepts of human consciousness\, the range of related concepts that the model explains easily and naturally\, and the extent of the theory’s agreement with scientific evidence
URL:https://cmsa.fas.harvard.edu/event/2020-2021-colloquium-wednesdays/
LOCATION:MA
CATEGORIES:Colloquium
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