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DTSTART:20211107T060000
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201028T103000
DTEND;TZID=America/New_York:20201028T120000
DTSTAMP:20260507T012426
CREATED:20240127T023513Z
LAST-MODIFIED:20240127T023513Z
UID:10001496-1603881000-1603886400@cmsa.fas.harvard.edu
SUMMARY:10/28/2020 Strongly Correlated Quantum Materials
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/10-28-2020-strongly-correlated-quantum-materials/
LOCATION:MA
CATEGORIES:Strongly Correlated Quantum Materials and High-Temperature Superconductors
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201028T140000
DTEND;TZID=America/New_York:20201028T150000
DTSTAMP:20260507T012426
CREATED:20240127T023200Z
LAST-MODIFIED:20240127T023200Z
UID:10001493-1603893600-1603897200@cmsa.fas.harvard.edu
SUMMARY:10/28/2020 RM&PT seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/10-28-2020-rmpt-seminar/
LOCATION:MA
CATEGORIES:Random Matrix & Probability Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201028T150000
DTEND;TZID=America/New_York:20201028T160000
DTSTAMP:20260507T012426
CREATED:20240127T031359Z
LAST-MODIFIED:20240515T201157Z
UID:10001502-1603897200-1603900800@cmsa.fas.harvard.edu
SUMMARY:Generalization bounds for rational self-supervised learning algorithms\, or "Understanding generalizations requires rethinking deep learning"
DESCRIPTION:Speakers: Boaz Barak and Yamini Bansal\, Harvard University Dept. of Computer Science \nTitle: Generalization bounds for rational self-supervised learning algorithms\, or “Understanding generalizations requires rethinking deep learning” \nAbstract: The generalization gap of a learning algorithm is the expected difference between its performance on the training data and its performance on fresh unseen test samples. Modern deep learning algorithms typically have large generalization gaps\, as they use more parameters than the size of their training set. Moreover the best known rigorous bounds on their generalization gap are often vacuous. In this talk we will see a new upper bound on the generalization gap of classifiers that are obtained by first using self-supervision to learn a complex representation of the (label free) training data\, and then fitting a simple (e.g.\, linear) classifier to the labels. Such classifiers have become increasingly popular in recent years\, as they offer several practical advantages and have been shown to approach state-of-art results. We show that (under the assumptions described below) the generalization gap of such classifiers tends to zero as long as the complexity of the simple classifier is asymptotically smaller than the number of training samples. We stress that our bound is independent of the complexity of the representation that can use an arbitrarily large number of parameters. Our bound assuming that the learning algorithm satisfies certain noise-robustness (adding small amount of label noise causes small degradation in performance) and rationality (getting the wrong label is not better than getting no label at all) conditions that widely (and sometimes provably) hold across many standard architectures. We complement this result with an empirical study\, demonstrating that our bound is non-vacuous for many popular representation-learning based classifiers on CIFAR-10 and ImageNet\, including SimCLR\, AMDIM and BigBiGAN. The talk will not assume any specific background in machine learning\, and should be accessible to a general mathematical audience. Joint work with Gal Kaplun. \n 
URL:https://cmsa.fas.harvard.edu/event/10-28-2020-new-technologies-in-mathematics-seminar/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-10.28.20.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201029T103000
DTEND;TZID=America/New_York:20201029T120000
DTSTAMP:20260507T012426
CREATED:20240127T023101Z
LAST-MODIFIED:20240127T023101Z
UID:10001492-1603967400-1603972800@cmsa.fas.harvard.edu
SUMMARY:10/29/2020 Quantum Matter Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/10-29-2020-quantum-matter-seminar/
LOCATION:MA
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201102T103000
DTEND;TZID=America/New_York:20201102T113000
DTSTAMP:20260507T012426
CREATED:20240127T021628Z
LAST-MODIFIED:20240127T021628Z
UID:10001483-1604313000-1604316600@cmsa.fas.harvard.edu
SUMMARY:11/9/2020 Math-Physics Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/11-9-2020-math-physics-seminar/
LOCATION:MA
CATEGORIES:Mathematical Physics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201102T103000
DTEND;TZID=America/New_York:20201102T113000
DTSTAMP:20260507T012426
CREATED:20240127T022854Z
LAST-MODIFIED:20240127T022854Z
UID:10001490-1604313000-1604316600@cmsa.fas.harvard.edu
SUMMARY:11/2/2020 Math-Physics Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/11-2-2020-math-physics-seminar/
LOCATION:MA
CATEGORIES:Mathematical Physics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201103T113000
DTEND;TZID=America/New_York:20201103T123000
DTSTAMP:20260507T012426
CREATED:20240127T022741Z
LAST-MODIFIED:20240127T022741Z
UID:10001489-1604403000-1604406600@cmsa.fas.harvard.edu
SUMMARY:11/3/2020 Computer Science for Mathematicians
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/11-3-2020-computer-science-for-mathematicians/
LOCATION:MA
CATEGORIES:Computer Science for Mathematicians Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201104T140000
DTEND;TZID=America/New_York:20201104T150000
DTSTAMP:20260507T012426
CREATED:20240127T021839Z
LAST-MODIFIED:20240127T021839Z
UID:10001485-1604498400-1604502000@cmsa.fas.harvard.edu
SUMMARY:11/04/2020 RMPT Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/11-04-2020-rmpt-seminar/
LOCATION:MA
CATEGORIES:Random Matrix & Probability Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201104T150000
DTEND;TZID=America/New_York:20201104T160000
DTSTAMP:20260507T012426
CREATED:20240127T021940Z
LAST-MODIFIED:20240515T200835Z
UID:10001486-1604502000-1604505600@cmsa.fas.harvard.edu
SUMMARY:Some exactly solvable models for machine learning via Statistical physics
DESCRIPTION:Speaker: Florent Krzakala\, EPFL \nTitle: Some exactly solvable models for machine learning via Statistical physics \nAbstract: The increasing dimensionality of data in the modern machine learning age presents new challenges and opportunities. The high dimensional settings allow one to use powerful asymptotic methods from probability theory and statistical physics to obtain precise characterizations and develop new algorithmic approaches. Statistical mechanics approaches\, in particular\, are very well suited for such problems. Will give examples of recent works in our group that build on powerful methods of statistical physics of disordered systems to analyze some relevant questions in machine learning and neural networks\, including overparameterization\, kernel methods\, and the behavior gradient descent algorithm in a high dimensional non-convex landscape.
URL:https://cmsa.fas.harvard.edu/event/11-4-2020-new-technologies-in-math/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-11.04.20.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201105T103000
DTEND;TZID=America/New_York:20201105T120000
DTSTAMP:20260507T012426
CREATED:20240127T021509Z
LAST-MODIFIED:20240127T021509Z
UID:10001482-1604572200-1604577600@cmsa.fas.harvard.edu
SUMMARY:11/05/2020 Quantum Matter Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/11-05-2020-quantum-matter-seminar/
LOCATION:MA
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201106T123000
DTEND;TZID=America/New_York:20201106T150000
DTSTAMP:20260507T012426
CREATED:20240127T021729Z
LAST-MODIFIED:20240127T021729Z
UID:10001484-1604665800-1604674800@cmsa.fas.harvard.edu
SUMMARY:11/6/2020 Strongly Correlated Quantum Materials Lecture
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/11-6-2020-strongly-correlated-quantum-materials-lecture/
LOCATION:MA
CATEGORIES:Strongly Correlated Quantum Materials and High-Temperature Superconductors
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201110T113000
DTEND;TZID=America/New_York:20201110T123000
DTSTAMP:20260507T012426
CREATED:20240127T021030Z
LAST-MODIFIED:20240127T021030Z
UID:10001479-1605007800-1605011400@cmsa.fas.harvard.edu
SUMMARY:11/10/2020 Computer Science for Mathematicians
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/11-10-2020-computer-science-for-mathematicians/
LOCATION:MA
CATEGORIES:Computer Science for Mathematicians Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201111T103000
DTEND;TZID=America/New_York:20201111T120000
DTSTAMP:20260507T012426
CREATED:20240127T020649Z
LAST-MODIFIED:20240127T020649Z
UID:10001476-1605090600-1605096000@cmsa.fas.harvard.edu
SUMMARY:11/11/2020 Quantum Matter Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/11-11-2020-quantum-matter-seminar/
LOCATION:MA
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201111T150000
DTEND;TZID=America/New_York:20201111T160000
DTSTAMP:20260507T012426
CREATED:20240127T021159Z
LAST-MODIFIED:20240515T200604Z
UID:10001480-1605106800-1605110400@cmsa.fas.harvard.edu
SUMMARY:Towards AI for mathematical modeling of complex biological systems: Machine-learned model reduction\, spatial graph dynamics\, and symbolic mathematics
DESCRIPTION:Speaker: Eric Mjolsness\, Departments of Computer Science and Mathematics\, UC Irvine \nTitle: Towards AI for mathematical modeling of complex biological systems: Machine-learned model reduction\, spatial graph dynamics\, and symbolic mathematics \nAbstract: The complexity of biological systems (among others) makes demands on the complexity of the mathematical modeling enterprise that could be satisfied with mathematical artificially intelligence of both symbolic and numerical flavors. Technologies that I think will be fruitful in this regard include (1) the use of machine learning to bridge spatiotemporal scales\, which I will illustrate with the “Dynamic Boltzmann Distribution” method for learning model reduction of stochastic spatial biochemical networks and the “Graph Prolongation Convolutional Network” approach to course-graining the biophysics of microtubules; (2) a meta-language for stochastic spatial graph dynamics\, “Dynamical Graph Grammars”\, that can represent structure-changing processes including microtubule dynamics and that has an underlying combinatorial theory related to operator algebras; and (3) an integrative conceptual architecture of typed symbolic modeling languages and structure-preserving maps between them\, including model reduction and implementation maps. \n  \n  \n 
URL:https://cmsa.fas.harvard.edu/event/11-11-2020-new-technologies-in-mathematics/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-11.11.20-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201111T150000
DTEND;TZID=America/New_York:20201111T160000
DTSTAMP:20260507T012426
CREATED:20240127T021307Z
LAST-MODIFIED:20240127T021307Z
UID:10001481-1605106800-1605110400@cmsa.fas.harvard.edu
SUMMARY:11/11/2020 RM&PT Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/11-11-2020-rmpt-seminar/
LOCATION:MA
CATEGORIES:Random Matrix & Probability Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201112T103000
DTEND;TZID=America/New_York:20201112T120000
DTSTAMP:20260507T012426
CREATED:20240127T020910Z
LAST-MODIFIED:20240127T020910Z
UID:10001478-1605177000-1605182400@cmsa.fas.harvard.edu
SUMMARY:11/12/2020 Condensed Matter Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/11-12-2020-condensed-matter-seminar/
LOCATION:MA
CATEGORIES:Colloquia & Seminar,Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201113T080000
DTEND;TZID=America/New_York:20201113T093000
DTSTAMP:20260507T012426
CREATED:20230707T112548Z
LAST-MODIFIED:20250328T201252Z
UID:10000145-1605254400-1605259800@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: Knot Invariants From Gauge Theory in Three\, Four\, and Five Dimensions
DESCRIPTION:Edward Witten (IAS) \nTitle: Knot Invariants From Gauge Theory in Three\, Four\, and Five Dimensions \nAbstract: I will explain connections between a sequence of theories in two\, three\, four\, and five dimensions and describe how these theories are related to the Jones polynomial of a knot and its categorification. \nTalk chair: Cliff Taubes \nVideo
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_witten/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Lecture_Witten-pdf.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201116T080000
DTEND;TZID=America/New_York:20201116T093000
DTSTAMP:20260507T012426
CREATED:20230707T112758Z
LAST-MODIFIED:20250328T200750Z
UID:10000895-1605513600-1605519000@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: Classical and quantum integrable systems in enumerative geometry
DESCRIPTION:Andrei Okounkov (Columbia University) \nTitle: Classical and quantum integrable systems in enumerative geometry \nAbstract: For more than a quarter of a century\, thanks to the ideas and questions originating in modern high-energy physics\, there has been a very fruitful interplay between enumerative geometry and integrable system\, both classical and quantum. While it is impossible to summarize even the most important aspects of this interplay in one talk\, I will try to highlight a few logical points with the goal to explain the place and the role of certain more recent developments. \nTalk chair: Cumrun Vafa \nVideo
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_okounkov/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Lecture_Okounkov-1-pdf.jpeg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201116T100000
DTEND;TZID=America/New_York:20201116T110000
DTSTAMP:20260507T012426
CREATED:20240127T020805Z
LAST-MODIFIED:20240127T020805Z
UID:10001477-1605520800-1605524400@cmsa.fas.harvard.edu
SUMMARY:11/16/2020 Mathematical Physics Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/11-16-2020-mathematical-physics-seminar/
LOCATION:MA
CATEGORIES:Mathematical Physics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201117T113000
DTEND;TZID=America/New_York:20201117T123000
DTSTAMP:20260507T012426
CREATED:20240127T020524Z
LAST-MODIFIED:20240127T020524Z
UID:10001475-1605612600-1605616200@cmsa.fas.harvard.edu
SUMMARY:11/17/2020 Computer Science for Mathematicians
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/11-17-2020-computer-science-for-mathematicians/
LOCATION:MA
CATEGORIES:Computer Science for Mathematicians Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201118T080000
DTEND;TZID=America/New_York:20201118T093000
DTSTAMP:20260507T012426
CREATED:20230707T113020Z
LAST-MODIFIED:20250328T201157Z
UID:10000896-1605686400-1605691800@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: Log Calabi-Yau fibrations
DESCRIPTION:Caucher Birkar (University of Cambridge) \nTitle: Log Calabi-Yau fibrations \nAbstract: Fano and Calabi-Yau varieties play a fundamental role in algebraic geometry\, differential geometry\, arithmetic geometry\, mathematical physics\, etc. The notion of log Calabi-Yau fibration unifies Fano and Calabi-Yau varieties\, their fibrations\, as well as their local birational counterparts such as flips and singularities. Such fibrations can be examined from many different perspectives. The purpose of this talk is to introduce the theory of log Calabi-Yau fibrations\, to remind some known results\, and to state some open problems. \nVideo \n 
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_birkar/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Lecture_Birkar-pdf.jpeg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201118T094500
DTEND;TZID=America/New_York:20201118T110000
DTSTAMP:20260507T012426
CREATED:20240209T115024Z
LAST-MODIFIED:20240507T202224Z
UID:10001870-1605692700-1605697200@cmsa.fas.harvard.edu
SUMMARY:Re-pricing avalanches
DESCRIPTION:Speaker: Jose A. Scheinkman (Columbia)\n\nTitle: Re-pricing avalanches\n\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.)
URL:https://cmsa.fas.harvard.edu/event/3-11-2020-colloquium/
LOCATION:Virtual
CATEGORIES:Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201118T103000
DTEND;TZID=America/New_York:20201118T120000
DTSTAMP:20260507T012426
CREATED:20240127T020411Z
LAST-MODIFIED:20240127T020411Z
UID:10001474-1605695400-1605700800@cmsa.fas.harvard.edu
SUMMARY:11/18/2020 Strongly Correlated Quantum Materials
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/11-18-2020-strongly-correlated-quantum-materials/
LOCATION:MA
CATEGORIES:Strongly Correlated Quantum Materials and High-Temperature Superconductors
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201118T140000
DTEND;TZID=America/New_York:20201118T150000
DTSTAMP:20260507T012426
CREATED:20240127T020254Z
LAST-MODIFIED:20240127T020254Z
UID:10001473-1605708000-1605711600@cmsa.fas.harvard.edu
SUMMARY:11/18/2020 RMPT
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/11-18-2020-rmpt/
LOCATION:MA
CATEGORIES:Random Matrix & Probability Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201118T150000
DTEND;TZID=America/New_York:20201118T160000
DTSTAMP:20260507T012426
CREATED:20240127T020145Z
LAST-MODIFIED:20240515T200420Z
UID:10001472-1605711600-1605715200@cmsa.fas.harvard.edu
SUMMARY:Universes as Big Data\, or Machine-Learning Mathematical Structures
DESCRIPTION:Speaker: Yang-Hui He\, Oxford University\, City University of London and Nankai University \nTitle: Universes as Big Data\, or Machine-Learning Mathematical Structures \nAbstract: We review how historically the problem of string phenomenology lead theoretical physics first to algebraic/differetial geometry\, and then to computational geometry\, and now to data science and AI. With the concrete playground of the Calabi-Yau landscape\, accumulated by the collaboration of physicists\, mathematicians and computer scientists over the last 4 decades\, we show how the latest techniques in machine-learning can help explore problems of physical and mathematical interest\, from geometry\, to group theory\, to combinatorics and number theory. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/11-18-2020-new-tech-in-math/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-11.18.20.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201119T113000
DTEND;TZID=America/New_York:20201119T120000
DTSTAMP:20260507T012426
CREATED:20240127T020029Z
LAST-MODIFIED:20240127T020029Z
UID:10001471-1605785400-1605787200@cmsa.fas.harvard.edu
SUMMARY:11/19/20 Strongly Correlated Quantum Materials
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/11-19-20-strongly-correlated-quantum-materials/
LOCATION:MA
CATEGORIES:Strongly Correlated Quantum Materials and High-Temperature Superconductors
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201120T080000
DTEND;TZID=America/New_York:20201120T093000
DTSTAMP:20260507T012426
CREATED:20230707T113302Z
LAST-MODIFIED:20250328T200635Z
UID:10000897-1605859200-1605864600@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: Homotopy spectra and Diophantine equations
DESCRIPTION:Yuri Manin (Max Planck Institute for Mathematics) \nTitle: Homotopy spectra and Diophantine equations \nAbstract: For a long stretch of time in the history of mathematics\, Number Theory and Topology formed vast\, but disjoint domains of mathematical knowledge. Origins of number theory can be traced back to the Babylonian clay tablet Plimpton 322 (about 1800 BC)  that contained a list of integer solutions of the “Diophantine” equation $a^2+b^2=c^2$: archetypal theme of number theory\, named after Diophantus of Alexandria (about 250 BC). Topology was born much later\, but arguably\, its cousin — modern measure theory\, — goes back to Archimedes\, author of Psammites (“Sand Reckoner”)\, who was approximately a contemporary of Diophantus. In modern language\, Archimedes measures the volume of observable universe by counting the number of small grains of sand necessary to fill this volume. Of course\, many qualitative geometric models and quantitative estimates of the relevant distances precede his calculations. Moreover\, since the estimated numbers of grains of sand are quite large (about $10^{64}$)\, Archimedes had to invent and describe a system of notation for large numbers going far outside the possibilities of any of the standard ancient systems. The construction of the first bridge between number theory and topology was accomplished only about fifty years ago: it is the theory of spectra in stable homotopy theory. In particular\, it connects $Z$\, the initial object in the theory of commutative rings\, with the sphere spectrum $S$. This connection poses the challenge: discover a new information in number theory using the developed independently machinery of homotopy theory. In this talk based upon the authors’ (Yu. Manin and M. Marcolli) joint research project\, I suggest to apply homotopy spectra to the problem of distribution of rational points upon algebraic manifolds. \nTalk chair: Michael Hopkins \nSlides | Video
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_manin/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Lecture_Manin-2-pdf.jpeg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201120T150200
DTEND;TZID=America/New_York:20210101T150200
DTSTAMP:20260507T012426
CREATED:20240209T015737Z
LAST-MODIFIED:20240307T111352Z
UID:10001789-1605884520-1609513320@cmsa.fas.harvard.edu
SUMMARY:Members’ Seminar
DESCRIPTION:The CMSA Members’ Seminar will occur every Friday at 9:30am ET on 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 seminar is organized by Tianqi Wu. The Schedule will be updated below. \nPrevious seminars can be found here. \nSpring 2021:\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n\n\n1/29/2021\nCancelled\n\n\n\n2/5/2021\nItamar Shamir\nTitle: Boundary CFT and conformal anomalies \nAbstract: Boundary and defects in quantum field theory play an important role in many recent developments in theoretical physics. I will discuss such objects in the setting of conformal field theories\, focusing mainly on conformal anomalies. Boundaries or defects can support various kinds of conformal anomalies on their world volume. Perhaps the one which is of greatest theoretical importance is associated with the Euler density in even dimensions. I will show how this anomaly is related to the one point function of exactly marginal deformations and how it arises explicitly from various correlation functions.\n\n\n2/12/2021\nLouis Fan\nTitle:  Joint distribution of Busemann functions in corner growth models \nAbstract: The 1+1 dimensional corner growth model with exponential weights is a centrally important exactly solvable model in the Kardar-Parisi-Zhang class of statistical mechanical models. While significant progress has been made on the fluctuations of the growing random shape\, understanding of the optimal paths\, or geodesics\, is less developed. The Busemann function is a useful analytical tool for studying geodesics. We present the joint distribution of the Busemann functions\, simultaneously in all directions of growth\, in terms of mappings that represent FIFO (first-in-first-out) queues. As applications of this description we derive a marked point process representation for the Busemann function across a single lattice edge and point out its implication on structure of semi-infinite  geodesics. This is joint work with Timo Seppäläinen.\n\n\n2/19/2021\nDaniel Junghans\nTitle: Control issues of the KKLT scenario in string theory \nAbstract: The simplest explanation for the observed accelerated expansion of the universe is that we live in a 4-dimensional de Sitter space. We analyze to which extent the KKLT proposal for the construction of such de Sitter vacua in string theory is quantitatively controlled. As our main finding\, we uncover and quantify an issue which one may want to call the “singular-bulk problem”. In particular\, we show that\, generically\, a significant part of the manifold on which string theory is compactified in the KKLT scenario becomes singular. This implies a loss of control over the supergravity approximation on which the construction relies.\n\n\n2/26/2021\nTsung-Ju Lee\nTitle: SYZ fibrations and complex affine structures \nAbstract: Strominger–Yau–Zaslow conjecture has been a guiding principle in mirror symmetry. The conjecture predicts the existence of special Lagrangian torus fibrations of a Calabi–Yau manifold near a large complex structure limit point. Moreover\, the mirror is given by the dual fibrations and the Ricci-flat metric is obtained from the semi-flat metric with corrections from holomorphic discs whose boundaries lie in a special Lagrangian fiber. By a result of Collins–Jacob–Lin\, the complement of a smooth elliptic curve in the projective plane admits a SYZ fibration. In this talk\, I will explain how to compute the complex affine structure induced from this SYZ fibration and show that it agrees with the affine structure used in Carl–Pumperla–Siebert. This is based on a joint work with Siu-Cheong Lau and Yu-Shen Lin.\n\n\n3/5/2021\nCancelled\n\n\n\n3/11/2021 \n9:00pm ET\nRyan Thorngren\nTitle:  Symmetry protected topological phases\, anomalies\, and their classification \nAbstract: I will give an overview of some mathematical aspects of the subject of symmetry protected topological phases (SPTs)\, especially as their theory relates to index theorems in geometry\, cobordism of manifolds\, and group cohomology.\n\n\n3/18/2021 \n9:00pm ET\nRyan Thorngren\nTitle:  Symmetry protected topological phases\, anomalies\, and their classification\nAbstract: I will give an overview of some mathematical aspects of the subject of symmetry protected topological phases (SPTs)\, especially as their theory relates to index theorems in geometry\, cobordism of manifolds\, and group cohomology.\n\n\n3/26/2021 \n8:30am ET\nAghil Alaee\nTitle:  Rich extra dimensions are hidden inside black holes \nAbstract: In this talk\, I present an argument that shows why it is difficult to see rich extra dimensions in the Universe.\n\n\n4/2/2021\n8:30am ET\nEnno Keßler\nTitle: Super Stable Maps of Genus Zero \nAbstract: I will report on a supergeometric generalization of J-holomorphic curves. Supergeometry is a mathematical theory of geometric spaces with anti-commuting coordinates and functions which is motivated by the concept of supersymmetry from theoretical physics. Super J-holomorphic curves and super stable maps couple the equations of classical J-holomorphic curves with a Dirac equation for spinors and might\, in the future\, lead to a supergeometric generalization of Gromov-Witten invariants.\n\n\n4/9/2021\nJuven Wang \nVideo\nTitle: Ultra Unification \nAbstract: Strong\, electromagnetic\, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). In this work\, we propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly matching and cobordism constraints (especially from the baryon minus lepton number B − L and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension\, whose low energy contains unitary topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase)\, or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase)\, or right-handed neutrinos\, or their combinations. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects\, etc.\, whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math\, QFT\, and condensed matter terminology\, and elaborate more on the nonperturbative global anomalies of Z2\, Z4\, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860\, arXiv:2008.06499\, arXiv:2006.16996\, arXiv:1910.14668.\n\n\n4/16/2021\nSergiy Verstyuk\nTitle: Deep learning methods for economics \nAbstract: The talk discusses some recent developments in neural network models and their applicability to problems in international economics as well as macro-via-micro economics. Along the way\, interpretability of neural networks features prominently.\n\n\n4/23/2021\nYifan Wang\nTitle: Virtues of Defects in Quantum Field Theories \nAbstract: Defects appear ubiquitously in many-body quantum systems as boundaries and impurities. They participate inextricably in the quantum dynamics and give rise to novel phase transitions and critical phenomena. Quantum field theory provides the natural framework to tackle these problems\, where defects define extended operators over sub-manifolds of the spacetime and enrich the usual operator algebra. Much of the recent progress in quantum field theory has been driven by the exploration of general structures in this extended operator algebra\, precision studies of defect observables\, and the implications thereof for strongly coupled dynamics. In this talk\, I will review selected developments along this line that enhance our understanding of concrete models in condensed matter and particle physics\, and that open new windows to nonperturbative effects in quantum gravity.\n\n\n4/30/2021\nYun Shi\nTitle: D-critical locus structure for local toric Calabi-Yau 3-fold \nAbstract: Donaldson-Thomas (DT) theory is an enumerative theory which produces a count of ideal sheaves of 1-dimensional subschemes on a Calabi-Yau 3-fold. Motivic Donaldson-Thomas theory\, originally introduced by Kontsevich-Soibelman\, is a categorification of the DT theory. This categorification contains more refined information of the moduli space. In this talk\, I will give a brief introduction to motivic DT theory following the definition of Bussi-Joyce-Meinhardt\, in particular the role of d-critical locus structure in the definition of motivic DT invariant. I will also discuss results on this structure on the Hilbert schemes of zero dimensional subschemes on local toric Calabi-Yau threefolds. This is based on joint work in progress with Sheldon Katz.\n\n\n5/7/2021\nThérèse Yingying Wu\nTitle: Topological aspects of Z/2Z eigenfunctions for the Laplacian on S^2 \nAbstract: In this talk\, I will present recent work with C. Taubes on an eigenvalue problem for the Laplacian on the round 2-sphere associated with a configuration of an even number of distinct points on that sphere\, denoted as C_2n. I will report our preliminary findings on how eigenvalues and eigenfunctions change as a function of the configuration space. I will also discuss how the compactification of C_2n is connected to the moduli space of algebraic curves (joint work with S.-T. Yau). There is a supergeometry tie-in too.\n\n\n5/14/2021\nDu Pei\nTitle: Three applications of TQFTs \nAbstract: Topological quantum field theories (TQFTs) often serve as a bridge between physics and mathematics. In this talk\, I will illustrate how TQFTs that arise in physics can help to shed light on 1) the quantization of moduli spaces 2) quantum invariants of 3-manifolds\, and 3) smooth structures on 4-manifolds.\n\n\n5/21/2021\nFarzan Vafa\nTitle: Active nematic defects and epithelial morphogenesis \nAbstract: Inspired by recent experiments that highlight the role of topological defects in morphogenesis\, we develop a minimal framework to study the dynamics of an active curved surface driven by its nematic texture (a rank 2 symmetric traceless tensor). Allowing the surface to evolve via relaxational dynamics (gradient flow) leads to a theory linking nematic defect dynamics\, cellular division rates\, and Gaussian curvature. Regions of large positive (negative) curvature and positive (negative) growth are colocalized with the presence of positive (negative) defects\, and cells accumulate at positive defects and are depleted at negative defects.  We also show that activity stabilizes a bound $+1$ defect state by creating an incipient tentacle\, while a bound $+1$ defect state surrounded by two $-1/2$ defects can create a stationary ring configuration of tentacles\, consistent with experimental observations. The talk is based on a recent paper with L Mahadevan [arXiv:2105.0106].\n\n\n\n\n\nFall 2020:\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n\n\n9/11/2020\nMoran Koren\nTitle:  Observational Learning and Inefficiencies in Waitlists \nAbstract: Many scarce resources are allocated through waitlists without monetary transfers. We consider a model\, in which objects with heterogeneous qualities are offered to strategic agents through a waitlist in a first-come-first-serve manner. Agents\, upon receiving an offer\, accept or reject it based on both a private signal about the quality of the object and the decisions of agents ahead of them on the list. This model combines observational learning and dynamic incentives\, two features that have been studied separately. We characterize the equilibrium and quantify the inefficiency that arises due to herding and selectivity. We find that objects with intermediate expected quality are discarded while objects with a lower expected quality may be accepted. These findings help in understanding the reasons for the substantial discard rate of transplant organs of various qualities despite the large shortage of organ supply.\n\n\n9/18/2020\nMichael Douglas\nTitle: A talk in two parts\, on strings and on computers and math \nAbstract: I am dividing my time between two broad topics. The first is string theory\, mostly topics in geometry and compactification. I will describe my current work on numerical Ricci flat metrics\, and list many open research questions. The second is computation and artificial intelligence. I will introduce transformer models (Bert\,GPT) which have led to breakthroughs on natural language processing\, describe their potential for helping us do math\, and sketch some related theoretical problems.\n\n\n9/25/2020\nCancelled – Math Science Lecture\n\n\n\n10/2/2020\nCancelled – Math Science Lecture\n\n\n\n10/9/2020\nWai Tong (Louis) Fan\nTitle: Stochastic PDE as scaling limits of interacting particle systems \nAbstract: Interacting particle models are often employed to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. These individual-based models capture fine details\, including randomness and discreteness of individuals\, that are not considered in continuum models such as partial differential equations (PDE) and integral-differential equations. The challenge is how to simultaneously retain key information in microscopic models as well as efficiency and robustness of macroscopic models.\nIn this talk\, I will discuss how this challenge can be overcome by elucidating the probabilistic connections between particle models and PDE. These connections also explain how stochastic partial differential equations (SPDE) arise naturally under a suitable choice of level of detail in modeling complex systems. I will also present some novel scaling limits including SPDE on graphs and coupled SPDE. These SPDE not only interpolate between particle models and PDE\, but also quantify the source and the order of magnitude of stochasticity. Scaling limit theorems and new duality formulas are obtained for these SPDE\, which connect phenomena across scales and offer insights about the genealogies and the time-asymptotic properties of the underlying population dynamics. Joint work with Rick Durrett.\n\n\n10/16/2020\nTianqi Wu\nTitle: Koebe circle domain conjecture and the Weyl problem in hyperbolic 3-space \nAbstract: In 1908\, Paul Koebe conjectured that every open connected set in the plane is conformally diffeomorphic to an open connected set whose boundary components are either round circles or points. The Weyl problem\, in the hyperbolic setting\, asks for isometric embedding of surfaces of curvature at least -1 into the hyperbolic 3-space. We show that there are close relationships among the Koebe conjecture\, the Weyl problem and the work of Alexandrov and Thurston on convex surfaces. This is a joint work with Feng Luo.\n\n\n10/23/2020\nChangji Xu\nTitle: Random Walk Among Bernoulli Obstacles \nAbstract: Place an obstacle with probability $1 – p$ independently at each vertex of $\mathbb Z^d$ and consider a simple symmetric random walk that is killed upon hitting one of the obstacles. This is called random walk among Bernoulli obstacles. The most prominent feature of this model is a strong localization effect: the random walk will be localized in a very small region conditional on the event that it survives for a long time. In this talk\, we will discuss some recent results about the behaviors of the conditional random walk\, in quenched\, annealed\, and biased settings.\n\n\n10/30/2020\nMichael Simkin\nTitle: The differential equation method in Banach spaces and the $n$-queens problem \nAbstract: The differential equation method is a powerful tool used to study the evolution of random combinatorial processes. By showing that the process is likely to follow the trajectory of an ODE\, one can study the deterministic ODE rather than the random process directly. We extend this method to ODEs in infinite-dimensional Banach spaces.\nWe apply this tool to the classical $n$-queens problem: Let $Q(n)$ be the number of placements of $n$ non-attacking chess queens on an $n \times n$ board. Consider the following random process: Begin with an empty board. For as long as possible choose\, uniformly at random\, a space with no queens in its row\, column\, or either diagonal\, and place on it a queen. We associate the process with an abstract ODE. By analyzing the ODE we conclude that the process almost succeeds in placing $n$ queens on the board. Furthermore\, we can obtain a complete $n$-queens placement by making only a few changes to the board. By counting the number of choices available at each step we conclude that $Q(n) \geq (n/C)^n$\, for a constant $C>0$ associated with the ODE. This is optimal up to the value of $C$.\n\n\n11/6/2020\nKenji Kawaguchi\nTitle: Deep learning: theoretical results on optimization and mixup \nAbstract: Deep neural networks have achieved significant empirical success in many fields\, including the fields of computer vision\, machine learning\, and artificial intelligence. Along with its empirical success\, deep learning has been theoretically shown to be attractive in terms of its expressive power. However\, the theory of the expressive power does not ensure that we can efficiently find an optimal solution in terms of optimization\, robustness\, and generalization\, during the optimization process of a neural network. In this talk\, I will discuss some theoretical results on optimization and the effect of mixup on robustness and generalization.\n\n\n11/13/2020\nOmri Ben-Eliezer\nTitle: Sampling in an adversarial environment \nAbstract: How many samples does one need to take from a large population in order to truthfully “represent” the population? While this cornerstone question in statistics is very well understood when the population is fixed in advance\, many situations in modern data analysis exhibit a very different behavior: the population interacts with and is affected by the sampling process. In such situations\, the existing statistical literature does not apply. \nWe propose a new sequential adversarial model capturing these situations\, where future data might depend on previously sampled elements; we then prove uniform laws of large numbers in this adversarial model. The results\, techniques\, and applications reveal close connections to various areas in mathematics and computer science\, including VC theory\, discrepancy theory\, online learning\, streaming algorithms\, and computational geometry. \nBased on joint works with Noga Alon\, Yuval Dagan\, Shay Moran\, Moni Naor\, and Eylon Yogev.\n\n\n11/20/2020\nCharles Doran\nTitle: The Calabi-Yau Geometry of Feynman Integrals \nAbstract: Over the past 30 years Calabi-Yau manifolds have proven to be the key geometric structures behind string theory and its variants. In this talk\, I will show how the geometry and moduli of Calabi-Yau manifolds provide a new framework for understanding and computing Feynman integrals. An important organizational principle is provided by mirror symmetry\, and specifically the DHT mirror correspondence. This is joint work with Andrey Novoseltsev and Pierre Vanhove.\n\n\n\nColloquia & Seminars\,Seminars
URL:https://cmsa.fas.harvard.edu/event/members-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201123T080000
DTEND;TZID=America/New_York:20201123T093000
DTSTAMP:20260507T012426
CREATED:20230707T113744Z
LAST-MODIFIED:20250328T200904Z
UID:10000899-1606118400-1606123800@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: Noncommutative Geometry\, the Spectral Aspect
DESCRIPTION:Alain Connes (Collège de France) \nTitle: Noncommutative Geometry\, the Spectral Aspect \nAbstract: This talk will be a survey of the spectral side of noncommutative geometry\, presenting the new paradigm of spectral triples and showing its relevance for the fine structure of space-time\, its large scale structure and also in number theory in connection with the zeros of the Riemann zeta function. \nTalk chair: Peter Kronheimer \nVideo 
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_connes/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Lecture_Connes-pdf.jpeg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201123T100000
DTEND;TZID=America/New_York:20201123T113000
DTSTAMP:20260507T012426
CREATED:20230707T113517Z
LAST-MODIFIED:20250328T200851Z
UID:10000898-1606125600-1606131000@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: Subfactors–in Memory of Vaughan Jones
DESCRIPTION:Zhengwei Liu (Tsinghua University) \nTitle: Subfactors–in Memory of Vaughan Jones \nAbstract: Jones initiated modern subfactor theory in the early 1980s and investigated this area for his whole academic life. Subfactor theory has both deep and broad connections with various areas in mathematics and physics. One well-known peak in the development of subfactor theory is the discovery of the Jones polynomial\, for which Jones won the Fields Medal in 1990. Let us travel back to the dark room at the beginning of the story\, to appreciate how radically our viewpoint has changed. \nTalk chair: Arthur Jaffe \nSlides | Video 
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_liu/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Lecture_Liu-pdf.jpeg
END:VEVENT
END:VCALENDAR