BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CMSA - ECPv6.17.1//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-ORIGINAL-URL:https://cmsa.fas.harvard.edu
X-WR-CALDESC:Events for CMSA
REFRESH-INTERVAL;VALUE=DURATION:PT1H
X-Robots-Tag:noindex
X-PUBLISHED-TTL:PT1H
BEGIN:VTIMEZONE
TZID:America/New_York
BEGIN:DAYLIGHT
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
TZNAME:EDT
DTSTART:20190310T070000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
TZNAME:EST
DTSTART:20191103T060000
END:STANDARD
BEGIN:DAYLIGHT
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
TZNAME:EDT
DTSTART:20200308T070000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
TZNAME:EST
DTSTART:20201101T060000
END:STANDARD
BEGIN:DAYLIGHT
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
TZNAME:EDT
DTSTART:20210314T070000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
TZNAME:EST
DTSTART:20211107T060000
END:STANDARD
BEGIN:DAYLIGHT
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
TZNAME:EDT
DTSTART:20220313T070000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
TZNAME:EST
DTSTART:20221106T060000
END:STANDARD
BEGIN:DAYLIGHT
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
TZNAME:EDT
DTSTART:20230312T070000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
TZNAME:EST
DTSTART:20231105T060000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201112T103000
DTEND;TZID=America/New_York:20201112T120000
DTSTAMP:20240127T020910Z
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:20201118T094500
DTEND;TZID=America/New_York:20201118T110000
DTSTAMP:20240507T202224Z
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:20201118T150000
DTEND;TZID=America/New_York:20201118T160000
DTSTAMP:20240515T200420Z
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:20201120T150200
DTEND;TZID=America/New_York:20210101T150200
DTSTAMP:20240307T111352Z
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:20201209T150000
DTEND;TZID=America/New_York:20201209T160000
DTSTAMP:20240515T200218Z
CREATED:20240127T015429Z
LAST-MODIFIED:20240515T200218Z
UID:10001466-1607526000-1607529600@cmsa.fas.harvard.edu
SUMMARY:Machine learning and su(3) structures on six manifolds
DESCRIPTION:Speaker: James Gray – Virginia Tech \nTitle: Machine learning and su(3) structures on six manifolds \nAbstract: In this talk we will discuss the application of Machine Learning techniques to obtain numerical approximations to various metrics of SU(3) structure on six manifolds. More precisely\, we will be interested in SU(3) structures whose torsion classes make them suitable backgrounds for various string compactifications. A variety of aspects of this topic will be covered. These will include learning moduli dependent Ricci-Flat metrics on Calabi-Yau threefolds and obtaining numerical approximations to torsional SU(3) structures. \n 
URL:https://cmsa.fas.harvard.edu/event/12-9-2020-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-12.09.20.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201216T120000
DTEND;TZID=America/New_York:20201216T130000
DTSTAMP:20250305T192329Z
CREATED:20240126T094639Z
LAST-MODIFIED:20250305T192329Z
UID:10001442-1608120000-1608123600@cmsa.fas.harvard.edu
SUMMARY:The Inside View: Raymarching and the Thurston Geometries
DESCRIPTION:On Wednesday\, December 16 at 12:00 p.m. EST\, WAM and CMSA will host a holiday seminar featuring Sabetta Matsumoto\, Georgia Institute of Technology who will present The Inside View: Raymarching and the Thurston Geometries. \nThe properties of euclidean space seem natural and obvious to us\, to the point that it took mathematicians over two thousand years to see an alternative to Euclid’s parallel postulate. The eventual discovery of hyperbolic geometry in the 19th century shook our assumptions\, revealing just how strongly our native experience of the world blinded us from consistent alternatives\, even in a field that many see as purely theoretical. Non-euclidean spaces are still seen as unintuitive and exotic\, but with direct immersive experiences we can get a better intuitive feel for them. The latest wave of virtual reality hardware\, in particular the HTC Vive\, tracks both the orientation and the position of the headset within a room-sized volume\, allowing for such an experience. We create realtime rendering to explore the three-dimensional geometries of the Thurston/Perelman geometrization theorem. In this talk\, we use the “inside view” of each manifold to try to understand its geometry and what life might be like on the inside. Joint work with Rémi Coulon\, Henry Segerman and Steve Trettel. \nVisit the event page
URL:https://cmsa.fas.harvard.edu/event/the-inside-view-raymarching-and-the-thurston-geometries/
LOCATION:MA
CATEGORIES:Colloquia & Seminar,Seminars
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/image002-1-600x338-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210113T150000
DTEND;TZID=America/New_York:20210113T160000
DTSTAMP:20240517T201031Z
CREATED:20240126T093843Z
LAST-MODIFIED:20240517T201031Z
UID:10001441-1610550000-1610553600@cmsa.fas.harvard.edu
SUMMARY:AI and Theorem Proving
DESCRIPTION:Speaker: Josef Urban\, Czech Technical University \nTitle: AI and Theorem Proving \nAbstract: The talk will discuss the main approaches that combine machine learning with automated theorem proving and automated formalization. This includes learning to choose relevant facts for “hammer” systems\, guiding the proof search of tableaux and superposition automated provers by interleaving learning and proving (reinforcement learning) over large ITP libraries\, guiding the application of tactics in interactive tactical systems\, and various forms of lemmatization and conjecturing. I will also show some demos of the systems\, and discuss autoformalization approaches such as learning probabilistic grammars from aligned informal/formal corpora\, combining them with semantic pruning\, and using neural methods to learn direct translation from Latex to formal mathematics.
URL:https://cmsa.fas.harvard.edu/event/1-13-2021-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-01.13.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210120T150000
DTEND;TZID=America/New_York:20210120T160000
DTSTAMP:20240515T191339Z
CREATED:20240126T093733Z
LAST-MODIFIED:20240515T191339Z
UID:10001440-1611154800-1611158400@cmsa.fas.harvard.edu
SUMMARY:Language Modeling for Mathematical Reasoning
DESCRIPTION:Speaker: Christian Szegedy \nTitle: Language Modeling for Mathematical Reasoning \nAbstract: In this talk\, I will summarize the current state of the art of transformer based language models and give examples on non-trivial reasoning task language models can solve in higher order logic reasoning. I will also discuss how to inject injective bias into transformer networks via pretraining on very simple synthetic tasks and representing graph structures for transformer networks. \n 
URL:https://cmsa.fas.harvard.edu/event/1-20-2021-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-01.20.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210127T150000
DTEND;TZID=America/New_York:20210127T160000
DTSTAMP:20240515T191649Z
CREATED:20240126T092449Z
LAST-MODIFIED:20240515T191649Z
UID:10001435-1611759600-1611763200@cmsa.fas.harvard.edu
SUMMARY:Knowledge graph representation: From recent models towards a theoretical understanding
DESCRIPTION:Speaker: Carl Allen and Ivana Balažević – University of Edinburgh School of Informatics \nTitle: Knowledge graph representation: From recent models towards a theoretical understanding \nAbstract: Knowledge graphs (KGs)\, or knowledge bases\, are large repositories of facts in the form of triples (subject\, relation\, object)\, e.g. (Edinburgh\, capital_of\, Scotland). Many models have been developed to succinctly represent KGs such that known facts can be recalled (question answering) and\, more impressively\, previously unknown facts can be inferred (link prediction). Subject and object entities are typically represented as vectors in R^d and relations as mappings (e.g. linear transformations) between them. Such representation can be interpreted as positioning entities in a space such that relations are implied by their relative locations. In this talk we give an overview of knowledge graph representation including select recent models; and\, by drawing a connection to word embeddings\, explain a theoretical model for how semantic relationships can correspond to geometric structure.
URL:https://cmsa.fas.harvard.edu/event/1-27-2021-new-tech-in-math-seminar/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-01.27.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210210T150000
DTEND;TZID=America/New_York:20210210T160000
DTSTAMP:20240515T195824Z
CREATED:20240126T092338Z
LAST-MODIFIED:20240515T195824Z
UID:10001434-1612969200-1612972800@cmsa.fas.harvard.edu
SUMMARY:A Mathematical Exploration of Why Language Models Help Solve Downstream Tasks
DESCRIPTION:Speaker: Nikunj Saunshi\, Dept. of Computer Science\, Princeton University \nTitle: A Mathematical Exploration of Why Language Models Help Solve Downstream Tasks \nAbstract: Autoregressive language models pretrained on large corpora have been successful at solving downstream tasks\, even with zero-shot usage. However\, there is little theoretical justification for their success. This paper considers the following questions: (1) Why should learning the distribution of natural language help with downstream classification tasks? (2) Why do features learned using language modeling help solve downstream tasks with linear classifiers? For (1)\, we hypothesize\, and verify empirically\, that classification tasks of interest can be reformulated as next word prediction tasks\, thus making language modeling a meaningful pretraining task. For (2)\, we analyze properties of the cross-entropy objective to show that eps-optimal language models in cross-entropy (log-perplexity) learn features that are O(sqrt{eps}) good on such linear classification tasks\, thus demonstrating mathematically that doing well on language modeling can be beneficial for downstream tasks. We perform experiments to verify assumptions and validate our theoretical results. Our theoretical insights motivate a simple alternative to the cross-entropy objective that performs well on some linear classification tasks. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/2-10-2021-new-tech-in-math/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-02.10.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210224T150000
DTEND;TZID=America/New_York:20210224T160000
DTSTAMP:20240517T194101Z
CREATED:20240126T085540Z
LAST-MODIFIED:20240517T194101Z
UID:10001422-1614178800-1614182400@cmsa.fas.harvard.edu
SUMMARY:A Mathematical Language
DESCRIPTION:  \nSpeaker: Thomas Hales\, Univ. of Pittsburgh Dept. of Mathematics \nTitle: A Mathematical Language \nAbstract: A controlled natural language for mathematics is an artificial language that is designed in an explicit way with precise computer-readable syntax and semantics.  It is based on a single natural language (which for us is English) and can be broadly understood by mathematically literate English speakers.  This talk will describe the design of a controlled natural language for mathematics that has been influenced by the Lean theorem prover\, by TeX\, and by earlier controlled natural languages. The semantics are provided by dependent type theory.
URL:https://cmsa.fas.harvard.edu/event/2-24-2021-new-technologies-in-mathematics/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-02.24.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210303T150000
DTEND;TZID=America/New_York:20210303T160000
DTSTAMP:20240517T194704Z
CREATED:20240126T084416Z
LAST-MODIFIED:20240517T194704Z
UID:10001419-1614783600-1614787200@cmsa.fas.harvard.edu
SUMMARY:Neural Theorem Proving in Lean using Proof Artifact Co-training and Language Models
DESCRIPTION:Speaker: Jason Rute\, CIBO Technologies \nTitle: Neural Theorem Proving in Lean using Proof Artifact Co-training and Language Models \nAbstract: Labeled data for imitation learning of theorem proving in large libraries of formalized mathematics is scarce as such libraries require years of concentrated effort by human specialists to be built. This is particularly challenging when applying large Transformer language models to tactic prediction\, because the scaling of performance with respect to model size is quickly disrupted in the data-scarce\, easily-overfitted regime. We propose PACT ({\bf P}roof {\bf A}rtifact {\bf C}o-{\bf T}raining)\, a general methodology for extracting abundant self-supervised data from kernel-level proof terms for co-training alongside the usual tactic prediction objective. We apply this methodology to Lean\, an interactive proof assistant which hosts some of the most sophisticated formalized mathematics to date. We instrument Lean with a neural theorem prover driven by a Transformer language model and show that PACT improves theorem proving success rate on a held-out suite of test theorems from 32% to 48%.
URL:https://cmsa.fas.harvard.edu/event/3-3-2021-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-03.03.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210310T150000
DTEND;TZID=America/New_York:20210310T160000
DTSTAMP:20240517T194750Z
CREATED:20240126T083441Z
LAST-MODIFIED:20240517T194750Z
UID:10001414-1615388400-1615392000@cmsa.fas.harvard.edu
SUMMARY:The Ramanujan Machine: Using Algorithms for the Discovery of Conjectures on Mathematical Constants
DESCRIPTION:Speaker: Ido Kaminer\, Technion – Israel Institute of Technology\, Faculty of Electrical Engineering \nTitle: The Ramanujan Machine: Using Algorithms for the Discovery of Conjectures on Mathematical Constants \nAbstract: In the past\, new conjectures about fundamental constants were discovered sporadically by famous mathematicians such as Newton\, Euler\, Gauss\, and Ramanujan. The talk will present a different approach – a systematic algorithmic approach that discovers new mathematical conjectures on fundamental constants. We call this approach “the Ramanujan Machine”. The algorithms found dozens of well-known formulas as well as previously unknown ones\, such as continued fraction representations of π\, e\, Catalan’s constant\, and values of the Riemann zeta function. Part of the conjectures were in retrospect simple to prove\, whereas others remained so far unproved. We will discuss these puzzles and wider open questions that arose from this algorithmic investigation – specifically\, a newly-discovered algebraic structure that seems to generalize all the known formulas and connect between fundamental constants. We will also discuss two algorithms that proved useful in finding conjectures: a variant of the meet-in-the-middle algorithm and a gradient descent algorithm tailored to the recurrent structure of continued fractions. Both algorithms are based on matching numerical values; consequently\, they conjecture formulas without providing proofs or requiring prior knowledge of the underlying mathematical structure. This way\, our approach reverses the conventional usage of sequential logic in formal proofs; instead\, using numerical data to unveil mathematical structures and provide leads to further mathematical research.
URL:https://cmsa.fas.harvard.edu/event/3-10-2021-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-03.10.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210324T150000
DTEND;TZID=America/New_York:20210324T160000
DTSTAMP:20240515T195432Z
CREATED:20240126T083019Z
LAST-MODIFIED:20240515T195432Z
UID:10001411-1616598000-1616601600@cmsa.fas.harvard.edu
SUMMARY:Word and Graph Embeddings for Machine Learning
DESCRIPTION:Speaker: Steve Skiena\, Dept. of Computer Science and AI Insititute\, Stony Brook University \nTitle: Word and Graph Embeddings for Machine Learning \nAbstract: DeepWalk is an approach we have developed to construct vertex embeddings: vector representations of vertices which be applied to a very general class of problems in data mining and information retrieval. DeepWalk exploits an appealing analogy between sentences as sequences of words and random walks as sequences of vertices to transfer deep learning (unsupervised feature learning) techniques from natural language processing to network analysis. It has become extremely popular\, having been cited by over 4600 research papers since its publication at KDD 2014. In this talk\, I will introduce the notion of graph embeddings\, and demonstrate why they make such powerful features for machine learning applications. I will focus on more recent efforts concerning (1) fast embedding methods for very large networks\, (2) techniques for embedding dynamic graphs\, and (3) embedding spaces as models for knowledge generation. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/3-24-2021-new-tech-in-math-seminar/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-03.24.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210331T150000
DTEND;TZID=America/New_York:20210331T160000
DTSTAMP:20240515T195507Z
CREATED:20240126T083143Z
LAST-MODIFIED:20240515T195507Z
UID:10001412-1617202800-1617206400@cmsa.fas.harvard.edu
SUMMARY:Doing Mathematics with Simple Types: Infinitary Combinatorics in Isabelle/HOL
DESCRIPTION:Speaker: Lawrence Paulson\, University of Cambridge Computer Laboratory  \nTitle: Doing Mathematics with Simple Types: Infinitary Combinatorics in Isabelle/HOL  \nAbstract: Are proof assistants relevant to mathematics? One approach to this question is to explore the breadth of mathematical topics that can be formalised. The partition calculus was introduced by Erdös and R. Rado in 1956 as the study of “analogues and extensions of Ramsey’s theorem”. Highly technical results were obtained by Erdös-Milner\, Specker and Larson (among many others) for the particular case of ordinal partition relations\, which is concerned with countable ordinals and order types. Much of this material was formalised last year (with the assistance of Džamonja and Koutsoukou-Argyraki). Some highlights of this work will be presented along with general observations about the formalisation of mathematics\, including ZFC\, in simple type theory. \n\n\n\n\n\n\n\n\n 
URL:https://cmsa.fas.harvard.edu/event/3-31-2021-new-tech-in-math/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-03.31.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210407T150000
DTEND;TZID=America/New_York:20210407T160000
DTSTAMP:20240515T193258Z
CREATED:20240126T073259Z
LAST-MODIFIED:20240515T193258Z
UID:10001398-1617807600-1617811200@cmsa.fas.harvard.edu
SUMMARY:Type theory from the perspective of artificial intelligence
DESCRIPTION:Speaker: David McAllester – Toyota Technological Institute at Chicago \nTitle: Type theory from the perspective of artificial intelligence \nAbstract: This talk will discuss dependent type theory from the perspective of artificial intelligence and cognitive science. From an artificial intelligence perspective it will be argued that type theory is central to defining the “game” of mathematics — an action space and reward structure for pure mathematics. From a cognitive science perspective type theory provides a model of the grammar of the colloquial (natural) language of mathematics. Of particular interest is the notion of a signature-axiom structure class and the three fundamental notions of equality in mathematics — set-theoretic equality between structure elements\, isomorphism between structures\, and Birkoff and Rota’s notion of cryptomorphism between structure classes. This talk will present a version of type theory based on set-theoretic semantics and the 1930’s notion of structure and isomorphism given by the Bourbaki group of mathematicians. It will be argued that this “Bourbaki type theory” (BTT) is more natural and accessible to classically trained mathematicians than Martin-Löf type theory (MLTT). BTT avoids the Curry-Howard isomorphism and axiom J of MLTT. The talk will also discuss BTT as a model of MLTT. The BTT model is similar to the groupoid model in that propositional equality is interpreted as isomorphism but different in various details. The talk will also briefly mention initial thoughts in defining an action space and reward structure for a game of mathematics.
URL:https://cmsa.fas.harvard.edu/event/4-7-2021-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-04.07.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210414T150000
DTEND;TZID=America/New_York:20210414T160000
DTSTAMP:20240517T194855Z
CREATED:20240126T064644Z
LAST-MODIFIED:20240517T194855Z
UID:10001384-1618412400-1618416000@cmsa.fas.harvard.edu
SUMMARY:A Bayesian neural network predicts the dissolution of compact planetary systems
DESCRIPTION:Speaker: Miles Cranmer – Princeton University \nTitle: A Bayesian neural network predicts the dissolution of compact planetary systems \nAbstract: Despite over three hundred years of effort\, no solutions exist for predicting when a general planetary configuration will become unstable. I will discuss our deep learning architecture (arxiv:2101.04117) which pushes forward this problem for compact systems. While current machine learning algorithms in this area rely on scientist-derived instability metrics\, our new technique learns its own metrics from scratch\, enabled by a novel internal structure inspired from dynamics theory. The Bayesian neural network model can accurately predict not only if\, but also when a compact planetary system with three or more planets will go unstable. Our model\, trained directly from short N-body time series of raw orbital elements\, is more than two orders of magnitude more accurate at predicting instability times than analytical estimators\, while also reducing the bias of existing machine learning algorithms by nearly a factor of three. Despite being trained on three-planet configurations\, the model demonstrates robust generalization to five-planet systems\, even outperforming models designed for that specific set of integrations. I will also discuss some work on recovering symbolic representations of such models using arxiv:2006.11287.
URL:https://cmsa.fas.harvard.edu/event/4-14-2021-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-04.14.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210421T150000
DTEND;TZID=America/New_York:20210421T160000
DTSTAMP:20240515T192602Z
CREATED:20240126T065403Z
LAST-MODIFIED:20240515T192602Z
UID:10001388-1619017200-1619020800@cmsa.fas.harvard.edu
SUMMARY:Homotopy type theory and the quest for extensionality
DESCRIPTION:Speaker: Michael Shulman – Dept. of Mathematics\, University of San Diego \nTitle: Homotopy type theory and the quest for extensionality \nAbstract: Over the past decades\, dependent type theory has proven to be a powerful framework for verified software and formalized mathematics.  However\, its treatment of equality has always been somewhat uncomfortable.  Recently\, homotopy type theory has made progress towards a more useful notion of equality\, which natively implements both isomorphism-invariance in mathematics and representation-independence in programming. This progress is based on ideas from abstract homotopy theory and higher category theory\, and with the development of cubical type theories it can be implemented as a true programming language.  In this talk\, I will survey these developments and their potential applications\, and suggest some directions for further improvement. \n 
URL:https://cmsa.fas.harvard.edu/event/4-21-2021-new-tech-in-math-seminar/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-04.21.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210909T140000
DTEND;TZID=America/New_York:20210909T150000
DTSTAMP:20240517T200424Z
CREATED:20240214T092250Z
LAST-MODIFIED:20240517T200424Z
UID:10002621-1631196000-1631199600@cmsa.fas.harvard.edu
SUMMARY:The complexity of matrix multiplication approached via algebraic geometry and representation theory
DESCRIPTION:Speaker: JM Landsberg\, Texas A&M \nTitle: The complexity of matrix multiplication approached via algebraic geometry and representation theory \nAbstract: In 1968 V. Strassen discovered the way we usually multiply matrices is not the most efficient possible\, and after considerable work by many authors\, it is generally conjectured by computer scientists that as the size of matrices becomes large\, it becomes almost as easy to multiply them as it is to add them. I will give a brief history of the problem\, explain how this conjecture is naturally understood in the framework of classical algebraic geometry and representation theory\, and conclude by describing recent advances using more sophisticated tools from algebraic geometry. For most of the talk\, no knowledge of algebraic geometry or representation theory will be needed.
URL:https://cmsa.fas.harvard.edu/event/9-22-2021-new-technologies-in-mathematics-seminar/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210910T093000
DTEND;TZID=America/New_York:20210910T103000
DTSTAMP:20240304T100309Z
CREATED:20240213T114336Z
LAST-MODIFIED:20240304T100309Z
UID:10002512-1631266200-1631269800@cmsa.fas.harvard.edu
SUMMARY:Threshold phenomena in random graphs and hypergraphs
DESCRIPTION:Member Seminar \nSpeaker: Michael Simkin \nTitle: Threshold phenomena in random graphs and hypergraphs \nAbstract: In 1959 Paul Erdos and Alfred Renyi introduced a model of random graphs that is the cornerstone of modern probabilistic combinatorics. Now known as the “Erdos-Renyi” model of random graphs it has far-reaching applications in combinatorics\, computer science\, and other fields. \nThe model is defined as follows: Given a natural number $n$ and a parameter $p \in [0\,1]$\, let $G(n;p)$ be the distribution on graphs with $n$ vertices in which each of the $\binom{n}{2}$ possible edges is present with probability $p$\, independent of all others. Despite their apparent simplicity\, the study of Erdos-Renyi random graphs has revealed many deep and non-trivial phenomena. \nA central feature is the appearance of threshold phenomena: For all monotone properties (e.g.\, connectivity and Hamiltonicity) there is a critical probability $p_c$ such that if $p >> p_c$ then $G(n;p)$ possesses the property with high probability (i.e.\, with probability tending to 1 as $n \to \infty$) whereas if $p << p_c$ then with high probability $G(n;p)$ does not possess the property. In this talk we will focus on basic properties such as connectivity and containing a perfect matching. We will see an intriguing connection between these global properties and the local property of having no isolated vertices. We will then generalize the Erdos-Renyi model to higher dimensions where many open problems remain.
URL:https://cmsa.fas.harvard.edu/event/9-10-2021-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210915T093000
DTEND;TZID=America/New_York:20210915T103000
DTSTAMP:20240501T205627Z
CREATED:20240214T044745Z
LAST-MODIFIED:20240501T205627Z
UID:10002533-1631698200-1631701800@cmsa.fas.harvard.edu
SUMMARY:Hyperbolic Geometry and Quantum Invariants
DESCRIPTION:Speaker: Tian Yang (Texas A&M University) \nTitle: Hyperbolic Geometry and Quantum Invariants \nAbstract: There are two very different approaches to 3-dimensional topology\, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk\, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.
URL:https://cmsa.fas.harvard.edu/event/hyperbolic-geometry-and-quantum-invariants/
LOCATION:Virtual
CATEGORIES:Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210915T093000
DTEND;TZID=America/New_York:20220525T103000
DTSTAMP:20240502T160729Z
CREATED:20240213T112446Z
LAST-MODIFIED:20240502T160729Z
UID:10002496-1631698200-1653474600@cmsa.fas.harvard.edu
SUMMARY:CMSA Colloquium 9/15/2021 - 5/25/2022
DESCRIPTION:During the 2021–22 academic year\, the CMSA will be hosting a Colloquium\, organized by Du Pei\, Changji Xu\, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars\, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed. \nSpring 2022\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n1/26/2022\nSamir Mathur (Ohio State University)\nTitle: The black hole information paradox \nAbstract: In 1975\, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997\, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center\,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox\, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown\, using some theorems from quantum information theory\, that these extrapolations were incorrect\, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines\, with a postulate that information would leak out through wormholes. Recently\, it was shown that this wormhole idea had some basic flaws\, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle. \nVideo\n\n\n2/2/2022\nAdam Smith (Boston University)\nTitle: Learning and inference from sensitive data \nAbstract: Consider an agency holding a large database of sensitive personal information—say\,  medical records\, census survey answers\, web searches\, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records. \nI will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically\, why such models must sometimes memorize training data points nearly completely. On the more positive side\, I will present differential privacy\, a rigorous definition of privacy in statistical databases that is now widely studied\, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics\, and lay out directions for future investigation.\n\n\n2/8/2022\nWenbin Yan (Tsinghua University)\n(special time: 9:30 pm ET)\nTitle: Tetrahedron instantons and M-theory indices \nAbstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk\, we will review instanton moduli spaces\, explain the construction\, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory. \nVideo\n\n\n2/16/2022\nTakuro Mochizuki (Kyoto University)\nTitle: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles \nAbstract: In 1960’s\, Narasimhan and Seshadri discovered the equivalence\nbetween irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s\, Donaldson\, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles\nand stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then\, many interesting generalizations have been studied. \nIn this talk\, we would like to review a stream in the study of such correspondences for Higgs bundles\, integrable connections\, $D$-modules and periodic monopoles.\n\n\n2/23/2022\nBartek Czech (Tsinghua University)\nTitle: Holographic Cone of Average Entropies and Universality of Black Holes \nAbstract:  In the AdS/CFT correspondence\, the holographic entropy cone\, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual\, is currently known only up to n=5 regions. I explain that average\nentropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily\, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average\nEntropies” (HCAE). I conjecture the exact form of HCAE\, and find that it has the following properties: (1) HCAE is the simplest it could be\, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture\, the extremal rays of HCAE represent stages of unitary black hole evaporation\, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel\, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n\, namely its bounding inequalities are n-independent. (6) In a precise sense I describe\, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.\n\n\n3/2/2022\nRichard Kenyon (Yale University)\n\n\n\n3/9/2022\nRichard Tsai (UT Austin)\n\n\n\n3/23/2022\nJoel Cohen (University of Maryland)\n\n\n\n3/30/2022\nRob Leigh (UIUC)\n\n\n\n4/6/2022\nJohannes Kleiner (LMU München)\n\n\n\n4/13/2022\nYuri Manin (Max-Planck-Institut für Mathematik)\n\n\n\n4/20/2022\nTBA\n\n\n\n4/27/2022\nTBA\n\n\n\n5/4/2022\nMelody Chan (Brown University)\n\n\n\n5/11/2022\nTBA\n\n\n\n5/18/2022\nTBA\n\n\n\n5/25/2022\nHeeyeon Kim (Rutgers University)\n\n\n\n\n\nFall 2021\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n9/15/2021\nTian Yang\, Texas A&M\nTitle: Hyperbolic Geometry and Quantum Invariants \nAbstract: There are two very different approaches to 3-dimensional topology\, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk\, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.\n\n\n9/29/2021\nDavid Jordan\, University of Edinburgh\nTitle: Langlands duality for 3 manifolds \nAbstract: Langlands duality began as a deep and still mysterious conjecture in number theory\, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds\, and hence the precise form of Langlands duality for them\, remains a mystery. \nIn this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi \, and I will explain a Langlands duality in this setting\, which we have conjectured with Ben-Zvi\, Gunningham and Safronov. \nIntriguingly\, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question\, beyond the scope of the talk.\n\n\n10/06/2021\nPiotr Sulkowski\, U Warsaw\nTitle: Strings\, knots and quivers \nAbstract: I will discuss a recently discovered relation between quivers and knots\, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence\, and it states that various invariants of a given knot are captured by characteristics of a certain quiver\, which can be associated to this knot. Among others\, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver\, it provides a new insight on knot categorification\, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.\n\n\n10/13/2021\nAlexei Oblomkov\, University of Massachusetts\nTitle: Knot homology and sheaves on the Hilbert scheme of points on the plane. \nAbstract: The knot homology (defined by Khovavov\, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However\, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details\, using physics ideas of Kapustin-Rozansky-Saulina\, in the joint work with Rozansky\, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane.  The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane\, the symmetry is the geometric counter-part of the mentioned Poincare duality.\n\n\n10/20/2021\nPeng Shan\, Tsinghua U\nTitle: Categorification and applications \nAbstract: I will give a survey of the program of categorification for quantum groups\, some of its recent development and applications to representation theory.\n\n\n10/27/2021\nKarim Adiprasito\, Hebrew University and University of Copenhagen\nTitle: Anisotropy\, biased pairing theory and applications \nAbstract: Not so long ago\, the relations between algebraic geometry and combinatorics were strictly governed by the former party\, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry\, specifically Hodge Theory. And so\, while we proved analogues for these results\, combinatorics felt subjugated to inspirations from outside of it.\nIn recent years\, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature\, we use intuitions from the Hall marriage theorem\, translated to algebra: once there\, they are statements about self-pairings\, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry\, which in turn established solutions to long-standing conjectures in combinatorics. \nI will survey this theory\, called biased pairing theory\, and new developments within it\, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki\, Vasiliki Petrotou and Johanna Steinmeyer.\n\n\n11/03/2021\nTamas Hausel\, IST Austria\nTitle: Hitchin map as spectrum of equivariant cohomology \nAbstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.\n\n\n11/10/2021\nPeter Keevash\, Oxford\nTitle: Hypergraph decompositions and their applications \nAbstract: Many combinatorial objects can be thought of as a hypergraph decomposition\, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example\, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general\, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs\, which I proved in 2014\, states that\, bar finitely many exceptions\, such decompositions exist whenever the necessary ‘divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting\, which implies an approximate formula for the number of designs; in particular\, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects\, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem)\, whist tournaments or generalised Sudoku squares. In this talk\, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.\n\n\n11/17/2021\nAndrea Brini\, U Sheffield\nTitle: Curve counting on surfaces and topological strings \nAbstract: Enumerative geometry is a venerable subfield of Mathematics\, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s\, in particular\, the interaction with String Theory has sent shockwaves through the subject\, giving both unexpected new perspectives and a remarkably powerful\, physics-motivated toolkit to tackle several traditionally hard questions in the field.\nI will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X\, D)\, with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X\, D)\, including the log Gromov-Witten invariants of the pair\, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety\, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds\, the Donaldson–Thomas theory of a class of symmetric quivers\, and certain open and closed Gopakumar-Vafa-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.\n\n\n12/01/2021\nRichard Wentworth\, University of Maryland\nTitle: The Hitchin connection for parabolic G-bundles \nAbstract: For a simple and simply connected complex group G\, I will discuss some elements of the proof of the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points. Under the isomorphism with the bundle of conformal blocks\, this connection is equivalent to the one constructed by conformal field theory. This is joint work with Indranil Biswas and Swarnava Mukhopadhyay.\n\n\n12/08/2021\nMaria Chudnovsky\, Princeton\nTitle: Induced subgraphs and tree decompositions \nAbstract: Tree decompositions are a powerful tool in both structural\ngraph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph. \nTree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction\, exploring both the classical notion of bounded tree-width\, and concepts of more structural flavor. This talk will survey some of these ideas and results.\n\n\n12/15/21\nConstantin Teleman (UC Berkeley)\nTitle: The Kapustin-Rozanski-Saulina “2-category” of a holomorphic integrable system \nAbstract: I will present a construction of the object in the title which\, applied to the classical Toda system\, controls the theory of categorical representations of compact Lie groups\, along with applications (some conjectural\, some rigorous) to gauged Gromov-Witten theory. Time permitting\, we will review applications to Coulomb branches and the categorified Weyl character formula.
URL:https://cmsa.fas.harvard.edu/event/cmsa-colloquium_2021-22/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210915T150000
DTEND;TZID=America/New_York:20210915T160000
DTSTAMP:20240517T200145Z
CREATED:20240214T091846Z
LAST-MODIFIED:20240517T200145Z
UID:10002618-1631718000-1631721600@cmsa.fas.harvard.edu
SUMMARY:Why abstraction is the key to intelligence\, and what we’re still missing
DESCRIPTION:Speaker: Francois Chollet\, Google \nTitle: Why abstraction is the key to intelligence\, and what we’re still missing \nAbstract: This talk provides a personal perspective on the way forward towards more human-like and more intelligent artificial systems. Traditionally\, symbolic and probabilistic methods have dominated the domains of concept formation\, abstraction\, and automated reasoning. More recently\, deep learning-based approaches have led to significant breakthroughs\, including successes in games and combinatorial search tasks. However\, the resulting systems are still limited in scope and capabilities — they remain brittle\, data-hungry\, and their generalization capabilities are limited. We will address a set of questions: why is conceptual abstraction essential for intelligence? What is the nature of abstraction\, and its relationship to generalization? What kind of abstraction can deep learning models generate\, and where do they fail? What are the methods that are currently successful in generating strong conceptual abstraction? Finally\, we will consider how to leverage a hybrid approach to reinforce the strength of different approaches while compensating for their respective weaknesses.
URL:https://cmsa.fas.harvard.edu/event/9-15-2021-new-technologies-in-mathematics-seminar/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210917T093000
DTEND;TZID=America/New_York:20210917T103000
DTSTAMP:20240301T112535Z
CREATED:20240214T080149Z
LAST-MODIFIED:20240301T112535Z
UID:10002577-1631871000-1631874600@cmsa.fas.harvard.edu
SUMMARY:Geometry\, Entanglement and Quasi Local Data
DESCRIPTION:Member Seminar \nSpeaker: Itamar Shamir \nTitle: Geometry\, Entanglement and Quasi Local Data \nAbstract: I will review some general ideas about gravity as motivation for an approach based on quasi local quantities.
URL:https://cmsa.fas.harvard.edu/event/9-17-2021-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210924T093000
DTEND;TZID=America/New_York:20210924T103000
DTSTAMP:20240301T112341Z
CREATED:20240214T075925Z
LAST-MODIFIED:20240301T112341Z
UID:10002575-1632475800-1632479400@cmsa.fas.harvard.edu
SUMMARY:Stability and convergence issues in mathematical cosmology
DESCRIPTION:Member Seminar \nSpeaker: Puskar Mondal \nTitle: Stability and convergence issues in mathematical cosmology \nAbstract: The standard model of cosmology is built on the fact that while viewed on a sufficiently coarse-grained scale the portion of our universe that is accessible to observation appears to be spatially homogeneous and isotropic. Therefore this observed `homogeneity and isotropy’ of our universe is not known to be dynamically derived. In this talk\, I will present an interesting dynamical mechanism within the framework of the Einstein flow (including physically reasonable matter sources) which suggests that many closed manifolds that do not support homogeneous and isotropic metrics at all will nevertheless evolve to be asymptotically compatible with the observed approximate homogeneity and isotropy of the physical universe. This asymptotic spacetime is naturally isometric to the standard FLRW models of cosmology. In order to conclude to what extent the asymptotic state is physically realized\, one needs to study its stability properties. Therefore\, I will briefly discuss the stability issue and its consequences (e.g.\, structure formation\, etc).
URL:https://cmsa.fas.harvard.edu/event/9-24-2021-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210929T150000
DTEND;TZID=America/New_York:20210929T160000
DTSTAMP:20240517T200354Z
CREATED:20240214T092650Z
LAST-MODIFIED:20240517T200354Z
UID:10002626-1632927600-1632931200@cmsa.fas.harvard.edu
SUMMARY:Constructions in combinatorics via neural networks
DESCRIPTION:Speaker: Adam Wagner\, Tel Aviv University \nTitle: Constructions in combinatorics via neural networks \nAbstract: Recently\, significant progress has been made in the area of machine learning algorithms\, and they have quickly become some of the most exciting tools in a scientist’s toolbox. In particular\, recent advances in the field of reinforcement learning have led computers to reach superhuman level play in Atari games and Go\, purely through self-play. In this talk I will give a very basic introduction to neural networks and reinforcement learning algorithms. I will also indicate how these methods can be adapted to the ““game” of trying to find a counterexample to a mathematical conjecture\, and show some examples where this approach was successful.
URL:https://cmsa.fas.harvard.edu/event/9-29-2021-new-technologies-in-mathematics-seminar/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210929T171500
DTEND;TZID=America/New_York:20210929T181500
DTSTAMP:20240304T065421Z
CREATED:20240214T055645Z
LAST-MODIFIED:20240304T065421Z
UID:10002546-1632935700-1632939300@cmsa.fas.harvard.edu
SUMMARY:Langlands duality for 3 manifolds
DESCRIPTION:Speaker: David Jordan (U Edinburgh) \nTitle: Langlands duality for 3 manifolds \nAbstract: Langlands duality began as a deep and still mysterious conjecture in number theory\, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds\, and hence the precise form of Langlands duality for them\, remains a mystery. \nIn this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi \, and I will explain a Langlands duality in this setting\, which we have conjectured with Ben-Zvi\, Gunningham and Safronov. \nIntriguingly\, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question\, beyond the scope of the talk.
URL:https://cmsa.fas.harvard.edu/event/langlands-duality-for-3-manifolds/
LOCATION:Virtual
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-09.29.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211001T093000
DTEND;TZID=America/New_York:20211001T103000
DTSTAMP:20240301T111944Z
CREATED:20240214T074545Z
LAST-MODIFIED:20240301T111944Z
UID:10002569-1633080600-1633084200@cmsa.fas.harvard.edu
SUMMARY:Instability of naked singularities in general relativity
DESCRIPTION:Member Seminar \nSpeaker: Jue Liu \nTitle: Instability of naked singularities in general relativity \nAbstract: One of the fundamental problems in mathematical relativity is the weak cosmic censorship conjecture\, proposed by Penrose\, which roughly states that for generic physical spacetime\, the singularities (if existed) must be hidden behind the black holes. Unfortunately\, the singularities visible to faraway observers\, which are called by naked singularities\, indeed exist. The first example constructed by Christodoulou in 1994 is a family of self-similar spherically symmetric spacetime\, in which the naked singularity forms due to a self-gravitating scalar field. Therefore the suitable censorship conjecture should be reduced to prove the instability of the naked singularities. In 1999 Christodoulou succeeded to prove the weak cosmic censorship conjecture in spherically symmetric cases\, and recently the co-author and I found that the corresponding results have a big probability to be extended to spacetime without symmetries. In this talk I will discuss how to prove the instability of naked singularities using the energy method\, and it is this wild method that helps us to extend some results to the asymmetric cases.
URL:https://cmsa.fas.harvard.edu/event/10-1-2021-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211006T093000
DTEND;TZID=America/New_York:20211006T103000
DTSTAMP:20240501T205719Z
CREATED:20240214T044013Z
LAST-MODIFIED:20240501T205719Z
UID:10002532-1633512600-1633516200@cmsa.fas.harvard.edu
SUMMARY:Strings\, knots and quivers
DESCRIPTION:Speaker: Piotr Sułkowski (University of Warsaw) \nTitle: Strings\, knots and quivers \nAbstract: I will discuss a recently discovered relation between quivers and knots\, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence\, and it states that various invariants of a given knot are captured by characteristics of a certain quiver\, which can be associated to this knot. Among others\, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver\, it provides a new insight on knot categorification\, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.
URL:https://cmsa.fas.harvard.edu/event/strings-knots-and-quivers/
LOCATION:Virtual
CATEGORIES:Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211006T150000
DTEND;TZID=America/New_York:20211006T160000
DTSTAMP:20240517T200621Z
CREATED:20240214T092921Z
LAST-MODIFIED:20240517T200621Z
UID:10002630-1633532400-1633536000@cmsa.fas.harvard.edu
SUMMARY:New results in Supergravity via ML Technology
DESCRIPTION:Speaker: Thomas Fischbacher\, Google \nTitle: New results in Supergravity via ML Technology \nAbstract: The infrastructure built to power the Machine Learning revolution has many other uses beyond Deep Learning. Starting from a general architecture-level overview over the lower levels of Google’s TensorFlow machine learning library\, we review how this has recently helped us to find all the stable vacua of SO(8) Supergravity in 3+1 dimensions\, has allowed major progress on other related questions about M theory\, and briefly discuss other applications in field theory and beyond.
URL:https://cmsa.fas.harvard.edu/event/10-6-2021-new-technologies-in-mathematics-seminar/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
END:VEVENT
END:VCALENDAR