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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220406T093000
DTEND;TZID=America/New_York:20220406T103000
DTSTAMP:20240304T073658Z
CREATED:20240214T035619Z
LAST-MODIFIED:20240304T073658Z
UID:10002517-1649237400-1649241000@cmsa.fas.harvard.edu
SUMMARY:What is Mathematical Consciousness Science?
DESCRIPTION:Speaker: Johannes Kleiner\, LMU München \nTitle: What is Mathematical Consciousness Science? \nAbstract: In the last three decades\, the problem of consciousness – how and why physical systems such as the brain have conscious experiences – has received increasing attention among neuroscientists\, psychologists\, and philosophers. Recently\, a decidedly mathematical perspective has emerged as well\, which is now called Mathematical Consciousness Science. In this talk\, I will give an introduction and overview of Mathematical Consciousness Science for mathematicians\, including a bottom-up introduction to the problem of consciousness and how it is amenable to mathematical tools and methods.
URL:https://cmsa.fas.harvard.edu/event/what-is-mathematical-consciousness-science/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/02CMSA-Colloquium-04.06.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220408T084500
DTEND;TZID=America/New_York:20220408T101500
DTSTAMP:20240301T105121Z
CREATED:20240214T084325Z
LAST-MODIFIED:20240301T105121Z
UID:10002595-1649407500-1649412900@cmsa.fas.harvard.edu
SUMMARY:Synthetic Regression Discontinuity: Estimating Treatment Effects using Machine Learning
DESCRIPTION:Speaker: Jörn Boehnke \nTitle: Synthetic Regression Discontinuity: Estimating Treatment Effects using Machine Learning \nAbstract:  In the standard regression discontinuity setting\, treatment assignment is based on whether a unit’s observable score (running variable) crosses a known threshold.  We propose a two-stage method to estimate the treatment effect when the score is unobservable to the econometrician while the treatment status is known for all units.  In the first stage\, we use a statistical model to predict a unit’s treatment status based on a continuous synthetic score.  In the second stage\, we apply a regression discontinuity design using the predicted synthetic score as the running variable to estimate the treatment effect on an outcome of interest.  We establish conditions under which the method identifies the local treatment effect for a unit at the threshold of the unobservable score\, the same parameter that a standard regression discontinuity design with known score would identify. We also examine the properties of the estimator using simulations\, and propose the use machine learning algorithms to achieve high prediction accuracy.  Finally\, we apply the method to measure the effect of an investment grade rating on corporate bond prices by any of the three largest credit ratings agencies.  We find an average 1% increase in the prices of corporate bonds that received an investment grade as opposed to a non-investment grade rating.
URL:https://cmsa.fas.harvard.edu/event/4-8-2022-member-seminar/
LOCATION:Virtual
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220413T093000
DTEND;TZID=America/New_York:20220413T103000
DTSTAMP:20240304T073600Z
CREATED:20240214T035353Z
LAST-MODIFIED:20240304T073600Z
UID:10002516-1649842200-1649845800@cmsa.fas.harvard.edu
SUMMARY:Quantisation in monoidal categories and quantum operads
DESCRIPTION:Abstract: The standard definition of symmetries of a structure given on a set S (in the sense of Bourbaki) is the group of bijective maps S to S\, compatible with this structure. But in fact\, symmetries of various structures related to storing and transmitting information (such as information spaces) are naturally embodied in various classes of loops such as Moufang loops\, – nonassociative analogs of groups. The idea of symmetry as a group is closely related to classical physics\, in a very definite sense\, going back at least to Archimedes. When quantum physics started to replace classical\, it turned out that classical symmetries must also be replaced by their quantum versions\, e.g. quantum groups. \nIn this talk we explain how to define and study quantum versions of symmetries\, relevant to information theory and other contexts.
URL:https://cmsa.fas.harvard.edu/event/quantisation-in-monoidal-categories-and-quantum-operads/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-04.13.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220427T093000
DTEND;TZID=America/New_York:20220427T103000
DTSTAMP:20240304T073208Z
CREATED:20240214T034934Z
LAST-MODIFIED:20240304T073208Z
UID:10002515-1651051800-1651055400@cmsa.fas.harvard.edu
SUMMARY:Long common subsequences between bit-strings and the zero-rate threshold of deletion-correcting codes
DESCRIPTION:Speaker: Venkatesan Guruswami\, UC Berkeley \nTitle: Long common subsequences between bit-strings and the zero-rate threshold of deletion-correcting codes \nAbstract: Suppose we transmit n bits on a noisy channel that deletes some fraction of the bits arbitrarily. What’s the supremum p* of deletion fractions that can be corrected with a binary code of non-vanishing rate? Evidently p* is at most 1/2 as the adversary can delete all occurrences of the minority bit. It was unknown whether this simple upper bound could be improved\, or one could in fact correct deletion fractions approaching 1/2.\nWe show that there exist absolute constants A and delta > 0 such that any subset of n-bit strings of size exp((log n)^A) must contain two strings with a common subsequence of length (1/2+delta)n. This immediately implies that the zero-rate threshold p* of worst-case bit deletions is bounded away from 1/2. \nOur techniques include string regularity arguments and a structural lemma that classifies bit-strings by their oscillation patterns. Leveraging these tools\, we find in any large code two strings with similar oscillation patterns\, which is exploited to find a long common subsequence. \nThis is joint work with Xiaoyu He and Ray Li.
URL:https://cmsa.fas.harvard.edu/event/long-common-subsequences-between-bit-strings-and-the-zero-rate-threshold-of-deletion-correcting-codes/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-04.27.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220429T093000
DTEND;TZID=America/New_York:20220429T110000
DTSTAMP:20240229T090935Z
CREATED:20240215T100221Z
LAST-MODIFIED:20240229T090935Z
UID:10002735-1651224600-1651230000@cmsa.fas.harvard.edu
SUMMARY:Machine Learning the Gravity Equation for International Trade
DESCRIPTION:Member Seminar \nSpeaker: Sergiy Verstyuk \nTitle: Machine Learning the Gravity Equation for International Trade \nAbstract: We will go through modern deep learning methods and existing approaches to their interpretation. Next\, I will describe a graph neural network framework. You will also be introduced to an economic analog of gravity. Finally\, we will see how these tools can help understand observed trade flows between 181 countries over 68 years. [Joint work with Michael R. Douglas.]
URL:https://cmsa.fas.harvard.edu/event/4-29-2022-member-seminar/
LOCATION:Virtual
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220513T093000
DTEND;TZID=America/New_York:20220513T110000
DTSTAMP:20240301T105004Z
CREATED:20240214T084053Z
LAST-MODIFIED:20240301T105004Z
UID:10002593-1652434200-1652439600@cmsa.fas.harvard.edu
SUMMARY:Cobordism and Deformation Class of the Standard Model and Beyond: Proton Stability and Neutrino Mass
DESCRIPTION:Member Seminar \nSpeaker: Juven Wang \nTitle: Cobordism and Deformation Class of the Standard Model and Beyond: Proton Stability and Neutrino Mass \nAbstract: ‘t Hooft anomalies of quantum field theories (QFTs) with an invertible global symmetry G (including spacetime and internal symmetries) in a d-dim spacetime are known to be classified by a d+1-dim cobordism group TPd+1(G)\, whose group generator is a d+1-dim cobordism invariant written as a d+1-dim invertible topological field theory. Deformation class of QFT is recently proposed to be specified by its symmetry G and a d+1-dim invertible topological field theory. Seemly different QFTs of the same deformation class can be deformed to each other via quantum phase transitions. We ask which deformation class controls the 4d ungauged or gauged (SU(3)×SU(2)×U(1))/Zq Standard Model (SM) for q=1\,2\,3\,6 with a continuous or discrete (B−L) symmetry and with also a compatible discrete baryon plus lepton Z_{2Nf} B+L symmetry. (The Z_{2Nf} B+L is discrete due to the ABJ anomaly under the BPST instanton.) We explore a systematic classification of candidate perturbative local and nonperturbative global anomalies of the 4d SM\, including all these gauge and gravitational backgrounds\, via a cobordism theory\, which controls the SM’s deformation class. While many Grand Unified Theories violating the discrete B+L symmetry suffer from the proton decay\, the SM and some versions of Ultra Unification (constrained by Z_{16} class global anomaly that replaces sterile neutrinos with new exotic gapped/gapless topological or conformal sectors) can have a stable proton. Dictated by a Z_2 class global mixed gauge-gravitational anomaly\, there can be a gapless deconfined quantum critical region between Georgi-Glashow and Pati-Salam models — the Standard Model and beyond occur as neighbor phases. We will also comment on a new mechanism to give the neutrino mass via topological field theories and topological defects. Work based on arXiv:2112.14765\, arXiv:2204.08393\, arXiv:2202.13498 and references therein.
URL:https://cmsa.fas.harvard.edu/event/5-13-2022-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220518T093000
DTEND;TZID=America/New_York:20220518T103000
DTSTAMP:20240502T151226Z
CREATED:20240214T055948Z
LAST-MODIFIED:20240502T151226Z
UID:10002547-1652866200-1652869800@cmsa.fas.harvard.edu
SUMMARY:Statistical Mechanics of Mutilated Sheets and Shells
DESCRIPTION:Speaker: David Nelson\, Harvard University \nTitle: Statistical Mechanics of Mutilated Sheets and Shells \nAbstract:  Understanding deformations of macroscopic thin plates and shells has a long and rich history\, culminating with the Foeppl-von Karman equations in 1904\, a precursor of general relativity characterized by a dimensionless coupling constant (the “Foeppl-von Karman number”) that can easily reach  vK = 10^7 in an ordinary sheet of writing paper.  However\, thermal fluctuations in thin elastic membranes fundamentally alter the long wavelength physics\, as exemplified by experiments that twist and bend individual atomically-thin free-standing graphene sheets (with vK = 10^13!)   A crumpling transition out of the flat phase for thermalized elastic membranes has been predicted when kT is large compared to the microscopic bending stiffness\, which could have interesting consequences for Dirac cones of electrons embedded in graphene.   It may be possible to lower the crumpling temperature for graphene to more readily accessible range by inserting a regular lattice of laser-cut perforations\, an expectation an confirmed by extensive molecular dynamics simulations.    We then move on to analyze the physics of sheets mutilated with puckers and stitches.   Puckers and stitches lead to Ising-like phase transitions riding on a background of flexural phonons\, as well as an anomalous coefficient of thermal expansion.  Finally\, we argue that thin membranes with a background curvature lead to thermalized spherical shells that must collapse beyond a critical size at room temperature\, even in the absence of an external pressure.
URL:https://cmsa.fas.harvard.edu/event/statistical-mechanics-of-mutilated-sheets-and-shells/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-05.18.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220722T093000
DTEND;TZID=America/New_York:20220722T110000
DTSTAMP:20240216T093333Z
CREATED:20240216T093333Z
LAST-MODIFIED:20240216T093333Z
UID:10002762-1658482200-1658487600@cmsa.fas.harvard.edu
SUMMARY:7/22/2020 Quantum Matter Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/7-22-2020-quantum-matter-seminar/
LOCATION:MA
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220909T120000
DTEND;TZID=America/New_York:20220909T130000
DTSTAMP:20240301T084734Z
CREATED:20240301T084734Z
LAST-MODIFIED:20240301T084734Z
UID:10002889-1662724800-1662728400@cmsa.fas.harvard.edu
SUMMARY:Duality in Einstein’s Gravity
DESCRIPTION:Title: Duality in Einstein’s Gravity \nAbstract: Electric-Magnetic duality has been a key feature behind our understanding of Quantum Field Theory for over a century. In this talk I will describe a similar property in Einstein’s gravity. The gravitational duality reveals\, in turn\, a wide range of new IR phenomena\, including aspects of the double copy for scattering amplitudes\, asymptotic symmetries and more.
URL:https://cmsa.fas.harvard.edu/event/duality-in-einsteins-gravity/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220914T120000
DTEND;TZID=America/New_York:20220914T130000
DTSTAMP:20240229T110925Z
CREATED:20240214T114614Z
LAST-MODIFIED:20240229T110925Z
UID:10002707-1663156800-1663160400@cmsa.fas.harvard.edu
SUMMARY:Strategyproof-Exposing Mechanisms Descriptions
DESCRIPTION:Colloquium \nSpeaker: Yannai Gonczarowski (Harvard)\n\nTitle: Strategyproof-Exposing Mechanisms Descriptions \nAbstract: One of the crowning achievements of the field of Mechanism Design has been the design and usage of the so-called “Deferred Acceptance” matching algorithm. Designed in 1962 and awarded the Nobel Prize in 2012\, this algorithm has been used around the world in settings ranging from matching students to schools to matching medical doctors to residencies. A hallmark of this algorithm is that unlike many other matching algorithms\, it is “strategy-proof”: participants can never gain by misreporting their preferences (say\, over schools) to the algorithm. Alas\, this property is far from apparent from the algorithm description. Its mathematical proof is so delicate and complex\, that (for example) school districts in which it is implemented do not even attempt to explain to students and parents why this property holds\, but rather resort to an appeal to authority: Nobel laureates have proven this property\, so one should listen to them. Unsurprisingly perhaps\, there is a growing body of evidence that participants in Deferred Acceptance attempt (unsuccessfully) to “game it\,” which results in a suboptimal match for themselves and for others. \nBy developing a novel framework of algorithm description simplicity—grounded at the intersection between Economics and Computer Science—we present a novel\, starkly different\, yet equivalent\, description for the Deferred Acceptance algorithm\, which\, in a precise sense\, makes its strategyproofness far more apparent. Our description does have a downside\, though: some other of its most fundamental properties—for instance\, that no school exceeds its capacity—are far less apparent than from all traditional descriptions of the algorithm. Using the theoretical framework that we develop\, we mathematically address the question of whether and to what extent this downside is unavoidable\, providing a possible explanation for why our description of the algorithm has eluded discovery for over half a century. Indeed\, it seems that in the design of all traditional descriptions of the algorithm\, it was taken for granted that properties such as no capacity getting exceeded should be apparent. Our description emphasizes the property that is important for participants to correctly interact with the algorithm\, at the expense of properties that are mostly of interest to policy makers\, and thus has the potential of vastly improving access to opportunity for many populations. Our theory provides a principled way of recasting algorithm descriptions in a way that makes certain properties of interest easier to explain and grasp\, which we also support with behavioral experiments in the lab. \nJoint work with Ori Heffetz and Clayton Thomas.
URL:https://cmsa.fas.harvard.edu/event/collquium-title-tba/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-09.14.22-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220914T140000
DTEND;TZID=America/New_York:20220914T150000
DTSTAMP:20240301T091205Z
CREATED:20230808T183823Z
LAST-MODIFIED:20240301T091205Z
UID:10001210-1663164000-1663167600@cmsa.fas.harvard.edu
SUMMARY:Breaking the one-mind-barrier in mathematics using formal verification
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Johan Commelin\, Mathematisches Institut\, Albert-Ludwigs-Universität Freiburg \nTitle: Breaking the one-mind-barrier in mathematics using formal verification \nAbstract: In this talk I will argue that formal verification helps break the one-mind-barrier in mathematics. Indeed\, formal verification allows a team of mathematicians to collaborate on a project\, without one person understanding all parts of the project. At the same time\, it also allows a mathematician to rapidly free mental RAM in order to work on a different component of a project. It thus also expands the one-mind-barrier. \nI will use the Liquid Tensor Experiment as an example\, to illustrate the above two points. This project recently finished the formalization of the main theorem of liquid vector spaces\, following up on a challenge by Peter Scholze. \nVideo
URL:https://cmsa.fas.harvard.edu/event/breaking-the-one-mind-barrier-in-mathematics-using-formal-verification/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220916T110000
DTEND;TZID=America/New_York:20220916T120000
DTSTAMP:20240301T084243Z
CREATED:20240214T105636Z
LAST-MODIFIED:20240301T084243Z
UID:10002686-1663326000-1663329600@cmsa.fas.harvard.edu
SUMMARY:Derivation of AdS/CFT for Vector Models
DESCRIPTION:Member Seminar\n\nSpeaker: Shai Chester\n\nTitle: Derivation of AdS/CFT for Vector Models\nAbstract: We derive an explicit map at finite N between the singlet sector of the free and critical O(N) and U(N) vector models in any spacetime dimension above two\, and a bulk higher spin theory in anti-de Sitter space in one higher dimension. For the boundary theory\, we use the bilocal formalism of Jevicki et al to restrict to the singlet sector of the vector model. The bulk theory is defined from the boundary theory via our mapping\, and is a consistent quantum higher spin theory with a well defined action. Our mapping relates bilocal operators in the boundary theory to higher spin fields in the bulk\, while single trace local operators in the boundary theory are related to boundary values of higher spin fields. We also discuss generalizations of the map to gauge theories\, and at finite temperature.
URL:https://cmsa.fas.harvard.edu/event/derivation-of-ads-cft-for-vector-models/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220921T123000
DTEND;TZID=America/New_York:20220921T133000
DTSTAMP:20240502T145616Z
CREATED:20240214T114047Z
LAST-MODIFIED:20240502T145616Z
UID:10002705-1663763400-1663767000@cmsa.fas.harvard.edu
SUMMARY:Moduli spaces of graphs
DESCRIPTION:Colloquium\n\nSpeaker: Melody Chan\, Brown\n\nTitle: Moduli spaces of graphs\n\nAbstract: A metric graph is a graph—a finite network of vertices and edges—together with a prescription of a positive real length on each edge. I’ll use the term “moduli space of graphs” to refer to certain combinatorial spaces—think simplicial complexes—that furnish parameter spaces for metric graphs. There are different flavors of spaces depending on some additional choices of decorations on the graphs\, but roughly\, each cell parametrizes all possible metrizations of a fixed combinatorial graph. Many flavors of these moduli spaces have been in circulation for a while\, starting with the work of Culler-Vogtmann in the 1980s on Outer Space. They have also recently played an important role in some recent advances using tropical geometry to study the topology of moduli spaces of curves and other related spaces. These advances give me an excuse to give what I hope will be an accessible introduction to moduli spaces of graphs and their connections with geometry.
URL:https://cmsa.fas.harvard.edu/event/collquium-92122/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-09.21.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220923T110000
DTEND;TZID=America/New_York:20220923T120000
DTSTAMP:20240301T083553Z
CREATED:20240214T105452Z
LAST-MODIFIED:20240301T083553Z
UID:10002685-1663930800-1663934400@cmsa.fas.harvard.edu
SUMMARY:Random determinants\, the elastic manifold\, and landscape complexity beyond invariance
DESCRIPTION:Member Seminar \nSpeaker: Ben McKenna \nTitle: Random determinants\, the elastic manifold\, and landscape complexity beyond invariance \nAbstract: The Kac-Rice formula allows one to study the complexity of high-dimensional Gaussian random functions (meaning asymptotic counts of critical points) via the determinants of large random matrices. We present new results on determinant asymptotics for non-invariant random matrices\, and use them to compute the (annealed) complexity for several types of landscapes. We focus especially on the elastic manifold\, a classical disordered elastic system studied for example by Fisher (1986) in fixed dimension and by Mézard and Parisi (1992) in the high-dimensional limit. We confirm recent formulas of Fyodorov and Le Doussal (2020) on the model in the Mézard-Parisi setting\, identifying the boundary between simple and glassy phases. Joint work with Gérard Ben Arous and Paul Bourgade.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-title-tba/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220928T123000
DTEND;TZID=America/New_York:20220928T133000
DTSTAMP:20240229T110654Z
CREATED:20230817T172722Z
LAST-MODIFIED:20240229T110654Z
UID:10001265-1664368200-1664371800@cmsa.fas.harvard.edu
SUMMARY:The Tree Property and uncountable cardinals
DESCRIPTION:Colloquium \nSpeaker: Dima Sinapova (Rutgers University) \nTitle: The Tree Property and uncountable cardinals \nAbstract: In the late 19th century Cantor discovered that there are different levels of infinity. More precisely he showed that there is no bijection between the natural numbers and the real numbers\, meaning that the reals are uncountable. He then went on to discover a whole hierarchy of infinite cardinal numbers. It is natural to ask if finitary and countably infinite combinatorial objects have uncountable analogues. It turns out that the answer is yes. \nWe will focus on one such key combinatorial property\, the tree property. A classical result from graph theory (König’s infinity lemma) shows the existence of this property for countable trees. We will discuss what happens in the case of uncountable trees.\n\n 
URL:https://cmsa.fas.harvard.edu/event/collquium-title-tba-2-2/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-09.28.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220928T140000
DTEND;TZID=America/New_York:20220928T150000
DTSTAMP:20240214T110335Z
CREATED:20230808T184138Z
LAST-MODIFIED:20240214T110335Z
UID:10001211-1664373600-1664377200@cmsa.fas.harvard.edu
SUMMARY:Statistical mechanics of neural networks: From the geometry of high dimensional error landscapes to beating power law neural scaling
DESCRIPTION:New Technologies in Mathematics \nSpeaker: Surya Ganguli\, Stanford University \n\nTitle: Statistical mechanics of neural networks: From the geometry of high dimensional error landscapes to beating power law neural scaling\n\n\n\n\nAbstract: Statistical mechanics and neural network theory have long enjoyed fruitful interactions.  We will review some of our recent work in this area and then focus on two vignettes. First we will analyze the high dimensional geometry of neural network error landscapes that happen to arise as the classical limit of a dissipative many-body quantum optimizer.  In particular\, we will be able to use the Kac-Rice formula and the replica method to calculate the number\, location\, energy levels\, and Hessian eigenspectra of all critical points of any index.  Second we will review recent work on neural power laws\, which reveal that the error of many neural networks falls off as a power law with network size or dataset size.  Such power laws have motivated significant societal investments in large scale model training and data collection efforts.  Inspired by statistical mechanics calculations\, we show both in theory and in practice how we can beat neural power law scaling with respect to dataset size\, sometimes achieving exponential scaling\, by collecting small carefully curated datasets rather than large random ones.\n\n\n\nReferences: Y. 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.\n\nSorscher\, Ben\, Robert Geirhos\, Shashank Shekhar\, Surya Ganguli\, and Ari S. Morcos. 2022. Beyond Neural Scaling Laws: Beating Power Law Scaling via Data Pruning https://arxiv.org/abs/2206.14486 (NeurIPS 2022).
URL:https://cmsa.fas.harvard.edu/event/8303/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-09.28.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220930T110000
DTEND;TZID=America/New_York:20220930T120000
DTSTAMP:20240301T081921Z
CREATED:20240214T105247Z
LAST-MODIFIED:20240301T081921Z
UID:10002683-1664535600-1664539200@cmsa.fas.harvard.edu
SUMMARY:Kahler geometry in twisted materials
DESCRIPTION:Member Seminar \nSpeaker: Jie Wang \nTitle: Kahler geometry in twisted materials \nAbstract: Flatbands are versatile platform for realizing exotic quantum phases due to the enhanced interactions. The canonical example is Landau level where fractional quantum Hall physics exists. Although interaction is strong\, the fractional quantum Hall effect is relatively well understood thanks to its model wavefunction\, exact parent Hamiltonian\, conformal field theory analogous and other exact aspects. In generic flatbands\, the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries\, in particular the Berry curvature and the Fubini-Study metric\, which are in general spatially non-uniform. It is commonly believed that the non-uniform geometries destroy these exact properties of fractional quantum Hall physics\, making many-body states less stable in flatbands. \nIn this talk\, I will disprove this common belief by showing a large family of flatbands (ideal flatbands) where quantum geometries can be highly non-uniform\, but still exhibit exact properties such as model wavefunctions\, density algebra\, exact parent Hamiltonians. I will discuss both the theory of ideal flatband\, its experimental realization in Dirac materials as well as implications.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-93022/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221005T140000
DTEND;TZID=America/New_York:20221005T160000
DTSTAMP:20240214T110102Z
CREATED:20230808T184616Z
LAST-MODIFIED:20240214T110102Z
UID:10001212-1664978400-1664985600@cmsa.fas.harvard.edu
SUMMARY:Minerva: Solving Quantitative Reasoning Problems with Language Models
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Guy Gur-Ari\, Google Research \nTitle: Minerva: Solving Quantitative Reasoning Problems with Language Models \nAbstract: Quantitative reasoning tasks which can involve mathematics\, science\, and programming are often challenging for machine learning models in general and for language models in particular. We show that transformer-based language models obtain significantly better performance on math and science questions when trained in an unsupervised way on a large\, math-focused dataset. Performance can be further improved using prompting and sampling techniques including chain-of-thought and majority voting. Minerva\, a model that combines these techniques\, achieves SOTA on several math and science benchmarks. I will describe the model\, its capabilities and limitations.
URL:https://cmsa.fas.harvard.edu/event/minerva-solving-quantitative-reasoning-problems-with-language-models/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/10.05.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221005T160000
DTEND;TZID=America/New_York:20221005T170000
DTSTAMP:20240229T110447Z
CREATED:20230817T173038Z
LAST-MODIFIED:20240229T110447Z
UID:10001266-1664985600-1664989200@cmsa.fas.harvard.edu
SUMMARY:Quantum statistical mechanics of charged black holes and strange metals
DESCRIPTION:Colloquium \nPlease note this colloquium will be held at a special time:  4:00-5:00 pm. \nSpeaker: Subir Sachdev (Harvard) \nTitle: Quantum statistical mechanics of charged black holes and strange metals\n\nAbstract: The Sachdev-Ye-Kitaev model was introduced as a toy model of interacting fermions without any particle-like excitations. I will describe how this toy model yields the universal low energy quantum theory of generic charged black holes in asymptotically 3+1 dimensional Minkowski space. I will also discuss how extensions of the SYK model yield a realistic theory of the strange metal phase of correlated electron systems.\n\n\nSlides: cmsa22
URL:https://cmsa.fas.harvard.edu/event/colloquium_10522/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.05.22-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221007T110000
DTEND;TZID=America/New_York:20221007T120000
DTSTAMP:20240301T081713Z
CREATED:20240214T105028Z
LAST-MODIFIED:20240301T081713Z
UID:10002681-1665140400-1665144000@cmsa.fas.harvard.edu
SUMMARY:Principal flow\, sub-manifold and boundary
DESCRIPTION:Member Seminar  \nSpeaker: Zhigang Yao \nTitle: Principal flow\, sub-manifold and boundary \nAbstract: While classical statistics has dealt with observations which are real numbers or elements of a real vector space\, nowadays many statistical problems of high interest in the sciences deal with the analysis of data which consist of more complex objects\, taking values in spaces which are naturally not (Euclidean) vector spaces but which still feature some geometric structure. I will discuss the problem of finding principal components to the multivariate datasets\, that lie on an embedded nonlinear Riemannian manifold within the higher-dimensional space. The aim is to extend the geometric interpretation of PCA\, while being able to capture the non-geodesic form of variation in the data. I will introduce the concept of a principal sub-manifold\, a manifold passing through the center of the data\, and at any point on the manifold extending in the direction of highest variation in the space spanned by the eigenvectors of the local tangent space PCA. We show the principal sub-manifold yields the usual principal components in Euclidean space. We illustrate how to find\, use and interpret the principal sub-manifold\, by which a principal boundary can be further defined for data sets on manifolds.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-10722/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221012T123000
DTEND;TZID=America/New_York:20221012T133000
DTSTAMP:20240222T165414Z
CREATED:20230817T173346Z
LAST-MODIFIED:20240222T165414Z
UID:10001267-1665577800-1665581400@cmsa.fas.harvard.edu
SUMMARY:Complete disorder is impossible: Some topics in Ramsey theory
DESCRIPTION:Colloquium \nSpeaker: James Cummings\,Carnegie Mellon University \nTitle: Complete disorder is impossible: Some topics in Ramsey theory \nAbstract: The classical infinite Ramsey theorem states that if we colour pairs of natural numbers using two colours\, there is an infinite set all of whose pairs get the same colour. This is the beginning of a rich theory\, which touches on many areas of mathematics including graph theory\, set theory and dynamics. I will give an overview of Ramsey theory\, emphasizing the diverse ideas which are at play in this area.
URL:https://cmsa.fas.harvard.edu/event/collquium-101222/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.12.22-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221014T110000
DTEND;TZID=America/New_York:20221014T120000
DTSTAMP:20240301T081027Z
CREATED:20240214T103536Z
LAST-MODIFIED:20240301T081027Z
UID:10002676-1665745200-1665748800@cmsa.fas.harvard.edu
SUMMARY:Quantum magnet chains and Kashiwara crystals
DESCRIPTION:Speaker: Leonid Rybnikov\, Harvard CMSA/National Research University Higher School of Economics \nTitle: Quantum magnet chains and Kashiwara crystals \nAbstract: Solutions of the algebraic Bethe ansatz for quantum magnet chains are\, generally\, multivalued functions of the parameters of the integrable system. I will explain how to compute some monodromies of solutions of Bethe ansatz for the Gaudin magnet chain. Namely\, the Bethe eigenvectors in the Gaudin model can be regarded as a covering of the Deligne-Mumford moduli space of stable rational curves\, which is unramified over the real locus of the Deligne-Mumford space. The monodromy action of the fundamental group of this space (called cactus group) on the eigenlines can be described very explicitly in purely combinatorial terms of Kashiwara crystals — i.e. combinatorial objects modeling the tensor category of finite-dimensional representations of a semisimple Lie algebra g. More specifically\, this monodromy action is naturally equivalent to the action of the same group by commutors (i.e. combinatorial analog of a braiding) on a tensor product of Kashiwara crystals. This is joint work with Iva Halacheva\, Joel Kamnitzer\, and Alex Weekes.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-101422/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-10.14.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221019T123000
DTEND;TZID=America/New_York:20221019T133000
DTSTAMP:20240214T113414Z
CREATED:20230817T173735Z
LAST-MODIFIED:20240214T113414Z
UID:10001268-1666182600-1666186200@cmsa.fas.harvard.edu
SUMMARY:The Mobility Edge of Lévy Matrices
DESCRIPTION:Colloquium \nSpeaker: Patrick Lopatto (Brown) \nTitle: The Mobility Edge of Lévy Matrices \nAbstract: Lévy matrices are symmetric random matrices whose entry distributions lie in the domain of attraction of an alpha-stable law; such distributions have infinite variance when alpha is less than 2. Due to the ubiquity of heavy-tailed randomness\, these models have been broadly applied in physics\, finance\, and statistics. When the entries have infinite mean\, Lévy matrices are predicted to exhibit a phase transition separating a region of delocalized eigenvectors from one with localized eigenvectors. We will discuss the physical context for this conjecture\, and describe a result establishing it for values of alpha close to zero and one. This is joint work with Amol Aggarwal and Charles Bordenave.
URL:https://cmsa.fas.harvard.edu/event/collquium-101922/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.19.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221019T140000
DTEND;TZID=America/New_York:20221019T150000
DTSTAMP:20240215T095357Z
CREATED:20230808T184955Z
LAST-MODIFIED:20240215T095357Z
UID:10001213-1666188000-1666191600@cmsa.fas.harvard.edu
SUMMARY:Towards Faithful Reasoning Using Language Models
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Antonia Creswell\, DeepMind \nTitle: Towards Faithful Reasoning Using Language Models \nAbstract: Language models are showing impressive performance on many natural language tasks\, including question-answering. However\, language models – like most deep learning models – are black boxes. We cannot be sure how they obtain their answers. Do they reason over relevant knowledge to construct an answer or do they rely on prior knowledge – baked into their weights – which may be biased? An alternative approach is to develop models whose output is a human interpretable\, faithful reasoning trace leading to an answer. In this talk we will characterise faithful reasoning in terms of logically valid reasoning and demonstrate where current reasoning models fall short. Following this\, we will introduce Selection-Inference\, a faithful reasoning model\, whose causal structure mirrors the requirements for valid reasoning. We will show that our model not only produces more accurate reasoning traces but also improves final answer accuracy. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/nt-101922/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/10.19.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221021T110000
DTEND;TZID=America/New_York:20221021T120000
DTSTAMP:20240301T080144Z
CREATED:20230809T110107Z
LAST-MODIFIED:20240301T080144Z
UID:10001226-1666350000-1666353600@cmsa.fas.harvard.edu
SUMMARY:Explicit Ramsey Graphs and Two Source Extractors
DESCRIPTION:Speaker: David Zuckerman\, Harvard CMSA/University of Texas at Austin \nTitle: Explicit Ramsey Graphs and Two Source Extractors \nAbstract: Ramsey showed that any graph on N nodes contains a clique or independent set of size (log N)/2.  Erdos showed that there exist graphs on N nodes with no clique or independent set of size 2 log N\, and asked for an explicit construction of such graphs.  This turns out to relate to the question of extracting high-quality randomness from two independent low-quality sources.  I’ll explain this connection and our recent exponential improvement in constructing two-source extractors.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-title-tba-5/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-10.21.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221026T123000
DTEND;TZID=America/New_York:20221026T133000
DTSTAMP:20240121T174027Z
CREATED:20230817T174027Z
LAST-MODIFIED:20240121T174027Z
UID:10001269-1666787400-1666791000@cmsa.fas.harvard.edu
SUMMARY:Clique listing algorithms
DESCRIPTION:Speaker: Virginia Vassilevska Williams (MIT) \nTitle: Clique listing algorithms \nAbstract: A k-clique in a graph G is a subgraph of G on k vertices in which every pair of vertices is linked by an edge. Cliques are a natural notion of social network cohesiveness with a long history. \nA fundamental question\, with many applications\, is “How fast can one list all k-cliques in a given graph?”. \nEven just detecting whether an n-vertex graph contains a k-Clique has long been known to be NP-complete when k can depend on n (and hence no efficient algorithm is likely to exist for it). If k is a small constant\, such as 3 or 4 (independent of n)\, even the brute-force algorithm runs in polynomial time\, O(n^k)\, and can list all k-cliques in the graph; though O(n^k) time is far from practical. As the number of k-cliques in an n-vertex graph can be Omega(n^k)\, the brute-force algorithm is in some sense optimal\, but only if there are Omega(n^k) k-cliques. In this talk we will show how to list k-cliques faster when the input graph has few k-cliques\, with running times depending on the number of vertices n\, the number of edges m\, the number of k-cliques T and more. We will focus on the case when k=3\, but we will note some extensions. \n(Based on joint work with Andreas Bjorklund\, Rasmus Pagh\, Uri Zwick\, Mina Dalirrooyfard\, Surya Mathialagan and Yinzhan Xu)
URL:https://cmsa.fas.harvard.edu/event/collquium_102722/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.26.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221026T140000
DTEND;TZID=America/New_York:20221026T150000
DTSTAMP:20240115T103149Z
CREATED:20230808T185319Z
LAST-MODIFIED:20240115T103149Z
UID:10001214-1666792800-1666796400@cmsa.fas.harvard.edu
SUMMARY:From Engine to Auto
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeakers: João Araújo\, Mathematics Department\, Universidade Nova de Lisboa and Michael Kinyon\, Department of Mathematics\, University of Denver \n\nTitle: From Engine to Auto \n\n\nAbstract: Bill McCune produced the program EQP that deals with first order logic formulas and in 1996 managed to solve Robbins’ Conjecture. This very powerful tool reduces to triviality any result that can be obtained by encoding the assumptions and the goals. The next step was to turn the program into a genuine assistant for the working mathematician: find ways to help the prover with proofs; reduce the lengths of the automatic proofs to better crack them;  solve problems in higher order logic; devise tools that autonomously prove results of a given type\, etc.\n\nIn this talk we are going to show some of the tools and strategies we have been producing. There will be real illustrations of theorems obtained for groups\, loops\, semigroups\, logic algebras\, lattices and generalizations\, quandles\, and many more.
URL:https://cmsa.fas.harvard.edu/event/nt-102622/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-10.26.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221028T110000
DTEND;TZID=America/New_York:20221028T120000
DTSTAMP:20240301T080243Z
CREATED:20230809T110603Z
LAST-MODIFIED:20240301T080243Z
UID:10001227-1666954800-1666958400@cmsa.fas.harvard.edu
SUMMARY:Some non-concave dynamic optimization problems in finance
DESCRIPTION:Member Seminar \nSpeaker: Shuaijie Qian (Harvard CMSA) \nTitle: Some non-concave dynamic optimization problems in finance \nAbstract: Non-concave dynamic optimization problems appear in many areas of finance and economics. Most of existing literature solves these problems using the concavification principle\, and derives equivalent\, concave optimization problems whose value functions are still concave. In this talk\, I will present our recent work on some non-concave dynamic optimization problems\, where the concavification principle may not hold and the resulting value function is indeed non-concave. \nThe first work is about the portfolio selection model with capital gains tax and a bitcoin mining model with exit options and technology innovation\, where the average tax basis and the average mining cost serves as an approximation\, respectively. This approximation results in a non-concave value function\, and the associated HJB equation problem turns out to admit infinitely many solutions. We show that the value function is the minimal (viscosity) solution of the HJB equation problem. Moreover\, the penalty method still works and converges to the value function. \nThe second work is about a non-concave utility maximization problem with portfolio constraints. We find that adding bounded portfolio constraints\, which makes the concavification principle invalid\, can significantly affect economic insights in the existing literature. As the resulting value function is likely discontinuous\, we introduce a new definition of viscosity solution\, prove the corresponding comparison principle\, and show that a monotone\, stable\, and consistent finite difference scheme converges to the solution of the utility maximization problem. \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-title-tba-6/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221102T124500
DTEND;TZID=America/New_York:20221102T134500
DTSTAMP:20240121T174258Z
CREATED:20230817T174336Z
LAST-MODIFIED:20240121T174258Z
UID:10001270-1667393100-1667396700@cmsa.fas.harvard.edu
SUMMARY:Doping and inverting Mott insulators on semiconductor moire superlattices
DESCRIPTION:Speaker: Liang Fu (MIT) \n\n\nTitle: Doping and inverting Mott insulators on semiconductor moire superlattices \nAbstract: Semiconductor bilayer heterostructures provide a remarkable platform for simulating Hubbard models on an emergent lattice defined by moire potential minima. As a hallmark of Hubbard model physics\, the Mott insulator state with local magnetic moments has been observed at half filling of moire band. In this talk\, I will describe new phases of matter that grow out of the canonical 120-degree antiferromagnetic Mott insulator on the triangular lattice. First\, in an intermediate range of magnetic fields\, doping this Mott insulator gives rise to a dilute gas of spin polarons\, which form a pseudogap metal. Second\, the application of an electric field between the two layers can invert the many-body gap of a charge-transfer Mott insulator\, resulting in a continuous phase transition to a quantum anomalous Hall insulator with a chiral spin structure. Experimental results will be discussed and compared with theoretical predictions.
URL:https://cmsa.fas.harvard.edu/event/collquium-11222/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-11.02.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221111T110000
DTEND;TZID=America/New_York:20221111T120000
DTSTAMP:20240209T052938Z
CREATED:20230809T111328Z
LAST-MODIFIED:20240209T052938Z
UID:10001228-1668164400-1668168000@cmsa.fas.harvard.edu
SUMMARY:Quantum trace and length conjecture for hyperbolic knot
DESCRIPTION:Member Seminar \nSpeaker: Mauricio Romo \nTitle: Quantum trace and length conjecture for hyperbolic knot \nAbstract: I will define the quantum trace map for an ideally triangulated hyperbolic knot complement on S^3. This map assigns an operator to each element L of  the Kauffman Skein module of knot complement.  Motivated by an interpretation of this operator in the context of SL(2\,C) Chern-Simons theory\, one can formulate a ‘length conjecture’ for the hyperbolic length of L.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-111122/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
END:VCALENDAR