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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240913T120000
DTEND;TZID=America/New_York:20240913T130000
DTSTAMP:20240911T193907Z
CREATED:20240907T183113Z
LAST-MODIFIED:20240911T193907Z
UID:10003414-1726228800-1726232400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Abundance for mixed characteristic threefolds
DESCRIPTION:Member Seminar \nSpeaker: Iacopo Brivio (CMSA) \nTitle: Abundance for mixed characteristic threefolds \nAbstract: The Minimal Model Program (MMP) predicts that every algebraic variety X is birational to either a fibration in Fano varieties\, or it admits a “minimal model” X’\, that is a birational model with nef canonical bundle K_X’. The Abundance conjecture predicts then that K_X’ is actually semiample\, in particular it endows X’ with the structure of a Calabi-Yau fibration. These conjectures were initially phrased for complex varieties\, but more recently there has been a lot of interest in working over positive characteristic fields\, or even mixed characteristic rings. In this talk I will give a broad overview of the subject\, starting from the case of complex surfaces. In the last part I will outline a proof of the Abundance conjecture for mixed characteristic threefolds (based on joint work with F. Bernasconi and L. Stigant).
URL:https://live-hu-cmsa-222.pantheonsite.io/event/member-seminar_91324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Member-Seminar-09.13.24.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240913T103000
DTEND;TZID=America/New_York:20240913T120000
DTSTAMP:20240911T210525Z
CREATED:20240911T210525Z
LAST-MODIFIED:20240911T210525Z
UID:10003497-1726223400-1726228800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/mml_meeting_91324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240912T143000
DTEND;TZID=America/New_York:20240912T154500
DTSTAMP:20240907T154504Z
CREATED:20240907T152919Z
LAST-MODIFIED:20240907T154504Z
UID:10003408-1726151400-1726155900@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Topics in Deep Learning Theory
DESCRIPTION:Topics in Deep Learning Theory \nEli Grigsby
URL:https://live-hu-cmsa-222.pantheonsite.io/event/deeplearning_91224/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Topics in Deep Learning Theory
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240912T100000
DTEND;TZID=America/New_York:20240912T110000
DTSTAMP:20240917T140551Z
CREATED:20240907T170232Z
LAST-MODIFIED:20240917T140551Z
UID:10003412-1726135200-1726138800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Twisted Tools for (Untwisted) Quantum Field Theory
DESCRIPTION:Mathematical Physics and Algebraic Geometry \nSpeaker: Justin Kulp (Simons Center for Geometry and Physics) \nTitle: Twisted Tools for (Untwisted) Quantum Field Theory \nAbstract: One of the most important properties of QFTs is that they can be deformed by “turning on interactions.” Essentially every observable can be viewed as coupling the theory to some external system. Famously\, adding interactions (generically) breaks scale invariance\, leading to familiar ideas of EFTs and RG flows in the space of QFTs. An underappreciated fact is that one can actually consider flows generated by any transformation\, not just the usual scale transformations. \nIn my talk\, I will discuss a flow in the space of QFTs coming from (an analogue of) BRST symmetry. The beta-function for this “BRST-flow” controls deformations of the QFT and is highly mathematically constrained\, endowing the space of interactions with an L∞ algebra structure. The structure constants/brackets of the L∞ algebra are highly computable (requiring only a first course in QFT to compute) and contain familiar information such as anomalies and Operator Product Expansion coefficients. I will prove a non-renormalization theorem for holomorphic-topological QFTs with more than one topological direction\, which can be thought of as a generalization of a formality theorem of Kontsevich. Time permitting\, I will discuss how this formalism enables the systematic computation of minimal BPS operators in supersymmetric QFTs and describe the “holomorphic confinement” of N=1 SYM.  Based on arXiv:2403.13049.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/mathphys_91224/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Mathematica-Physics-and-Algebraic-Geometry-09.12.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240911T103000
DTEND;TZID=America/New_York:20240911T120000
DTSTAMP:20240911T210751Z
CREATED:20240907T155038Z
LAST-MODIFIED:20240911T210751Z
UID:10003444-1726050600-1726056000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/mml_meeting_91124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240910T160000
DTEND;TZID=America/New_York:20240910T180000
DTSTAMP:20240910T150123Z
CREATED:20240905T130004Z
LAST-MODIFIED:20240910T150123Z
UID:10003443-1725984000-1725991200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:BPS Algebras in Landau-Ginzburg Models
DESCRIPTION:Speaker: Ahsan Khan (CMSA) \nTitle: BPS Algebras in Landau-Ginzburg Models \nAbstract: The study of BPS states in supersymmetric quantum field theory has been a fruitful source of both mathematical and physical insights. In particular their study often leads to rich algebraic structures – from the “Algebra of the Infrared” of Gaiotto-Moore-Witten to the “Cohomological Hall Algebras” of Kontsevich-Soibelman. In this talk\, I will provide an overview of some of these algebraic constructions\, with a particular emphasis on BPS states in two-dimensional Landau-Ginzburg models. In the second half of the talk\, I will discuss how these algebraic structures can be extended to more general Landau-Ginzburg models defined by closed holomorphic one-forms.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/geometry-and-quantum-theory-seminar_91024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Geometry and Quantum Theory Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Geometry-Quantum-Theory-09.10.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240910T143000
DTEND;TZID=America/New_York:20240910T154500
DTSTAMP:20240905T173435Z
CREATED:20240905T173435Z
LAST-MODIFIED:20240905T173435Z
UID:10003403-1725978600-1725983100@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Topics in Deep Learning Theory
DESCRIPTION:Topics in Deep Learning Theory \nEli Grigsby
URL:https://live-hu-cmsa-222.pantheonsite.io/event/deeplearning_91024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Topics in Deep Learning Theory
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240909T163000
DTEND;TZID=America/New_York:20240909T173000
DTSTAMP:20240903T152309Z
CREATED:20240827T200454Z
LAST-MODIFIED:20240903T152309Z
UID:10003406-1725899400-1725903000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Combinatorics and geometry of the amplituhedron
DESCRIPTION:Colloquium \nSpeaker: Lauren Williams\, Harvard University \nTitle: Combinatorics and geometry of the amplituhedron \nAbstract: The amplituhedron is a geometric object introduced by Arkani-Hamed and Trnka to compute scattering amplitudes in N=4 super Yang Mills theory. It generalizes interesting objects such as cyclic polytopes and the positive Grassmannian. It has connections to tropical geometry\, cluster algebras\, and combinatorics (plane partitions\, Catalan numbers). I’ll give a gentle introduction to the amplituhedron\, then survey some recent progress on some of the main conjectures about the amplituhedron: the Magic Number Conjecture\, the BCFW tiling conjecture\, and the Cluster Adjacency conjecture.  Based on joint works withEvan-Zohar\, Lakrec\, Parisi\, Sherman-Bennett\, and Tessler.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/colloquium_9924/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Colloquium-09.09.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240903T100000
DTEND;TZID=America/New_York:20240905T160000
DTSTAMP:20240918T190637Z
CREATED:20240105T031946Z
LAST-MODIFIED:20240918T190637Z
UID:10001110-1725357600-1725552000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Mathematics and Machine Learning Program Opening Workshop
DESCRIPTION:Mathematics and Machine Learning Program Opening Workshop \nDates: September 3 – 5\, 2024 \nLocation: Room G10\, CMSA\, 20 Garden Street\, Cambridge MA & via Zoom Webinar \nAI for Mathematicians\, with Leon Bottou\, François Charton\, David McAllester\, Adam Wagner\, Boris Hanin\, and Geordie Williamson.  A series of 6 tutorial lectures introducing concepts of AI and of theorem proving\, with many case studies of AI applied to mathematics\, and including lectures and discussion sessions on open questions\, future prospects\, and ethical questions.\n  \nSpeakers \n\nLeon Bottou (Meta AI)\nFrançois Charton (Meta AI)\nMichael R. Douglas (Harvard CMSA)\nBoris Hanin (Princeton)\nDavid McAllester (TTIC)\nAdam Wagner (WPI)\nGeordie Williamson (University of Sydney)\n\nSchedule (link to downloadable pdf) \nVideos from the Opening Workshop (Youtube Link) \n\n\n\nTuesday Sep. 3\, 2024\n\n\n9:30–10:00 am\nMorning refreshments\n\n\n10:00–11:30 am\nMike Douglas: Overview of AI for mathematics\nSlides (pdf)\n\n\n11:30 am–12:00 pm\nDiscussion\n\n\n12:00–1:30 pm\nBreak\n\n\n1:30–2:30 pm\nDavid McAllester: Logic and formal methods\nSlides (pdf)\n\n\n2:30–3:00 pm\nCoffee break\n\n\n3:00–4:00 pm\nPanel Discussion: Automated mathematical discovery\n\n\n\n  \n\n\n\nWednesday Sep. 4\, 2024\n\n\n9:30–10:00 am\nMorning refreshments\n\n\n10:00–11:30 am\nBoris Hanin: Theory of Machine Learning\nSlides (pdf)\n\n\n11:30 am–12:00 pm\nDiscussion\n\n\n12:00–1:30 pm\nBreak\n\n\n1:30–2:30 pm\nAdam Wagner: Case studies I: Reinforcement learning and pattern finding\nSlides (pdf)\n\n\n2:30–3:00 pm\nCoffee break\n\n\n\n  \n\n\n\nThursday Sep. 5\, 2024\n\n\n9:30–10:00 am\nMorning refreshments\n\n\n10:00–11:30 am\nFrançois Charton (slides-pdf)\nand Geordie Williamson: Case studies II\n\n\n11:30 am–12:00 pm\nDiscussion\n\n\n12:00–1:30 pm\nBreak\n\n\n1:30–2:30 pm\nLeon Bottou: Open questions in AI\nSlides (pdf)\n\n\n2:30–3:00 pm\nCoffee break\n\n\n3:00–4:00 pm\nPanel Discussion: How might AI change mathematics?\n\n\n\n  \n  \n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/mmlworkshop_924/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Workshop
ATTACH;FMTTYPE=image/jpeg:https://live-hu-cmsa-222.pantheonsite.io/media/ML_Opening-workshop-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240903T090000
DTEND;TZID=America/New_York:20241101T170000
DTSTAMP:20250305T175957Z
CREATED:20240105T033600Z
LAST-MODIFIED:20250305T175957Z
UID:10001112-1725354000-1730480400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Mathematics and Machine Learning Program
DESCRIPTION:Mathematics and Machine Learning Program \nDates: September 3 – November 1\, 2024 \nLocation: Harvard CMSA\, 20 Garden Street\, Cambridge\, MA 0213 \nMachine learning and AI are increasingly important tools in all fields of research. Recent milestones in machine learning for mathematics include data-driven discovery of theorems in knot theory and representation theory\, the discovery and proof of new singular solutions of the Euler equations\, new counterexamples and lower bounds in graph theory\, and more. Rigorous numerical methods and interactive theorem proving are playing an important part in obtaining these results. Conversely\, much of the spectacular progress in AI has a surprising simplicity at its core. Surely there are remarkable mathematical structures behind this\, yet to be elucidated. \nThe program will begin and end with two week-long workshops\, and will feature focus weeks on number theory\, knot theory\, graph theory\, rigorous numerics in PDE\, and interactive theorem proving\, as well as a course on geometric aspects of deep learning.\n\n  \nSeptember 3–5\, 2024: Opening Workshop: AI for Mathematicians\, with Leon Bottou\, François Charton\, David McAllester\, Adam Wagner and Geordie Williamson.   A series of six lectures covering logic and theorem proving\, AI methods\, theory of machine learning\, two lectures on case studies in math-AI\, and a lecture and discussion on open problems and the ethics of AI in science.\nOpening Workshop Youtube Playlist \n\nSeptember 6–7\, 2024: Big Data Conference \n  \nSeptember 9–13\, 2024: Applying Machine Learning to Math\, with François Charton and Geordie Williamson\nPublic Lecture September 12\, 2024: Geordie Williamson\, University of Sydney: Can AI help with hard mathematics? (Youtube link)\nThe focus of this week will be on practical examples and techniques for the mathematics researcher keen to explore or deepen their use of AI techniques. We will have talks showcasing easily stated problems\, on which machine learning techniques can be employed profitably. These provide excellent toy examples for generating intuition. We will also have expert talks on some of the technical subtleties which arise. There are several instances where the accepted heuristics emerging from the study of large language models (LLM) and image recognition don’t appear to apply on mathematics problems\, and we will try to highlight these subtleties.\nApplying Machine Learning to Math Youtube Playlist \n  \nSeptember 16–20\, 2024: Number theory\, with Drew Sutherland\nThe focus of this week will be on the use of ML as a tool for finding and understanding statistical patterns in number-theoretic datasets\, using the recently discovered (and still largely unexplained) “murmurations” in the distribution of Frobenius traces in families of elliptic curves and other arithmetic L-functions as a motivating example.\nNumber Theory Youtube Playlist \n  \nSeptember 23–27\, 2024: Knot theory\, with Sergei Gukov\nKnot theory is a great source of labeled data that can be synthetically generated. Moreover\, many outstanding problems in knot theory and low-dimensional topology can be formulated as decision and classification tasks\, e.g. “Is the knot 123_45 slice?” or “Can two given Kirby diagrams be related by a sequence of Kirby moves?” During this focus week we will explore various ways in which AI can be applied to problems in knot theory and how\, based on these applications\, mathematical reasoning can advance development of AI algorithms. Another goal will be to develop formal knot theory libraries (e.g. contributions to mathlib) and to apply AI models to formal proof systems\, in particular in the context of knot theory.\nKnot Theory Youtube Playlist \n  \nSeptember 30: Teaching and Machine Learning Panel Discussion\, 3:30-5:30 pm ET \n  \nSeptember 30–October 4\, 2024: Graph theory and combinatorics\, with Adam Wagner\nThis week\, we will consider how machine learning can help us solve problems in combinatorics and graph theory\, broadly interpreted\, in practice. The advantage of these fields is that they deal with finite objects that are simple to set up using computers\, and programs that work for one problem can often be adapted to work for several other related problems as well. Many times\, the best constructions for a problem are easy to interpret\, making it simpler to judge how well a particular algorithm is performing. On the other hand\, there are lots of open conjectures that are simple to state\, for which the best-known constructions are counterintuitive\, making it perhaps more likely that machine learning methods can spot patterns that are difficult to understand otherwise.\nGraph Theory and Combinatorics Youtube Playlist \n  \nOctober 7–11\, 2024: More number theory\, with Drew Sutherland\nThe focus of this week will be on the use of AI as a tool to search for and/or construct interesting or extremal examples in number theory and arithmetic geometry\, using LLM-based genetic algorithms\, generative adversarial networks\, game-theoretic methods\, and heuristic tree pruning as alternatives to conventional local search strategies.\nMore Number Theory Youtube Playlist \n  \nOctober 14 –18\, 2024: Interactive theorem proving\nThis week we will discuss the use of interactive theorem proving systems such as Lean\, Coq and Isabelle in mathematical research\, and AI systems which prove theorems and translate between informal and formal mathematics.\nInteractive Theorem Proving Youtube Playlist \n  \nOctober 21–25\, 2024: Numerical Partial Differential Equations (PDE)\, with Tristan Buckmaster and Javier Gomez-Serrano\nThe focus of this week will be on constructing solutions to partial differential equations and dynamical systems (finite and infinite dimensional) more broadly defined. We will discuss several toy problems and comment on issues like sampling strategies\, optimization algorithms\, ill-posedness\, or convergence. We will also outline strategies about further developing machine-learning findings and turn them into mathematical theorems via computer-assisted approaches.\nNumerical PDEs Youtube Playlist \n  \nOctober 28–Nov. 1\, 2024: Closing Workshop: The closing workshop will provide a forum for discussing the most current research in these areas\, including work in progress and recent results from program participants.\nMath and Machine Learning Closing Workshop Youtube Playlist \n  \nSeptember 3–Nov. 1: Graduate topics in deep learning theory (Boston College) taught by Eli Grigsby\, held at the CMSA Tuesdays and Thursdays 2:30–3:45 pm Eastern Time. Course website (link).\nGraduate Topics in Deep Learning Youtube Playlist \nCourse description: This is a course on geometric aspects of deep learning theory. Broadly speaking\, we’ll investigate the question: How might human-interpretable concepts be expressed in the geometry of their data encodings\, and how does this geometry interact with the computational units and higher-level algebraic structures in various parameterized function classes\, especially neural network classes? During the portion of the course Sep. 3-Nov. 1\, the course will be presented as part of the Math and Machine Learning program at the CMSA in Cambridge. During that portion\, we will focus on the current state of research on mechanistic interpretability of transformers\, the architecture underlying large language models like Chat-GPT. \n\n\n\n\nPrerequisites: This course is targeted to graduate students and advanced undergraduates in mathematics and theoretical computer science. No prior background in machine learning or learning theory will be assumed\, but I will assume a degree of mathematical maturity (at the level of–say—the standard undergraduate math curriculum+ first-year graduate geometry/topology sequence)\n\n\n\n\n\nProgram Organizers \n\nFrancois Charton (Meta AI)\nMichael R. Douglas (Harvard CMSA)\nMichael Freedman (Harvard CMSA)\nFabian Ruehle (Northeastern)\nGeordie Williamson (Univ. of Sydney)\n\n\nProgram Schedule  \nMonday\n10:30–noon\nOpen Discussion\nRoom G10 \n12:00–1:30 pm\nGroup lunch\nCMSA Common Room \nTuesday\n2:30–3:45 pm\nTopics in deep learning theory\nRoom G10 \n4:00–5:00 pm\nOpen Discussion/Tea\nCMSA Common Room \nWednesday\n10:30 am–12:00 pm\nOpen Discussion\nRoom G10 \n2:00–3:00 pm\nNew Technologies in Mathematics Seminar\nRoom G10 \nThursday\n2:30–3:45 pm\nTopics in deep learning theory\nRoom G10 \nFriday\n10:30 am–12:00 pm\nOpen Discussion\nRoom G10 \n\nHarvard CMSA thanks Mistral AI for a generous donation of computing credit.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/mml2024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Programs
ATTACH;FMTTYPE=image/jpeg:https://live-hu-cmsa-222.pantheonsite.io/media/Machine-Learning-Program-poster-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240828T140000
DTEND;TZID=America/New_York:20240828T153000
DTSTAMP:20240826T155342Z
CREATED:20240822T161627Z
LAST-MODIFIED:20240826T155342Z
UID:10003416-1724853600-1724859000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Instanton in Lattice QCD from Higher Categories and Higher Anafunctors
DESCRIPTION:Speaker: Jing-Yuan Chen\, Tsinghua University \nTitle: Instanton in Lattice QCD from Higher Categories and Higher Anafunctors\n\n\nAbstract:  Putting continuum QFT (not just TQFT) on the lattice is important for both fundamental understandings and practical numerics. The traditional way of doing so\, based on simple intuitions\, however\, does not admit natural definitions for general topological operators of continuous-valued fields—one such example is the long standing problem in lattice QCD of lacking a natural definition for Yang-Mills instantons.\nIn this talk\, I will explain a more systematic way to relate continuum and lattice QFT\, based on higher categories and higher anafunctors\, so that the topological operators in the continuum can be naturally defined on the lattice. The idea\, though formulated formally\, is physically very intuitive—we want to effectively capture the different possibilities of how a lattice field may interpolate into the continuum\, so the higher categories that are employed to study higher homotopy theory should be naturally involved. Via this formalism\, we resolve the long-standing problem of defining instanton (as well as Chern-Simons term) in lattice Yang-Mills theory\, in terms of multiplicative bundle gerbes. Moreover\, when the fields become discrete\, our formalism can recover the Dijkgraaf-Witten and Turaev-Viro theory\, so we hope this formalism to be a good starting point towards (in the very long term) a comprehensive categorical understanding of QFT that encompass both continuous and discrete degrees of freedom\, applicable both to IR and to UV.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/qm_82824/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-QMMP-08.28.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240815T110000
DTEND;TZID=America/New_York:20240815T120000
DTSTAMP:20240808T164904Z
CREATED:20240801T143800Z
LAST-MODIFIED:20240808T164904Z
UID:10003404-1723719600-1723723200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Compactified Hyperboloidal Evolution in Numerical Relativity
DESCRIPTION:Speaker: Shalabh Gautam\, International Center for Theoretical Sciences\, Tata Institute of Fundamental Research \nTitle: Compactified Hyperboloidal Evolution in Numerical Relativity \nAbstract: In the field of numerical relativity\, a major challenge is to incorporate future null infinity into the computational domain using a well-posed formulation. Achieving this goal would not only allow us to accurately simulate any astrophysical system\, such as binary black holes\, and extract the resulting signal\, like gravitational waves\, at future null infinity\, but it would also facilitate the study of various fundamental phenomena. One proposed solution is to use hyperboloidal slices. In this presentation\, I will introduce an alternative approach to numerical relativity that leverages these slices in spherical symmetry. I will also discuss our ongoing efforts to establish a well-posed formulation of the Einstein Field Equations on these slices\, and propose numerical schemes to ensure stability and convergence for linear hyperbolic systems over long durations. Additionally\, I will present our method for constructing initial data corresponding to an asymptotically flat spacetime. A natural extension of our work will be to generalize these methods to the Einstein Field Equations with appropriate initial data in the full 3d.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/compactified-hyperboloidal-evolution-in-numerical-relativity/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-GR-Seminar-08.15.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240621T140000
DTEND;TZID=America/New_York:20240621T153000
DTSTAMP:20240620T133710Z
CREATED:20240620T133636Z
LAST-MODIFIED:20240620T133710Z
UID:10003393-1718978400-1718983800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Landscape of Tensor Network States Preparable from Measurement
DESCRIPTION:Quantum Matter in Mathematics and Physics Seminar \nSpeaker: Rahul Sahay (Harvard)\n\nTitle: Landscape of Tensor Network States Preparable from Measurement\n\nAbstract: Measurements and feedback have emerged as powerful resources for creating many-body quantum states. However\, a detailed understanding of what is possible is restricted to fixed-point representatives of phases of matter. In this talk\, we go beyond this\, characterizing more general patterns of many-body entanglement that can be deterministically created from measurement. In 1D\, a complete framework is developed for the case where a single round of measurements is the only entangling operation. Specifically\, we completely classify the space of 1D preparable quantum states (forming a strict subset of all matrix product states)\, and characterize their physical constraints. In doing so\, we find an intriguing physical trade-off between the richness of the preparable entanglement spectrum and correlation functions\, naturally implying a powerful no-go theorem for preparing certain quantum states. Moreover\, our classification enables one to search for and engineer preparable quantum states with a range of desired correlation lengths and entanglement properties. We conclude by charting out generalizations\, such as higher dimensional examples\, considering multiple rounds of measurements\, and implementing matrix product operators. At a high level\, our work offers a resource-theoretic perspective on preparable quantum entanglement and shows how to systematically create states of matter\, away from their fixed points\, in quantum devices. This is based on two recent works with Ruben Verresen [arXiv:2404.17087; arXiv:2404.16753].\n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/qm_62124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-QMMP-06.21.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240607T143000
DTEND;TZID=America/New_York:20240607T160000
DTSTAMP:20240603T150758Z
CREATED:20240529T212219Z
LAST-MODIFIED:20240603T150758Z
UID:10003392-1717770600-1717776000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Phases and Phase Transitions of Spin Chains with Non-invertible Symmetries
DESCRIPTION:Quantum Matter in Mathematics and Physics Seminar \nSpeaker: Arkya Chatterjee (MIT) \nTitle: Phases and Phase Transitions of Spin Chains with Non-invertible Symmetries \nAbstract: Non-invertible symmetries are often emergent at low-energies in gapless states of quantum matter. It is useful to construct lattice models that have these as exact symmetries in order to provide a UV-complete setting in which they are well-controlled. To that end\, we propose to study one-dimensional Hamiltonians defined on tensor product Hilbert spaces with finite on-site dimension — referred to as “spin chains” in short — with exact non-invertible symmetries. We focus on two concrete examples: a spin chain with (invertible) S_3 symmetry and one with (non-invertible) Rep(S_3) symmetry. These models are largely analytically tractable and demonstrate all spontaneous symmetry breaking (SSB) phases of these symmetries. With the aid of tensor network algorithms\, we systematically study the phase transitions between these SSB phases. Both models possess (intrinsically) non-invertible self-duality symmetries\, for which we provide sequential circuit implementations. On the self-dual manifold in parameter space\, we discover an incommensurate gapless phase with an anomalous U(1) symmetry which emanates from lattice translation. \n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/qmmp_6724/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-QMMP-06.07.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240529T090000
DTEND;TZID=America/New_York:20240531T170000
DTSTAMP:20240624T164905Z
CREATED:20240105T071351Z
LAST-MODIFIED:20240624T164905Z
UID:10001120-1716973200-1717174800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Amplituhedra\, Cluster Algebras\, and Positive Geometry
DESCRIPTION:Amplituhedra\, Cluster Algebras\, and Positive Geometry \nDates: May 29-31\, 2024 \nLocation: Harvard CMSA\, 20 Garden Street\, Cambridge MA 02138 & via Zoom \nIn recent years\, a remarkable paradigm shift has occurred in understanding quantum observables in particle physics and cosmology\, revealing their emergence from underlying novel mathematical objects known as positive geometries. The conference will center on the amplituhedron—the first and major example of a positive geometry. Building on the work of Lusztig and Postnikov on the positive Grassmannian\, the physicists Arkani-Hamed and Trnka introduced the amplituhedron in 2013 as a geometric object that “explains” the so-called BCFW recurrence for scattering amplitudes in N = 4 super Yang Mills theory (SYM). Simultaneously\, cluster algebras\, originally introduced by Fomin and Zelevinsky to study total positivity\, have been revealed to have a crucial role in describing singularities of N = 4 SYM scattering amplitudes. Thus\, one can use ideas from quantum field theory (QFT) to connect cluster algebras to positive geometries\, and in particular to the amplituhedron. Additionally\, QFT can also be used to discover new examples of positive geometries. The conference will bring together a wide range of mathematicians and physicists both to draw new connections within algebraic combinatorics and geometry and to advance our physical understanding of scattering amplitudes and QFT. \nThe conference features: Introductory Lectures\, an Open Problems Forum\, Emerging Scholars Talks\, and talks by experts in the fields. \n  \nConference Videos (Youtube Playlist) \n  \nConfirmed Speakers: \n\nEvgeniya Akhmedova\, Weizmann Institute of Science\nNima Arkani-Hamed\, IAS\nPaolo Benincasa\, MPI\nNick Early\, Weizmann Institute of Science\nCarolina Figueiredo\, Princeton University\nYu-tin Huang\, National Taiwan University\nDani Kaufman\, University of Copenhagen\nChia-Kai Kuo\, National Taiwan University\nThomas Lam\, University of Michigan\nYelena Mandelshtam\, UC Berkeley\nShruti Paranjape\, UC Davis\nLizzie Pratt\, UC Berkeley\nLecheng Ren\, Brown University\nSebastian Seemann\, KU Leuven\nKhrystyna Serhiyenko\, University of Kentucky\nMelissa Sherman-Bennett\, MIT & UC Davis\nMarcus Spradlin\, Brown University\nRan Tessler\, Weizmann Institute of Science\nHugh Thomas\, Université du Québec à Montréal\nJaroslav Trnka\, UC Davis\nAnastasia Volovich\, Brown University\n\nOrganizers: \n\nMatteo Parisi\, Harvard CMSA\nLauren Williams\, Harvard Mathematics\n\nParticipants (PDF) \nThis event is co-funded by the National Science Foundation. \nLimited funding to help defray travel expenses is available for graduate students and recent PhDs. If you are a graduate student or postdoc and would like to apply for support\, please register above and send an email to amplituhedra@cmsa.fas.harvard.edu no later than Friday\, April 19\, 2024. \nPlease include your name\, address\, current status\, university affiliation\, citizenship\, and area of study. F1 visa holders are eligible to apply for support. If you are a graduate student\, please send a brief letter of recommendation from a faculty member to explain the relevance of the conference to your studies or research. If you are a postdoc\, please include a copy of your CV. \n\nSCHEDULE (pdf download) \nWednesday\, May 29\, 2024\n8:30 – 9:00 am\nRegistration and Breakfast \n9:00 – 10:00 am\nJaroslav Trnka\, UC Davis\nTitle: Amplituhedron\nAbstract: I will review basics of the Amplituhedron\, connection to the positive Grassmannian on the mathematical side\, and the scattering amplitudes on the physics side. \n10:00 – 10:15 am\nCoffee Break \n10:15 – 11:15 am\nvia Zoom\nKhrystyna Serhiyenko\, University of Kentucky\nTitle: Introduction to Cluster Algebras\nAbstract: Cluster algebras is a class of commutative rings with an intricate combinatorial structure. They were introduced by Fomin and Zelevinsky in 2002 to study total positivity and canonical basis in Lie Theory\, but quickly evolved into a highly active research area with surprising connections to numerous other areas of mathematics and physics.\nIn this course we will introduce cluster algebras and discuss their basic properties including positivity and Laurent phenomenon. We will also review cluster structures coming from coordinate rings of Grassmannians and the combinatorics of plabic graphs. \n11:15 – 11:30 am\nCoffee Break \n11:30 – 12:30 pm\nThomas Lam\, University of Michigan\nTitle: Introductory Lecture on Positive Geometries\nAbstract: Positive geometries are semialgebraic spaces that appear in the study of scattering amplitudes. Examples include polytopes\, totally nonnegative parts of flag varieties\, and conjecturally\, the amplituhedron. We will give a broad introduction to positive geometries\, and to their canonical forms. \n12:30 – 2:00 pm\nLunch Break \n2:00 – 2:50 pm\nAnastasia Volovich\, Brown University\nTitle: Scattering Amplitudes and Cluster Algebras\nAbstract: I will review some of the deep connections between cluster algebras and the (loop level) scattering amplitudes in N=4 super Yang-Mills theory\, focusing on the cases of n=6 and 7 particles where the corresponding Grassmannian cluster algebras Gr(4\,n) are finite and certain features of the amplitudes are known or believed to be true to all loop order. \n2:50 – 3:00 pm\nCoffee Break \n3:00 – 3:50 pm\nMarcus Spradlin\, Brown University\nTitle: Scattering Amplitudes\, Positive Geometry and the Amplituhedron\nAbstract: I will review the status of (loop level) scattering amplitudes in N=4 super Yang-Mills theory for n>7\, where the corresponding Grassmannian cluster algebras Gr(4\,n) are infinite and novel features emerge\, notably the appearance of certain “marginally positive” algebraic functions of cluster variables. \n3:50 – 4:00 pm\nCoffee Break \n4:00 – 4:30 pm\nCarolina Figueiredo\, Princeton University\nTitle: All-order splits and multi-soft limits for particle and string amplitude\nAbstract: The most important aspects of scattering amplitudes have long been thought to be associated with their poles. Recently a very different sort of “split” factorizations for a wide range of particle and string tree amplitudes have been discovered away from poles. In this talk\, I will explain how natural properties of the binary geometry of the curve integral formulation for scattering amplitudes for Tr$(\Phi^3)$ theory give a simple\, conceptual origin for these splits\, that generalizes them to all orders in the topological expansion. I will also explain how the splits allow us to access and compute loop-integrated multi-soft limits for particle and string amplitudes in Tr$(\Phi^3)$ theory\, the non-linear sigma model and Yang-Mills theory. \n4:30 – 5:15 pm\nYelena Mandelshtam\, UC Berkeley\nTitle: Combinatorics of m=1 Grasstopes\nAbstract: A Grasstope is a linear projection of the totally nonnegative Grassmannian to a smaller Grassmannian. This is a generalization of the amplituhedron\, a geometric object of great importance to calculating scattering amplitudes in physics. The amplituhedron is a Grasstope arising from a totally positive linear map. While amplituhedra are relatively well-studied\, much less is known about general Grasstopes. In this talk\, I will discuss combinatorics and geometry of Grasstopes in the m=1 case. In particular\, I will show that they can be characterized as unions of cells of a hyperplane arrangement satisfying a certain sign variation condition and argue that amplituhedra are (in a certain sense) minimal Grasstopes. This is based on joint work with Dmitrii Pavlov and Lizzie Pratt. \n5:30 – 6:30 pm\nWelcome Reception \n  \nThursday\, May 30\, 2024 \n8:30 – 9:00 am\nBreakfast \n9:00 – 10:00 am\nNima Arkani-Hamed\, IAS\nTitle: Surface Kinematics and THE all-loop integrand for gluon amplitudes \n10:00 – 10:30 am\nCoffee Break \n10:30 – 11:20 am\nHugh Thomas\, Université du Québec à Montréal\nTitle: u-equations from finite dimensional algebras\nAbstract: In this talk\, I will explain how to write down and solve a system of u-equations associated to any finite dimensional algebra with finitely many indecomposable representations. These vastly generalize the system of equations written down by Koba and Nielsen in 1969\, which from our point of view are associated to the representation theory of a Dynkin type A quiver. I will discuss features of the resulting solution spaces\, including connections to tau-tilting theory\, and the relationships that exist among different spaces of solutions. I will also say something about how different choices of finite-dimensional algebra put us in (i) the setting of cluster algebras\, (ii) the Grassmannian combinatorics of non-kissing complexes\, or (iii) the curves-on-surfaces model directly relevant to amplitudes. This talk reports on joint work with Nima Arkani-Hamed\, Hadleigh Frost\, Pierre-Guy Plamondon\, and Giulio Salvatori. \n11:20 – 11:30 am\nCoffee Break \n11:30 – 12:20 pm\nDani Kaufman\, University of Copenhagen\nTitle: Affine Cluster Algebras\nAbstract: Affine cluster algebras form the simplest examples of non-finite type cluster algebras. While they have infinitely many clusters\, they are still mutation finite and have essentially one mutation sequence which produces infinitely many clusters. I will give an introduction to these cluster algebras by comparing them with finite cluster algebras. I will also show how some structures similar to finite type cluster algebras appear “in the limit” along this infinite mutation sequence. If time I will also mention how the “infinite cluster variables” which live in the limit are related to the algebraic letters appearing in the symbol alphabet for 8 particle N=4 SYM amplitudes. \n12:30-12:45 pm\nGroup Photo\, 20 Garden Street\, front entrance stairs outside building \n12:45 – 2:00 pm\nLunch Break \n2:00 – 2:50 pm\nvia Zoom\nRan Tessler\, Weizmann Institute of Science\nTitle: The magic number for the m=2 amplituhedron\nAbstract: We will start by reviewing the amplituhedron and its tilings.\nWe will then show that all tilings of the m=2 amplituhedron have the same cardinality (“the magic number”)\, proving the m=2 case of a conjecture that the same holds for all even-m amplituhedra. If time permits we will discuss related results and consequences.\nBased on a joint work with Parisi\, Sherman-Bennett and Williams. \n2:50 – 3:00 pm\nCoffee Break \n3:00 – 3:50 pm\nMelissa Sherman-Bennett\, MIT & UC Davis\nTitle: Cluster algebras and tilings of amplituhedra\nAbstract: Physicists Arkani-Hamed and Trnka introduced the amplituhedron to better understand scattering amplitudes in N=4 super Yang-Mills theory. The amplituhedron is the image of the totally nonnegative Grassmannian under the “amplituhedron map”. Examples of amplituhedra include cyclic polytopes\, the totally nonnegative Grassmannian itself\, and cyclic hyperplane arrangements. Of primary interest to physics are tilings of amplituhedra\, which are roughly analogous to subdivisions of polytopes. I will discuss joint work with Even-Zohar\, Lakrec\, Parisi\, Tessler and Williams on BCFW tilings of m=4 amplituhedra and the surprising connection between these tilings and the cluster algebra structure of the Grassmannian. \n3:50 – 4:00 pm\nCoffee Break \n4:00 – 5:30 pm\nOpen Problems Forum \n6:00 – 8:00 pm\nConference Dinner (by invitation) \n  \nFriday\, May 31\, 2024 \n8:30 – 9:00 am\nBreakfast \n9:00 – 10:00 am\nYu-tin Huang\, National Taiwan University\nTitle: Chambers and all loop geometry for four-point correlators\nAbstract: The all loop amplituhedron for N=4 SYM (and ABJM theory) can be recast into the notion of loop fibration over tree geometry. This leads to a further dissection of the tree geometry into “chambers”\, whose boundaries represents when the associated loop-form changes. In this talk I will present a new geometry associated with the all loop four-point correlator of N=4 SYM\, where similar description is present. Interestingly\, at four-loops\, this gives a first example where the chamber form is rational even though it’s loop form contains elliptic integrals. \n10:00 – 10:15 am\nCoffee Break \n10:15 – 12:30 am\nEmerging Scholar Talks \n10:15 – 10:40 am\nEvgeniya Akhmedova\, Weizmann Institute of Science\nTitle: The tropical amplituhedron\nAbstract: The Amplituhedron is a geometric object discovered recently by Arkani-Hamed and Trnka\, that provides a completely new direction for calculating scattering amplitudes in quantum field theory. We define a tropical analogue of this object\, the tropicial amplituhedron and study its structure and boundaries. It can be considered as both the tropical limit of the amplituhedron and a generalization of the tropical positive Grassmannian. \n10:40 – 11:10 am\nLizzie Pratt\, UC Berkeley\nTitle: The Chow-Lam Form\nAbstract: The classical Chow form encodes any projective variety by one equation. We introduce the Chow-Lam form for subvarieties of a Grassmannian. By evaluating the Chow-Lam form at twistor coordinates\, we obtain universal projection formulas\, which were pioneered by Thomas Lam for positroid varieties in the study of amplituhedra. This is joint work with Bernd Sturmfels. \n11:10– 11:30 am\nSebastian Seemann\, KU Leuven\nTitle: Vandermonde cells as positive geometries\nAbstract: Vandermonde cells represent semialgebraic subsets of R^n\, characterized as the image of a simplex under the Vandermonde map. However\, within the realm of positive geometry\, several challenges arise in establishing canonical forms for these cells. These include issues such as non-normal boundaries\, non-transversal intersections\, and singularities of boundary curves. Even more difficulties appear when considing the limiting Vandermonde cell\, which is not semi-algebraic and thus doesn’t fit within the standard framework of positive geometries. In this presentation\, I will first review the notion of Polypols and their canonical forms\, examining the complexities encountered when dealing with Vandermonde cells. In particular\, I will explain what goes wrong in the case of Vandermonde cells and which obstructions we can deal with. \n11:30 – 11:40 am\nCoffee break \n11:40 – 12:10 pm\nChia-Kai Kuo\, National Taiwan University\nTitle: Geometric transition from maximal SYM to ABJM\nAbstract: Recently\, the ABJM amplituhedron has been proposed\, encoding all-loop and all-multiplicity ABJM amplitudes. It is constructed by slightly modifying the original definition. In this talk\, I will explore the significance of these modifications in transitioning theoretical models from super Yang-Mills theory to ABJM theory. A key focus will be on how symplectic reduction and the overall sign change in the positivity conditions ensure the consistency of ABJM amplitudes. Additionally\, I will discuss some distinct features of this geometry. \n12:10– 12:30 pm\nLecheng Ren\, Brown University\nTitle: Symbol alphabets from tensor diagrams\nAbstract: We propose to use tensor diagrams and the Fomin-Pylyavskyy conjectures to explore the connection between symbol alphabets of n-particle amplitudes in planar N= 4 Yang-Mills theory and certain polytopes associated to the Grassmannian Gr(4\, n). We show how to assign a web (a planar tensor diagram) to each facet of these polytopes. Webs with no inner loops are associated to cluster variables (rational symbol letters). For webs with a single inner loop we propose and explicitly evaluate an associated web series that contains information about algebraic symbol letters. In this manner we reproduce the results of previous analyses of n ≤ 8\, and find that the polytope C(4\,9) encodes all rational letters\, and all square roots of the algebraic letters\, of known nine-particle amplitudes. \n12:30 – 2:00 pm\nLunch Break \n2:00 – 2:50 pm\nvia Zoom\nPaolo Benincasa\,  MPI\nTitle: Cosmological Polytopes & Beyond\nAbstract: Together with being the source of the most profound questions in fundamental physics\, cosmology turns out to be an arena from where novel combinatorial structures emerge. In this talk\, I will give a gentle introduction to the cosmological polytopes\, describing the so-called Bunch-Davies wavefunction for a large class of scalar theories\, and how it can be used to define and characterize less conventional objects\, named optical polytopes and weighted cosmological polytopes\, which provide examples of non-convex and weighted geometries respectively. \n2:50 – 3:00 pm\nCoffee Break \n3:00 – 3:45 pm\nShruti Paranjape\, UC Davis\nTitle: Loops in a loop expansion\nAbstract: In a paper by Arkani-Hamed\, Henn and Trnka\, it was shown that the amplituhedron construction of N=4 SYM can be recast in terms of negative geometries with a certain hierarchy of loops (closed cycles) in the space of loop momentum twistors. Furthermore\, using differential equation methods\, it was possible to calculate and resum integrated expressions and obtain strong coupling results. In this talk\, we provide a more general framework for the loops of loops expansion and outline a powerful method for the determination of differential forms for higher-order geometries. In particular\, we will focus on the case of 1 closed cycle in loop space and select integrated results. \n3:45 – 4:30 pm\nNick Early\, Weizmann Institute of Science\nTitle: Minimal Kinematics on $\mathcal{M}_{0\,n}$\, and beyond\nAbstract: Minimal Kinematics (MK) identifies kinematic degenerations of the CHY scattering potential where the critical points are given by rational formulas. These rest on the Horn uniformization of Kapranov-Huh; they are specified combinatorially by 2-trees. On the other hand\, Planar Kinematics (PK) identifies the locus in $M_{0\,n}$ which is fixed by cyclic permutation.  Combining MK and PK realizes a maximally thin relative of the associahedron known as the PK polytope; it is a reflexive polytope\, and its polar dual\, the root polytope\, has volume a Catalan number. In this talk\, we start by exploring MK and PK on the moduli space $M_{0\,n}$.  We explain how this story generalizes to moduli spaces $X(k\,n)$ of points in projective space $\mathbb{P}^{k-1}$\, to CEGM amplitudes and beyond. \n4:30 – 5:00 pm\nCoffee and Farewell \n  \n \n  \nAbout the image: \n\nLeft: the 3-dimensional associahedron\, Fomin and Zelevinsky\n\nCenter: artistic depiction of the amplituhedron\, Gilmore\nRight: Schlegel diagram of a hypersimplex\, Ziegler
URL:https://live-hu-cmsa-222.pantheonsite.io/event/amplituhedra2024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Conference
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/amplituhedron_cluster-algebras_posgeometry.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240522T110000
DTEND;TZID=America/New_York:20240522T120000
DTSTAMP:20240510T202735Z
CREATED:20240415T182841Z
LAST-MODIFIED:20240510T202735Z
UID:10003373-1716375600-1716379200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Mathematical Aspects of Scattering Amplitudes Lecture
DESCRIPTION:Mathematical Aspects of Scattering Amplitudes Lecture \nSpeaker: Chaim Even-Zohar\, Technion \nTitle: Amplituhedron tiles and twistor polynomials
URL:https://live-hu-cmsa-222.pantheonsite.io/event/scatteringamplitudes_52224/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Scattering Amplitudes Lectures
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240521T110000
DTEND;TZID=America/New_York:20240521T120000
DTSTAMP:20240520T144708Z
CREATED:20240415T182747Z
LAST-MODIFIED:20240520T144708Z
UID:10003372-1716289200-1716292800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Mathematical Aspects of Scattering Amplitudes Lecture
DESCRIPTION:Mathematical Aspects of Scattering Amplitudes Lecture \nSpeaker: Michael Borinsky\, ETH Zurich \nTitle: On the Euler characteristic of the commutative graph complex and the top-weight cohomology of the moduli space of curves
URL:https://live-hu-cmsa-222.pantheonsite.io/event/scatteringamplitudes_52124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Scattering Amplitudes Lectures
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240517T103000
DTEND;TZID=America/New_York:20240517T120000
DTSTAMP:20240425T140248Z
CREATED:20240411T151408Z
LAST-MODIFIED:20240425T140248Z
UID:10001514-1715941800-1715947200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Love and Naturalness
DESCRIPTION:Quantum Matter in Mathematics and Physics Seminar \nSpeaker: Mikhail Ivanov (MIT) \nTitle: Love and Naturalness \nAbstract: Recent progress in gravitational wave astronomy has spurred the development of efficient tools to describe gravitational binary dynamics. One such tool is classical worldline effective field theory (EFT). In the first part of my talk\, I will show how to use this EFT for systematic studies of tidal heating and deformations (Love numbers) of compact objects. I will present a gauge-invariant definition of Love numbers and show how to extract them in a coordinate-independent way from scattering amplitudes of the gravitational Raman process. I will show that the worldline EFT exhibits strong fine-tuning when applied to black holes. This gives rise to a naturalness paradox associated with the vanishing of black hole static Love numbers. In the second part of my talk\, I will present a new symmetry of black holes (Love symmetry) that elegantly resolves this paradox. The Love symmetry is tightly connected to isometries of extremal black holes that appear in many holographic constructions. It also provides a curious example of IR/UV mixing\, which may give insights for other hierarchy problems.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/qm_51724/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Matter
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END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240516T150000
DTEND;TZID=America/New_York:20240516T160000
DTSTAMP:20240510T175234Z
CREATED:20240510T170616Z
LAST-MODIFIED:20240510T175234Z
UID:10003387-1715871600-1715875200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Geometry of Generalized Lienard Equations\, Contact Geometry and Metriplectic Structure
DESCRIPTION:Speaker: Partha Guha\, Khalifa University\, Abu Dhabi \nTitle: Geometry of Generalized Lienard Equations\, Contact Geometry and Metriplectic Structure \nAbstract: We start with a self-contained brief review of the construction of non-standard Lagrangian and Hamiltonian structures using the Jacobi Last Multiplier for the (generalized) reduced Lienard equations satisfying Chiellini integrability condition\, we then explore its connection with the contact Hamiltonian mechanics. We also explore Lienard equations\, of reaction-diffusion class and conformal (or contact) Hamiltonian Structures. Finally\, we present the geometric formulation of the generalized Lienard equations in terms of metriplectic structure. \nJoint work with Jose Carinena and Anindya Ghose Choudhury
URL:https://live-hu-cmsa-222.pantheonsite.io/event/geometry_51624/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Special Seminar
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END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240516T130000
DTEND;TZID=America/New_York:20240516T140000
DTSTAMP:20240510T175438Z
CREATED:20240416T181859Z
LAST-MODIFIED:20240510T175438Z
UID:10003377-1715864400-1715868000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Controlling chaotic advection in 2D active nematics
DESCRIPTION:Active Matter Seminar \nSpeaker: Kevin Mitchell\, University of California\, Merced \nTitle: Controlling chaotic advection in 2D active nematics \nAbstract: Recent years have seen a surge of interest in active materials\, in which energy injected at the microscale gives rise to mesoscale coherent motion. One prominent example is an active 2D “liquid crystal” composed of microtubules in the nematic phase. The activity is generated by molecular motors that consume ATP to generate local shearing between the microtubules. The resulting 2D fluid flow exhibits self-generated mesoscale chaotic dynamics with a characteristic folding and stretching pattern. We analyze this dynamics from the perspective of chaotic advection\, in which the fluid can be viewed as “stirred” by topological defects in the nematic order parameter. Typically\, these defects move in an irregular\, chaotic pattern. We explore conditions\, both theoretically and in experiments\, under which the topological defects can be coaxed to perform regular periodic motion\, thus bringing some degree of order to the chaos.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/active-matter-51624/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Active Matter Seminar
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END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240516T103000
DTEND;TZID=America/New_York:20240516T113000
DTSTAMP:20240514T183407Z
CREATED:20240416T133753Z
LAST-MODIFIED:20240514T183407Z
UID:10003374-1715855400-1715859000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Mirror symmetry and log del Pezzo surfaces
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nSpeaker: Franco Rota\, University of Glasgow \nTitle: Mirror symmetry and log del Pezzo surfaces \nAbstract: The homological mirror symmetry conjecture predicts a duality\, expressed in terms of categorical equivalences\, between the complex geometry of a variety X (the B side) and the symplectic geometry of its mirror object Y (the A side). Motivated by this\, we study a series of singular surfaces (called log del Pezzo). I will describe the category arising in the B side\, using the McKay correspondence and explicit birational geometry. I will discuss early results on the A side\, using the language of pseudolattices to focus on the special case of a smooth degree 2 del Pezzo surface. This is joint work with Giulia Gugiatti.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/agist_51624/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebraic Geometry in String Theory Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/Algebraic-Geometry-in-String-Theory-05.16.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240515T150000
DTEND;TZID=America/New_York:20240515T160000
DTSTAMP:20240517T135756Z
CREATED:20240415T182551Z
LAST-MODIFIED:20240517T135756Z
UID:10003371-1715785200-1715788800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Mathematical Aspects of Scattering Amplitudes Lecture
DESCRIPTION:Mathematical Aspects of Scattering Amplitudes Lecture \nSpeaker: Matteo Parisi\, Harvard CMSA \nTitle: The amplituhedron and cluster algebras
URL:https://live-hu-cmsa-222.pantheonsite.io/event/scatteringamplitudes_51524/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Scattering Amplitudes Lectures
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240514T150000
DTEND;TZID=America/New_York:20240514T160000
DTSTAMP:20240510T144105Z
CREATED:20240415T180344Z
LAST-MODIFIED:20240510T144105Z
UID:10003369-1715698800-1715702400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Mathematical Aspects of Scattering Amplitudes Lecture
DESCRIPTION:Mathematical Aspects of Scattering Amplitudes Lecture \nSpeaker: James Drummond\, University of Southampton\n \nTitle: Multiple light-like Wilson loops in N=4 super Yang-Mills theory
URL:https://live-hu-cmsa-222.pantheonsite.io/event/scatteringamplitudes_51424/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Scattering Amplitudes Lectures
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240514T123000
DTEND;TZID=America/New_York:20240514T133000
DTSTAMP:20240510T202406Z
CREATED:20240424T200426Z
LAST-MODIFIED:20240510T202406Z
UID:10003382-1715689800-1715693400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Quasilocal mass for general domains in space
DESCRIPTION:CMSA Member Seminar \nSpeaker: Jue Liu \nTitle: Quasilocal mass for general domains in space \nAbstract: Diffeomorphism-invariant quasilocal mass in classical general relativity has been studied for decades\, but it is still an open problem how to define quasi-local mass for general domains with multiple boundaries in space. Using the Hamiltonian formulation\, we will provide a new way to define the nonnegative quasi-local mass\, and give recent progress in overcoming the difficulties.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/member-seminar-51424/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Member-Seminar-05.14.24.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240513T163000
DTEND;TZID=America/New_York:20240513T173000
DTSTAMP:20240508T203329Z
CREATED:20240130T151206Z
LAST-MODIFIED:20240508T203329Z
UID:10000814-1715617800-1715621400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Errors and Correction in Cumulative Knowledge
DESCRIPTION:Colloquium \nSpeaker: Madhu Sudan\, Harvard University \nTitle: Errors and Correction in Cumulative Knowledge \nAbstract: Societal accumulation of knowledge is a complex\, and arguably error-prone\, process. The correctness of new units of knowledge depends not only on the correctness of the new reasoning\, but also on the correctness of old units that the new one builds on. If left unchecked\, errors could completely ruin the validity of most of this knowledge so there must some error-correcting going on. What are the error-corrections processes employed in nature and how effective are they? In this talk\, we describe our attempts to model such phenomena using probablistic models – we describe models for growth of cumulative knowledge\, emergence of errors and methods to check for errors and eliminate them. We then analyze in this compound model\, when effects of errors may survive\, and when they are totally eliminated. \nThe central discovery in our work is the following optimistic statement: If we do checking correctly (most of the time) investing just a constant factor (<1) of our effort in checking (and saving the remaining constant factor towards deriving new units of knowledge)\, then effects of errors can be kept in check. Notably the amount of effort expended on checking does not scale with the volume of total knowledge or the depth of dependencies in the new units of knowledge\, either of which would be overwhelming. \nBased on the papers: \nIs this correct? Let’s check!\nOmri Ben-Eliezer\, Dan Mikulincer\, Elchanan Mossel\, Madhu Sudan\narXiv:2211.12301 \nErrors are Robustly Tamed in Cumulative Knowledge Processes\nAnna Brandenberger\, Cassandra Marcussen\, Elchanan Mossel\, Madhu Sudan\narXiv:2309.05638
URL:https://live-hu-cmsa-222.pantheonsite.io/event/colloquium-4124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Colloquium-05.13.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240513T133000
DTEND;TZID=America/New_York:20240513T143000
DTSTAMP:20240509T162010Z
CREATED:20240509T150634Z
LAST-MODIFIED:20240509T162010Z
UID:10003386-1715607000-1715610600@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Improving Mean-Field Theory for Quantum Magnets
DESCRIPTION:Quantum Matter in Mathematics and Physics Seminar \nSpeaker: Junyi Zhang\, Johns Hopkins University \nTitle: Improving Mean-Field Theory for Quantum Magnets \nAbstract: Frustrated magnets have garnered significant attention because of their potential to host exotic spin liquids\, while many real material candidates exhibit magnetic orders.  Due to their proximity to spin liquid phases\, the semiclassical descriptions of these magnetic orders often fall short in capturing their intricate quantum behaviors. In this talk\, I will introduce an improved mean-field method\, named density-matrix mean-field theory (DMMFT)\, for these quantum magnets. Using local reduced density matrix\, DMMFT can systematically incorporate the quantum fluctuations beyond conventional mean-field theories. Notably\, it not only quantitatively evaluates the renormalization of order parameters induced by quantum fluctuations but also has the capability to detect the topological order of quantum phases. DMMFT offers an efficient approach to explore phases displaying unconventional quantum orders\, particularly beneficial for investigating frustrated spin systems in high spatial dimensions. \nRef: https://arxiv.org/abs/2401.06236
URL:https://live-hu-cmsa-222.pantheonsite.io/event/qm_51324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-QMMP-05.13.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240513T110000
DTEND;TZID=America/New_York:20240513T120000
DTSTAMP:20240514T142424Z
CREATED:20240411T181646Z
LAST-MODIFIED:20240514T142424Z
UID:10003354-1715598000-1715601600@live-hu-cmsa-222.pantheonsite.io
SUMMARY:An analogue of non-interacting quantum field theory in Riemannian signature
DESCRIPTION:General Relativity Seminar \nSpeaker: Mikhail Molodyk\, Stanford \nTitle: An analogue of non-interacting quantum field theory in Riemannian signature \nAbstract: Recent advances using microlocal tools have led to constructions\, for wave operators on various classes of spacetimes\, of four distinguished Fredholm inverses which have the singular behavior required of retarded\, advanced\, Feynman\, and anti-Feynman propagators in QFT. Vasy and Wrochna have used these to define a QFT on asymptotically Minkowski spacetimes\, for which they construct Hadamard states described by asymptotic data at infinity. I will describe an analogue of this construction on Riemannian manifolds with two asymptotically conic ends\, defining quantum fields satisfying the Helmholtz equation and using scattering data to construct states satisfying a wavefront mapping-property version of the Hadamard condition. The absence of a spacetime interpretation lends itself to a sharper focus on the theory’s analytic structure\, from whose perspective the Feynman propagators are no less natural than the advanced/retarded ones. I will also highlight some differences between Feynman propagators defined as distinguished inverses and as time-ordered expectations. Based on joint work with András Vasy.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/general-relativity-51324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-GR-Seminar-05.13.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240510T120000
DTEND;TZID=America/New_York:20240510T130000
DTSTAMP:20240507T190133Z
CREATED:20240416T185907Z
LAST-MODIFIED:20240507T190133Z
UID:10000695-1715342400-1715346000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:On the landscape of 4d N=2 SCFTs
DESCRIPTION:CMSA Member Seminar \nSpeaker: Robert Moscrop\, Harvard CMSA \nTitle: On the landscape of 4d N=2 SCFTs \nAbstract: Four-dimensional conformal field theories with sufficient (N = 2) supersymmetry are highly constrained. So much so\, there has been an ongoing effort to classify them using only information about their moduli space of vacua. In this talk\, I will review recent progress in this classification before detailing a subclass of theories for which the classification problem is particularly tractable.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/member-seminar-51024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Member-Seminar-05.10.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240510T100000
DTEND;TZID=America/New_York:20240510T113000
DTSTAMP:20240508T195139Z
CREATED:20240507T190917Z
LAST-MODIFIED:20240508T195139Z
UID:10001518-1715335200-1715340600@live-hu-cmsa-222.pantheonsite.io
SUMMARY:From quantum Hall to Hubbard physics in twisted bilayer graphene
DESCRIPTION:Quantum Matter in Mathematics and Physics Seminar \nSpeaker: Eslam Khalaf (Harvard) \nTitle: From quantum Hall to Hubbard physics in twisted bilayer graphene \n\nAbstract: Early on it was noticed that twisted bilayer graphene (TBG) has elements in common with two paradigmatic examples of strongly correlated physics: Hubbard physics and quantum Hall physics. On the one hand\, TBG hosts flat topological Landau-level-like bands which realize quantum anomalous Hall states and orbital ferromagnetism under the right conditions. On the other hand\, these bands are characterized by concentrated charge density and show experimental signs of fluctuating magnetism\, and unconventional superconductivty; all characteristics of Hubbard-model-like physics. The emergence of fluctuating moments is particularly surprising\, as localized Wannier states do not exist in topological bands. I will discuss a phenomenological model for the flat bands in TBG that centers the concentration of charge density and\, relatedly\, the concentration of Berry flux. The bands obtained have excellent quantitative agreement with the Bistritzer-Macdonald model for realistic parameters. I will show that\, rather remarkably\, the model hosts decoupled flavor moments which despite being only power-law delocalized with infinite localization length\, have parametrically small overlap with each other. I will show how this unifies many of the observations in TBG and leads to a novel Mott semimetal phase for intermediate temperatures where moments are thermally disordered but charge fluctuations are mostly frozen.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/qm_51024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-QMMP-05.10.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240509T103000
DTEND;TZID=America/New_York:20240509T113000
DTSTAMP:20240507T152049Z
CREATED:20240416T133629Z
LAST-MODIFIED:20240507T152049Z
UID:10000890-1715250600-1715254200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Computing periods of hypersurfaces and elliptic surfaces via effective homology
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nSpeaker: Eric Pichon-Pharabod\, Universite Paris-Saclay \nTitle: Computing periods of hypersurfaces and elliptic surfaces via effective homology \nAbstract: The period matrix of a smooth complex projective variety X encodes the isomorphism between its singular homology and its algebraic De Rham cohomology. Numerical approximations with sufficient precision of the entries of this matrix\, called periods\, allow to recover some algebraic invariants of the variety\, such as the Néron-Severi group in the case of surfaces. In this talk\, we will present a method relying on the computation of an effective description of the homology for obtaining such numerical approximations of the periods of hypersurfaces and elliptic surfaces.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/agst-5924/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebraic Geometry in String Theory Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/Algebraic-Geometry-in-String-Theory-05.09.2024.docx-1.png
END:VEVENT
END:VCALENDAR