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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231016T100000
DTEND;TZID=America/New_York:20231016T113000
DTSTAMP:20260505T002059
CREATED:20240222T075624Z
LAST-MODIFIED:20240222T075624Z
UID:10002790-1697450400-1697455800@cmsa.fas.harvard.edu
SUMMARY:Moduli of boundary polarized Calabi-Yau pairs
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nPre-talk Speaker: Rosie Shen (Harvard): 10:00-10:30 am \nPre-talk Title: Introduction to the singularities of the MMP \n\nSpeaker: Dori Bejleri (Harvard Math & CMSA) \nTitle: Moduli of boundary polarized Calabi-Yau pairs \nAbstract: The theories of KSBA stability and K-stability furnish compact moduli spaces of general type pairs and Fano pairs respectively. However\, much less is known about the moduli theory of Calabi-Yau pairs. In this talk I will present an approach to constructing a moduli space of Calabi-Yau pairs which should interpolate between KSBA and K-stable moduli via wall-crossing.  I will explain how this approach can be used to construct projective moduli spaces of plane curve pairs. This is based on joint work with K. Ascher\, H. Blum\, K. DeVleming\, G. Inchiostro\, Y. Liu\, X. Wang. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/agst-101623/
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://cmsa.fas.harvard.edu/media/CMSA-Algebraic-Geometry-in-String-Theory-10.16.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231016T140000
DTEND;TZID=America/New_York:20231016T150000
DTSTAMP:20260505T002059
CREATED:20240222T090812Z
LAST-MODIFIED:20240222T090812Z
UID:10002793-1697464800-1697468400@cmsa.fas.harvard.edu
SUMMARY:Breaking ergodicity: quantum scars and regular eigenstates
DESCRIPTION:Topological Quantum Matter Seminar \nSpeaker: Ceren Dag\, Harvard \nTitle: Breaking ergodicity: quantum scars and regular eigenstates \nAbstract: Quantum many-body scars (QMBS) consist of a few low-entropy eigenstates in an otherwise chaotic many-body spectrum and can weakly break ergodicity resulting in robust oscillatory dynamics. The notion of QMBS follows the original single-particle scars introduced within the context of quantum billiards\, where scarring manifests in the form of a quantum eigenstate concentrating around an underlying classical unstable periodic orbit (UPO). A direct connection between these notions remains an outstanding problem. Here\, we study a many-body spinor condensate that\, owing to its collective interactions\, is amenable to the diagnostics of scars. We characterize the system’s rich dynamics\, spectrum\, and phase space\, consisting of both regular and chaotic states. The former are low in entropy\, violate the Eigenstate Thermalization Hypothesis (ETH)\, and can be traced back to integrable effective Hamiltonians\, whereas most of the latter are scarred by the underlying semiclassical UPOs\, while satisfying ETH. We outline an experimental proposal to probe our theory in trapped spin-1 Bose-Einstein condensates. If time permits\, I will also mention our latest efforts in introducing spatial dimension to this model with a true semiclassical limit\, and how quantum scars persist to exist in a many-body system. Reference: arXiv 2306.10411\, in peer review.
URL:https://cmsa.fas.harvard.edu/event/tqms_101623/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Topological Quantum Matter Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Topological-Seminar-10.16.23.docx-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231016T163000
DTEND;TZID=America/New_York:20231016T173000
DTSTAMP:20260505T002059
CREATED:20240223T093426Z
LAST-MODIFIED:20251026T063911Z
UID:10002844-1697473800-1697477400@cmsa.fas.harvard.edu
SUMMARY:An exploration of infinite games—infinite Wordle and the Mastermind numbers
DESCRIPTION:Speaker: Joel D. Hamkins (Notre Dame and Oxford) \nTitle: An exploration of infinite games—infinite Wordle and the Mastermind numbers \nAbstract: Let us explore the nature of strategic reasoning in infinite games\, focusing on the cases of infinite Wordle and infinite Mastermind. The familiar game of Wordle extends naturally to longer words or even infinite words in an idealized language\, and Mastermind similarly has natural infinitary analogues. What is the nature of play in these infinite games? Can the codebreaker play so as to win always at a finite stage of play? The analysis emerges gradually\, and in the talk I shall begin slowly with some easy elementary observations. By the end\, however\, we shall engage with sophisticated ideas in descriptive set theory\, a kind of infinitary information theory. Some assertions about the minimal size of winning sets of guesses\, for example\, turn out to be independent of the Zermelo-Fraenkel ZFC axioms of set theory. Some questions remain open.
URL:https://cmsa.fas.harvard.edu/event/colloquium-101623/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.16.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231018T123000
DTEND;TZID=America/New_York:20231018T133000
DTSTAMP:20260505T002059
CREATED:20240223T113304Z
LAST-MODIFIED:20240223T113334Z
UID:10002866-1697632200-1697635800@cmsa.fas.harvard.edu
SUMMARY:Composite fermions and the fractional quantum anomalous Hall effect
DESCRIPTION:Topological Quantum Matter Seminar \nSpeaker: Hart Goldman\, University of Chicago \nTitle: Composite fermions and the fractional quantum anomalous Hall effect \nAbstract: Recent experiments have revealed evidence for fractional quantum anomalous Hall (FQAH) states at zero magnetic field in a growing number of moire materials. In this talk\, I will argue that a composite fermion description\, already a unifying framework for the phenomenology of 2d electron gases at high magnetic fields\, provides a similarly powerful perspective in this new zero-field context. In particular\, a central prediction of the composite fermion framework is a non-Fermi liquid metal of composite fermions at even-denominator fillings. To this end\, I will present exact diagonalization evidence for such composite Fermi liquid states at zero magnetic field in twisted MoTe2 bilayers\, at fillings n = 1/2 and n = 3/4. Dubbing these states anomalous composite Fermi liquids (ACFLs)\, I will argue that they play a central organizing role in the FQAH phase diagram. I will also develop a long wavelength theory for this ACFL state\, which offers concrete experimental predictions that I will discuss in relation to current measurements. For example\, upon doping the composite Fermi sea\, one obtains a Jain sequence of FQAH states consistent with those observed experimentally\, as well as a new type of commensurability oscillations originating from the superlattice potential intrinsic to the system. Finally\, I will discuss opportunities for new physics not possible in quantum Hall systems at finite magnetic field.
URL:https://cmsa.fas.harvard.edu/event/tqms_101823/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Topological Quantum Matter Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Topological-Seminar-10.18.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231018T140000
DTEND;TZID=America/New_York:20231018T150000
DTSTAMP:20260505T002059
CREATED:20240223T114049Z
LAST-MODIFIED:20240223T114049Z
UID:10002867-1697637600-1697641200@cmsa.fas.harvard.edu
SUMMARY:Physics of Language Models: Knowledge Storage\, Extraction\, and Manipulation
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Yuanzhi Li\, CMU Dept. of Machine Learning and Microsoft Research \nTitle: Physics of Language Models: Knowledge Storage\, Extraction\, and Manipulation \nAbstract: Large language models (LLMs) can memorize a massive amount of knowledge during pre-training\, but can they effectively use this knowledge at inference time? In this work\, we show several striking results about this question. Using a synthetic biography dataset\, we first show that even if an LLM achieves zero training loss when pretraining on the biography dataset\, it sometimes can not be finetuned to answer questions as simple as “What is the birthday of XXX” at all. We show that sufficient data augmentation during pre-training\, such as rewriting the same biography multiple times or simply using the person’s full name in every sentence\, can mitigate this issue. Using linear probing\, we unravel that such augmentation forces the model to store knowledge about a person in the token embeddings of their name rather than other locations. \nWe then show that LLMs are very bad at manipulating knowledge they learn during pre-training unless a chain of thought is used at inference time. We pretrained an LLM on the synthetic biography dataset\, so that it could answer “What is the birthday of XXX” with 100% accuracy.  Even so\, it could not be further fine-tuned to answer questions like “Is the birthday of XXX even or odd?” directly.  Even using Chain of Thought training data only helps the model answer such questions in a CoT manner\, not directly. \nWe will also discuss preliminary progress on understanding the scaling law of how large a language model needs to be to store X pieces of knowledge and extract them efficiently. For example\, is a 1B parameter language model enough to store all the knowledge of a middle school student? \n  \n 
URL:https://cmsa.fas.harvard.edu/event/nt-101823/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/NTM-10.18.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231018T153000
DTEND;TZID=America/New_York:20231018T163000
DTSTAMP:20260505T002059
CREATED:20240223T075212Z
LAST-MODIFIED:20240223T075212Z
UID:10002829-1697643000-1697646600@cmsa.fas.harvard.edu
SUMMARY:Geometry of the doubly periodic Aztec dimer model
DESCRIPTION:Probability Seminar \nSpeaker: Tomas Berggren (MIT) \nTitle: Geometry of the doubly periodic Aztec dimer model \nAbstract: Random dimer models (or equivalently tiling models) have been a subject of extensive research in mathematics and physics for several decades. In this talk\, we will discuss the doubly periodic Aztec diamond dimer model of growing size\, with arbitrary periodicity and only mild conditions on the edge weights. In this limit\, we see three types of macroscopic regions — known as rough\, smooth and frozen regions. We will discuss how the geometry of the arctic curves\, the boundary of these regions\, can be described in terms of an associated amoeba and an action function. In particular\, we determine the number of frozen and smooth regions and the number of cusps on the arctic curves. We will also discuss the convergence of local fluctuations to the appropriate translation-invariant Gibbs measures. Joint work with Alexei Borodin. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/probability-101123/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-10.18.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231020T090000
DTEND;TZID=America/New_York:20231020T090000
DTSTAMP:20260505T002059
CREATED:20240221T112317Z
LAST-MODIFIED:20240221T112317Z
UID:10002781-1697792400-1697792400@cmsa.fas.harvard.edu
SUMMARY:CMSA Director Dan Freed featured in Harvard Gazette
DESCRIPTION:CMSA Director Dan Freed featured in Harvard Gazette\n“Center welcomes new director\, a Harvard alum who will explore ‘beautiful\, deep’ interactions between mathematics\, science.” \nLink to article.\nStory by Anne J. Manning\, Harvard Staff Writer \nPhoto courtesy of Niles Singer\, Harvard University.
URL:https://cmsa.fas.harvard.edu/event/cmsa-director-dan-freed-featured-in-harvard-gazette/
ATTACH;FMTTYPE=image/webp:https://cmsa.fas.harvard.edu/media/2500_Dan_Freed_Portrait_NS_200-1500x1000.jpg.webp
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231020T120000
DTEND;TZID=America/New_York:20231020T130000
DTSTAMP:20260505T002059
CREATED:20240223T110405Z
LAST-MODIFIED:20240223T110405Z
UID:10002856-1697803200-1697806800@cmsa.fas.harvard.edu
SUMMARY:Black Holes as Quantum Systems
DESCRIPTION:Member Seminar \nSpeaker: Daniel Kapec (CMSA) \nTitle: Black Holes as Quantum Systems \nAbstract: To an outside observer\, a black hole appears to be an ordinary quantum mechanical system with finite entropy and highly chaotic internal dynamics. Nevertheless\, the low-temperature thermodynamics of the Kerr black hole presents several puzzles. For instance\, the leading order semiclassical approximation to the black hole density of states predicts a surprisingly large ground state degeneracy\, while poorly understood quantum corrections are known to become increasingly important at low temperatures. I will review the modern picture of black holes as quantum systems and then discuss a recent result on the leading correction to the low-temperature thermodynamics of the Kerr black hole that resolves many of the old puzzles. \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-102023/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231023T103000
DTEND;TZID=America/New_York:20231023T113000
DTSTAMP:20260505T002059
CREATED:20240222T073026Z
LAST-MODIFIED:20240222T073026Z
UID:10002789-1698057000-1698060600@cmsa.fas.harvard.edu
SUMMARY:Gauged Linear Sigma Models and Cohomological Field Theories
DESCRIPTION:Algebraic Geometry in String Theory Seminar \n\nSpeaker: David Favero\, University of Minnesota \n\nTitle: Gauged Linear Sigma Models and Cohomological Field Theories \nAbstract: This talk is dedicated to the memory of my friend and collaborator Bumsig Kim and based on joint work with Ciocan-Fontanine-Guere-Kim-Shoemaker.  Gauged Linear Sigma Models (GLSMs)  serve as a means of interpolating between Kahler geometry and singularity theory.  In enumerative geometry\, they should specialize to both Gromov-Witten and Fan-Jarvis-Ruan-Witten theory.   In joint work with Bumsig Kim (see arXiv:2006.12182)\, we constructed such enumerative invariants for GLSMs.  Furthermore\, we proved that these invariants form a Cohomological Field Theory.   In this lecture\, I will describe GLSMs and Cohomological Field Theories\, review the history of their development in enumerative geometry\, and discuss the construction of these general invariants.  Briefly\, the invariants are obtained by forming the analogue of a virtual fundamental class which lives in the twisted Hodge complex over a certain “moduli space of maps to the GLSM”.  This virtual fundamental class roughly comes as the Atiyah class of a “virtual matrix factorization” associated to the GLSM data.
URL:https://cmsa.fas.harvard.edu/event/agst-102323/
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://cmsa.fas.harvard.edu/media/CMSA-Algebraic-Geometry-in-String-Theory-10.23.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231023T163000
DTEND;TZID=America/New_York:20231023T173000
DTSTAMP:20260505T002059
CREATED:20240223T092904Z
LAST-MODIFIED:20240223T092904Z
UID:10002843-1698078600-1698082200@cmsa.fas.harvard.edu
SUMMARY: On Provable Copyright Protection for Generative Model
DESCRIPTION:Speaker: Boaz Barak (Harvard) \nTitle: On Provable Copyright Protection for Generative Model \nAbstract: There is a growing concern that learned conditional generative models may output samples that are substantially similar to some copyrighted data C that was in their training set. We give a formal definition of near access-freeness (NAF) and prove bounds on the probability that a model satisfying this definition outputs a sample similar to C\, even if C is included in its training set. \nRoughly speaking\, a generative model p is k-NAF if for every potentially copyrighted data C\, the output of p diverges by at most k-bits from the output of a model q that did not access C at all. We also give generative model learning algorithms\, which efficiently modify the original generative model learning algorithm in a black box manner\, that output generative models with strong bounds on the probability of sampling protected content. Furthermore\, we provide promising experiments for both language (transformers) and image (diffusion) generative models\, showing minimal degradation in output quality while ensuring strong protections against sampling protected content. \nJoint work with Nikhil Vyas and Sham Kakade. Paper appeared in ICML 2023 and is on https://arxiv.org/abs/2302.10870
URL:https://cmsa.fas.harvard.edu/event/colloquium-102323/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.23.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231024T110000
DTEND;TZID=America/New_York:20231024T120000
DTSTAMP:20260505T002059
CREATED:20240223T053357Z
LAST-MODIFIED:20240223T053357Z
UID:10002817-1698145200-1698148800@cmsa.fas.harvard.edu
SUMMARY:Resolving memory in numerical relativity\, and fixing BMS frames for modeling
DESCRIPTION:General Relativity Seminar \nSpeaker: Leo Stein (Mississippi) \nTitle: Resolving memory in numerical relativity\, and fixing BMS frames for modeling \nAbstract: Numerical relativity waveforms serve as ground truth for detection and parameter estimation of binary black hole mergers. Most NR waveforms to date miss memory effects\, as they were extracted from simulations using an approximation called extrapolation. I will report on the SXS collaboration’s capacity to resolve memory effects in production NR simulations using Cauchy-characteristic evolution (CCE)\, and in the future with Cauchy-characteristic matching (CCM). I will further report on how BH perturbation and post-Newtonian theory furnish natural BMS frames. With these BMS frames\, we can extract well-defined remnant quantities\, perform precision ringdown modeling\, and build complete surrogate waveform models that capture memory effects.
URL:https://cmsa.fas.harvard.edu/event/gr_102423/
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231024T123000
DTEND;TZID=America/New_York:20231024T133000
DTSTAMP:20260505T002059
CREATED:20240223T083135Z
LAST-MODIFIED:20240223T083135Z
UID:10002837-1698150600-1698154200@cmsa.fas.harvard.edu
SUMMARY:CMSA Q and A Seminar 10/24/23
DESCRIPTION:CMSA Q and A Seminar \nSpeakers: Xi Yin (Harvard Physics) and Peter Kronheimer (Harvard Math)\n\nTopics:\nXi Yin: What is string field theory?\nPeter Kronheimer: What is Seiberg-Witten theory?
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_102423/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:CMSA Q&A Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231025T140000
DTEND;TZID=America/New_York:20231025T150000
DTSTAMP:20260505T002059
CREATED:20240223T105453Z
LAST-MODIFIED:20240223T105453Z
UID:10002853-1698242400-1698246000@cmsa.fas.harvard.edu
SUMMARY:Llemma: an open language model for mathematics
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Sean Welleck\, CMU\, Language Technologies Institute \nTitle: Llemma: an open language model for mathematics \nAbstract: We present Llemma: 7 billion and 34 billion parameter language models for mathematics. The Llemma models are initialized with Code Llama weights\, then trained on the Proof-Pile II\, a 55 billion token dataset of mathematical web data\, code\, and scientific papers. The resulting models show improved mathematical capabilities\, and can be adapted to various tasks. For instance\, Llemma outperforms the unreleased Minerva model suite on an equi-parameter basis\, and is capable of tool use and formal theorem proving without any further fine-tuning. We openly release all artifacts\, including the Llemma models\, the Proof-Pile II\, and code to replicate our experiments. We hope that Llemma serves as a platform for new research and tools at the intersection of generative models and mathematics. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/nt-102523/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/NTM-10.25.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231025T153000
DTEND;TZID=America/New_York:20231025T163000
DTSTAMP:20260505T002059
CREATED:20240223T055628Z
LAST-MODIFIED:20240223T055719Z
UID:10002822-1698247800-1698251400@cmsa.fas.harvard.edu
SUMMARY:Tail estimates for stationary KPZ models
DESCRIPTION:Probability Seminar \nSpeaker: Benjamin Landon (University of Toronto) \nTitle: Tail estimates for stationary KPZ models \nAbstract: The limiting distributions of the KPZ universality class exhibit tail exponents of 3/2 and 3. In this talk we will review recent work studying the upper tail exponent 3/2 in the moderate deviations regime of several KPZ models at finite size\, including the stochastic six vertex model\, the ASEP and a class of non-integrable interacting diffusions. \nJoint work with Christian Noack and Phil Sosoe. \n 
URL:https://cmsa.fas.harvard.edu/event/probability-102523/
LOCATION:Virtual
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-10.25.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231026T130000
DTEND;TZID=America/New_York:20231026T140000
DTSTAMP:20260505T002059
CREATED:20240223T070828Z
LAST-MODIFIED:20240223T070828Z
UID:10002825-1698325200-1698328800@cmsa.fas.harvard.edu
SUMMARY:Scaling behavior and control of nuclear wrinkling
DESCRIPTION:Active Matter Seminar\n\n\nSpeaker: Nicolas Romeo (UChicago) \nTitle: Scaling behavior and control of nuclear wrinkling \nAbstract: The cell nucleus is enveloped by a complex membrane\, whose wrinkling has been implicated in disease and cellular aging. The biophysical dynamics and spectral evolution of nuclear wrinkling during multicellular development remain poorly understood due to a lack of direct quantitative measurements. We characterize the onset and dynamics of nuclear wrinkling during egg development in the fruit fly when nurse cell nuclei increase in size and display stereotypical wrinkling behaviour. A spectral analysis of three-dimensional high-resolution live-imaging data from several hundred nuclei reveals a robust asymptotic power-law scaling of angular fluctuations consistent with renormalization and scaling predictions from a nonlinear elastic shell model. We further demonstrate that nuclear wrinkling can be reversed through osmotic shock and suppressed by microtubule disruption\, providing tunable physical and biological control parameters for probing the mechanical properties of the nuclear envelope\, highlighting in passing the importance of nonlinear response to biological robustness.
URL:https://cmsa.fas.harvard.edu/event/am-102623/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Active Matter Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Active-Matter-Seminar-10.26.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20231027
DTEND;VALUE=DATE:20231029
DTSTAMP:20260505T002059
CREATED:20230904T060021Z
LAST-MODIFIED:20240624T182341Z
UID:10000002-1698364800-1698537599@cmsa.fas.harvard.edu
SUMMARY:Mathematics in Science: Perspectives and Prospects
DESCRIPTION:Mathematics in Science: Perspectives and Prospects\nA showcase of mathematics in interaction with physics\, computer science\, biology\, and beyond. \nOctober 27–28\, 2023 \nLocation: Harvard University Science Center Hall D & via Zoom. \nDirections and Recommended Lodging \nMathematics in Science: Perspectives and Prospects Youtube Playlist \n  \n\nSpeakers \n\nNima Arkani-Hamed (IAS)\nConstantinos Daskalakis (MIT)\nAlison Etheridge (Oxford)\nMike Freedman (Harvard CMSA)\nGreg Moore (Rutgers)\nBernd Sturmfels (MPI Leipzig)\n\n\nOrganizers \n\nMichael R. Douglas (Harvard CMSA)\nDan Freed (Harvard Math & CMSA)\nMike Hopkins (Harvard Math)\nCumrun Vafa (Harvard Physics)\nHorng-Tzer Yau (Harvard Math)\n\nSchedule\nFriday\, October 27\, 2023 \n\n\n\n2:00–3:15 pm\n\nGreg Moore (Rutgers) \nTitle: Remarks on Physical Mathematics \nAbstract: I will describe some examples of the vigorous modern dialogue between mathematics and theoretical physics (especially high energy and condensed matter physics). I will begin by recalling Stokes’ phenomenon and explain how it is related to some notable developments in quantum field theory from the past 30 years. Time permitting\, I might also say something about the dialogue between mathematicians working on the differential topology of four-manifolds and physicists working on supersymmetric quantum field theories. But I haven’t finished writing the talk yet\, so I don’t know how it will end any more than you do. \nSlides (PDF) \n \n\n\n\n3:15–3:45 pm\nBreak\n\n\n3:45–5:00 pm\n\nBernd Sturmfels (MPI Leipzig) \nTitle: Algebraic Varieties in Quantum Chemistry \nAbstract: We discuss the algebraic geometry behind coupled cluster (CC) theory of quantum many-body systems. The high-dimensional eigenvalue problems that encode the electronic Schroedinger equation are approximated by a hierarchy of polynomial systems at various levels of truncation. The exponential parametrization of the eigenstates gives rise to truncation varieties. These generalize Grassmannians in their Pluecker embedding. We explain how to derive Hamiltonians\, we offer a detailed study of truncation varieties and their CC degrees\, and we present the state of the art in solving the CC equations. This is joint work with Fabian Faulstich and Svala Sverrisdóttir. \nSlides (PDF) \n \n\n\n\n\n  \nSaturday\, October 28\, 2023 \n\n\n\n9:00 am\nBreakfast\n\n\n9:30–10:45 am\n\nMike Freedman (Harvard CMSA) \nTitle: ML\, QML\, and Dynamics: What mathematics can help us understand and advance machine learning? \nAbstract: Vannila deep neural nets DNN repeatedly stretch and fold. They are reminiscent of the logistic map and the Smale horseshoe.  What kind of dynamics is responsible for their expressivity and trainability. Is chaos playing a role? Is the Kolmogorov Arnold representation theorem relevant? Large language models are full of linear maps. Might we look for emergent tensor structures in these highly trained maps in analogy with emergent tensor structures at local minima of certain loss functions in high-energy physics. \nSlides (PDF) \n \n\n\n\n10:45–11:15 am\nBreak\n\n\n11:15 am–12:30 pmvia Zoom\n\nNima Arkani-Hamed (IAS) \nTitle: All-Loop Scattering as A Counting Problem \nAbstract: I will describe a new understanding of scattering amplitudes based on fundamentally combinatorial ideas in the kinematic space of the scattering data. I first discuss a toy model\, the simplest theory of colored scalar particles with cubic interactions\, at all loop orders and to all orders in the topological ‘t Hooft expansion. I will present a novel formula for loop-integrated amplitudes\, with no trace of the conventional sum over Feynman diagrams\, but instead determined by a beautifully simple counting problem attached to any order of the topological expansion. A surprisingly simple shift of kinematic variables converts this apparent toy model into the realistic physics of pions and Yang-Mills theory. These results represent a significant step forward in the decade-long quest to formulate the fundamental physics of the real world in a new language\, where the rules of spacetime and quantum mechanics\, as reflected in the principles of locality and unitarity\, are seen to emerge from deeper mathematical structures. \n \n\n\n\n12:30–2:00 pm\nLunch break\n\n\n2:00–3:15 pm\n\nConstantinos Daskalakis (MIT) \nTitle: How to train deep neural nets to think strategically \nAbstract: Many outstanding challenges in Deep Learning lie at its interface with Game Theory: from playing difficult games like Go to robustifying classifiers against adversarial attacks\, training deep generative models\, and training DNN-based models to interact with each other and with humans. In these applications\, the utilities that the agents aim to optimize are non-concave in the parameters of the underlying DNNs; as a result\, Nash equilibria fail to exist\, and standard equilibrium analysis is inapplicable. So how can one train DNNs to be strategic? What is even the goal of the training? We shed light on these challenges through a combination of learning-theoretic\, complexity-theoretic\, game-theoretic and topological techniques\, presenting obstacles and opportunities for Deep Learning and Game Theory going forward. \nSlides (PDF) \n \n\n\n\n3:15–3:45 pm\nBreak\n\n\n3:45–5:00 pm\n\nAlison Etheridge (Oxford) \nTitle: Modelling hybrid zones \nAbstract: Mathematical models play a fundamental role in theoretical population genetics and\, in turn\, population genetics provides a wealth of mathematical challenges. In this lecture we investigate the interplay between a particular (ubiquitous) form of natural selection\, spatial structure\, and\, if time permits\, so-called genetic drift. A simple mathematical caricature will uncover the importance of the shape of the domain inhabited by a species for the effectiveness of natural selection. \nSlides (PDF) \n \n\n\n\n\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 mathsci2023@cmsa.fas.harvard.edu no later than October 9\, 2023. \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\n 
URL:https://cmsa.fas.harvard.edu/event/mathematics-in-science/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Conference,Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/MathScience2023Poster_8.5x11.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231027T120000
DTEND;TZID=America/New_York:20231027T130000
DTSTAMP:20260505T002059
CREATED:20240223T110834Z
LAST-MODIFIED:20240223T110834Z
UID:10002858-1698408000-1698411600@cmsa.fas.harvard.edu
SUMMARY:Extension of pluricanonical forms in positive and mixed characteristics
DESCRIPTION:Member Seminar \nSpeaker: Iacopo Brivio (CMSA) \nTitle: Extension of pluricanonical forms in positive and mixed characteristics \nAbstract: The geometry of a complex manifold $X$ is to a large extent determined by its pluricanonical forms\, i.e. global sections of $(\Omega^{\dim X}_X)^{\otimes m}$ for $m\geq 0$. A famous theorem of Siu states that when $X\to D$ is a smooth projective family of complex manifolds\, then every pluricanonical form on $X_0$ extends to the whole of $X$. Both this theorem and the tools used in its proof had a deep impact in higher dimensional birational geometry and moduli theory. In this talk I am going to give an overview of the extension problem for pluricanonical forms when $D$ is the spectrum of a positive or mixed characteristic discrete valuation ring. \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-102723/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231030T163000
DTEND;TZID=America/New_York:20231030T173000
DTSTAMP:20260505T002059
CREATED:20240223T084547Z
LAST-MODIFIED:20240223T084547Z
UID:10002840-1698683400-1698687000@cmsa.fas.harvard.edu
SUMMARY:Homotopy categories of rings: some properties and consequences in module categories
DESCRIPTION:Speaker: Manuel Cortés-Izurdiaga (University of Malaga) \nTitle:  Homotopy categories of rings: some properties and consequences in module categories \nAbstract: Given a non-necessarily commutative ring with unit and an additive subcategory of the category of right modules\, one can consider complexes of modules in the subcategory and the corresponding homotopy category. Sometimes\, these homotopy categories are the first step in studying other (algebraic) homotopy categories\, such as those associated to a scheme. To study these categories\, one can use results from the category of modules or the category of complexes. In the first part of the talk\, we will see how some results of homotopy categories of complexes extend to homotopy categories of N-complexes\, for a natural number N greater than or equal to 2\, using some techniques from module categories\, such us the deconstruction of a class of modules. \nAnother approximation is to use other methods for studying homotopy categories\, like those coming from triangulated categories. In some cases\, the results obtained in homotopy categories imply some consequences in the category of modules. In the second part of the talk\, we will see how to prove the existence of Gorenstein-projective precovers for some specific rings using this approach.
URL:https://cmsa.fas.harvard.edu/event/colloquium-103023/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.30.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231101T103000
DTEND;TZID=America/New_York:20231101T113000
DTSTAMP:20260505T002059
CREATED:20240222T111415Z
LAST-MODIFIED:20240222T111747Z
UID:10002806-1698834600-1698838200@cmsa.fas.harvard.edu
SUMMARY:Unveiling Correlated Topological Insulators through Fermionic Tensor Network States
DESCRIPTION:Topological Quantum Matter Seminar \nSpeaker: Shenghan Jiang\, Kavli Institute for Theoretical Sciences UCAS \nTitle: Unveiling Correlated Topological Insulators through Fermionic Tensor Network States \nAbstract: The study of topological band insulators has revealed fascinating phases characterized by band topology indices\, harboring extraordinary boundary modes protected by anomalous symmetry actions. In strongly correlated systems\, it has been established that topological insulator phases persist as stable phases. However\, due to the inability to express the ground states of such systems as Slater determinants\, the formulation of generic variational wavefunctions for numerical simulations is highly desirable.\nIn this talk\, we tackle this challenge by developing a comprehensive framework with fermionic tensor network states. Starting from simple assumptions\, we write down tensor equations\, construct edge theories and extract quantum anomaly data for topological insulators. By exhaustively exploring all possible sets of equations\, we achieve a systematic classification of topological insulator phases. Imposing the solutions of a given set of equations onto local tensors\, we obtain generic variational wavefunctions for corresponding topological insulator phases. Our methodology provides a crucial first step towards simulating topological insulators in strongly correlated systems. \n 
URL:https://cmsa.fas.harvard.edu/event/tqms_11123/
LOCATION:Virtual
CATEGORIES:Topological Quantum Matter Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Topological-Seminar-11.01.23.docx-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231101T153000
DTEND;TZID=America/New_York:20231101T163000
DTSTAMP:20260505T002059
CREATED:20240223T054758Z
LAST-MODIFIED:20240223T054856Z
UID:10002821-1698852600-1698856200@cmsa.fas.harvard.edu
SUMMARY:Universality of max-margin classifiers
DESCRIPTION:Probability Seminar \nSpeaker: Youngtak Sohn (MIT) \nTitle: Universality of max-margin classifiers \nAbstract: Many modern learning methods\, such as deep neural networks\, are so complex that they perfectly fit the training data. Despite this\, they generalize well to the unseen data. Motivated by this phenomenon\, we consider high-dimensional binary classification with linearly separable data. First\, we consider Gaussian covariates and characterize linear classification problems for which the minimum norm interpolating prediction rule\, namely the max-margin classification\, has near-optimal prediction accuracy. Then\, we discuss universality of max-margin classification. In particular\, we characterize the prediction accuracy of the non-linear random features model\, a two-layer neural network with random first layer weights. The spectrum of the kernel random matrices plays a crucial role in the analysis. Finally\, we consider the wide-network limit\, where the number of neurons tends to infinity\, and show how non-linear max-margin classification with random features collapse to a linear classifier with a soft-margin objective. \nJoint work with Andrea Montanari\, Feng Ruan\, Jun Yan\, and Basil Saeed.
URL:https://cmsa.fas.harvard.edu/event/probability-11123/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-11.01.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231102T153000
DTEND;TZID=America/New_York:20231102T163000
DTSTAMP:20260505T002059
CREATED:20240223T113003Z
LAST-MODIFIED:20240223T113003Z
UID:10002865-1698939000-1698942600@cmsa.fas.harvard.edu
SUMMARY:Solving spin systems\, the Babylonian way
DESCRIPTION:Probability Seminar \nSpeaker: Nicola Kistler (Johann Wolfgang Goethe-Universität Frankfurt am Main) \nTitle: Solving spin systems\, the Babylonian way \nAbstract: The replica method\, together with Parisi’s symmetry breaking mechanism\, is an extremely powerful tool to compute the limiting free energy of virtually any mean field disordered system. Unfortunately\, the tool is dramatically flawed from a mathematical point of view. I will discuss a truly elementary procedure which allows to rigorously implement two (out of three) steps of the replica method\, and conclude with some remarks on the relation between this new point of view and old work by Mezard and Virasoro on the microstructure of ultrametricity\, the latter being the fundamental yet unjustified Ansatz in the celebrated Parisi solution. We are still far from a clear understanding of the issues\, but quite astonishingly\, evidence is mounting that Parisi’s ultrametricity assumption\, the onset of scales and the universal hierarchical self-organisation of random systems in the infinite volume limit\, is intimately linked to hidden geometrical properties of large random matrices which satisfy rules reminiscent of the popular SUDOKU game.
URL:https://cmsa.fas.harvard.edu/event/probability-92023/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-09.20.23.docx-1-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231102T163000
DTEND;TZID=America/New_York:20231102T180000
DTSTAMP:20260505T002059
CREATED:20240222T112133Z
LAST-MODIFIED:20240222T112133Z
UID:10002808-1698942600-1698948000@cmsa.fas.harvard.edu
SUMMARY:Landscape of quantum phases in quantum materials
DESCRIPTION:Joint Quantum Matter in Mathematics and Physics and Topological Quantum Matter Seminar \nSpeaker: Liujun Zou (Perimeter Institute) \nTitle: Landscape of quantum phases in quantum materials\n\nAbstract: A central goal of condensed matter physics is to understand which quantum phases of matter can emerge in a quantum material. For this purpose\, one should be able to not only describe the quantum phases using some effective field theories\, but also capture the important microscopic information of the material via mathematical formulation. In this talk\, I will present a framework to classify quantum phases in quantum materials\, where the microscopic information of a material is encoded in its quantum anomaly. I will talk about the application of this framework to classify various exotic quantum phases of matter in different lattice systems. Using our framework\, we have obtained many results unexpected from the previous literature.
URL:https://cmsa.fas.harvard.edu/event/tqms_102523/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Matter,Topological Quantum Matter Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Special-Joint-QMMP-Topological-QM-11.02.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231103T120000
DTEND;TZID=America/New_York:20231103T130000
DTSTAMP:20260505T002059
CREATED:20240227T113702Z
LAST-MODIFIED:20240227T113702Z
UID:10002880-1699012800-1699016400@cmsa.fas.harvard.edu
SUMMARY:Deformations of Landau-Ginzburg models and their fibers
DESCRIPTION:Member Seminar \nSpeaker: Zi Yang Kang \nTitle: Deformations of Landau-Ginzburg models and their fibers \nAbstract: In mirror symmetry\, the dual object to a Fano variety is a Landau-Ginzburg model. Broadly\, a Landau-Ginzburg model is quasi-projective variety Y with a superpotential function w\, but not all such pairs correspond to Fano varieties under mirror symmetry\, so a very natural question to ask is: Which Landau-Ginzburg models are mirror to Fano varieties? In this talk\, I will discuss a cohomological characterization of mirrors of (semi-)Fano varieties\, focusing on the case of threefolds. I’ll discuss how this characterization relates to the deformation and Hodge theory of (Y\,w)\, and in particular\, how the classification of (semi-)Fano threefolds is related to questions about moduli spaces of lattice polarized K3 surfaces.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-11323/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231106T103000
DTEND;TZID=America/New_York:20231106T113000
DTSTAMP:20260505T002059
CREATED:20240222T071857Z
LAST-MODIFIED:20240222T152725Z
UID:10002788-1699266600-1699270200@cmsa.fas.harvard.edu
SUMMARY:Deformations of Landau-Ginzburg models and their fibers
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nSpeaker: Andrew Harder\, Lehigh University \nTitle: Deformations of Landau-Ginzburg models and their fibers \nAbstract: In mirror symmetry\, the dual object to a Fano variety is a Landau-Ginzburg model. Broadly\, a Landau-Ginzburg model is quasi-projective variety Y with a superpotential function w\, but not all such pairs correspond to Fano varieties under mirror symmetry\, so a very natural question to ask is: Which Landau-Ginzburg models are mirror to Fano varieties? In this talk\, I will discuss a cohomological characterization of mirrors of (semi-)Fano varieties\, focusing on the case of threefolds. I’ll discuss how this characterization relates to the deformation and Hodge theory of (Y\,w)\, and in particular\, how the classification of (semi-)Fano threefolds is related to questions about moduli spaces of lattice polarized K3 surfaces.
URL:https://cmsa.fas.harvard.edu/event/agst-11623/
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://cmsa.fas.harvard.edu/media/CMSA-Algebraic-Geometry-in-String-Theory-11.06.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231106T163000
DTEND;TZID=America/New_York:20231106T173000
DTSTAMP:20260505T002059
CREATED:20240223T083208Z
LAST-MODIFIED:20240223T083208Z
UID:10002838-1699288200-1699291800@cmsa.fas.harvard.edu
SUMMARY:Impossibility results in classical dynamical systems
DESCRIPTION:Speaker: Matthew Foreman (UC Irvine) \nTitle: Impossibility results in classical dynamical systems \nAbstract: In 1932\, motivated by questions in statistical and celestial mechanics\, von Neumann proposed classifying the statistical behavior of dynamical systems. In the 1960’s\, motivated by work of Poincaré\, Smale proposed classifying the qualitative behavior of dynamical systems.  These questions laid the groundwork for enormous amounts of work\, but the fundamental questions remain open. This talk shows that they are impossible to answer in a rigorous sense. The talk will discuss various kinds of impossibility results and describe how they apply to von Neumann’s program and Smale’s program. \n 
URL:https://cmsa.fas.harvard.edu/event/colloquium-11623/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-11.06.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231107T110000
DTEND;TZID=America/New_York:20231107T120000
DTSTAMP:20260505T002059
CREATED:20240223T052707Z
LAST-MODIFIED:20240223T052707Z
UID:10002816-1699354800-1699358400@cmsa.fas.harvard.edu
SUMMARY:Fluid stabilization in slowly expanding cosmological spacetime
DESCRIPTION:General Relativity Seminar \nSpeaker: David Fajman (Vienna) \nTitle: Fluid stabilization in slowly expanding cosmological spacetime \nAbstract: Relativistic fluids are known to form shocks during their evolution from near-homogeneous initial data. In expanding spacetimes\, shock formation is suppressed\, if the expansion is sufficiently strong. We refer to this effect as fluid stabilization. The occurrence of this phenomenon depends on features of the fluid and has implications for our understanding of structure formation and cosmological evolution. While the effect is well studied in the regime of accelerated expansion\, in recent years it has been shown that fluid stabilization occurs as well in spacetimes with slower expansion rates. In this talk we present different recent results on fluid stabilization in slowly expanding spacetimes and aspects of the methods involved in the respective proofs. \n  \nTalk via Zoom\, broadcast in G10 \n 
URL:https://cmsa.fas.harvard.edu/event/gr_11723/
LOCATION:Hybrid – G10
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-11.07.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231107T123000
DTEND;TZID=America/New_York:20231107T133000
DTSTAMP:20260505T002059
CREATED:20240223T083628Z
LAST-MODIFIED:20240223T083628Z
UID:10002839-1699360200-1699363800@cmsa.fas.harvard.edu
SUMMARY:CMSA Q and A Seminar 11/7/2023
DESCRIPTION:CMSA Q and A Seminar \nSpeakers: Michael Hopkins (Harvard Math) and Minhea Popa (Harvard Math) \nTopics: \nMike Hopkins: What are topological modular forms? \nMihnea Popa: What is the abundance conjecture and why should it to be true? \n 
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_11723/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:CMSA Q&A Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231107T163000
DTEND;TZID=America/New_York:20231107T180000
DTSTAMP:20260505T002059
CREATED:20240222T091622Z
LAST-MODIFIED:20240222T091622Z
UID:10002794-1699374600-1699380000@cmsa.fas.harvard.edu
SUMMARY: A Long Exact Sequence in Symmetry Breaking
DESCRIPTION:Quantum Matter Seminar \nSpeaker: Cameron Krulewski (MIT) and Leon Liu (Harvard) \nTitle: A Long Exact Sequence in Symmetry Breaking \nAbstract: We study defects in symmetry breaking phases\, such as domain walls\, vortices\, and hedgehogs. In particular\, we focus on the localized gapless excitations that sometimes occur at the cores of these objects. These are topologically protected by an ’t Hooft anomaly. We classify different symmetry breaking phases in terms of the anomalies of these defects and relate them to the anomaly of the broken symmetry by an anomaly-matching formula. We also derive the obstruction to the existence of a symmetry breaking phase with a local defect. We obtain these results using a long exact sequence of groups of invertible field theories\, which we call the “symmetry breaking long exact sequence” (SBLES). \nThe mathematical backbone of the SBLES is the Smith homomorphism\, which gives a family of maps between twisted bordism groups. Though many examples have been studied\, we give the first completely general account of the Smith homomorphism. We lift it to a map of Thom \nspectra and identify the cofiber\, producing a long exact sequence of twisted bordism groups; the SBLES is the Anderson dual of that long exact sequence. Our work develops further the theory of higher Berry phase and its bulk-boundary correspondence and serves as a new computational tool for classifying symmetry protected topological phases.
URL:https://cmsa.fas.harvard.edu/event/qm_11723/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-11.07.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231108T140000
DTEND;TZID=America/New_York:20231108T150000
DTSTAMP:20260505T002059
CREATED:20240222T095919Z
LAST-MODIFIED:20240222T095919Z
UID:10002798-1699452000-1699455600@cmsa.fas.harvard.edu
SUMMARY:Peano: Learning Formal Mathematical Reasoning Without Human Data
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Gabriel Poesia\, Dept. of Computer Science\, Stanford University \nTitle: Peano: Learning Formal Mathematical Reasoning Without Human Data \nAbstract: Peano is a theorem proving environment in which a computational agent can start tabula rasa in a new domain\, learn to solve problems through curiosity-driven exploration\, and create its own higher level actions. Gabriel will describe the system\, present case studies on learning to solve simple algebra problems from the Khan Academy platform\, and describe work on progress on learning the Natural Number Game\, a popular introduction to theorem proving in Lean for mathematicians. \n 
URL:https://cmsa.fas.harvard.edu/event/nt-11823/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/NTM-11.08.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231108T153000
DTEND;TZID=America/New_York:20231108T163000
DTSTAMP:20260505T002059
CREATED:20240222T113928Z
LAST-MODIFIED:20240222T113941Z
UID:10002810-1699457400-1699461000@cmsa.fas.harvard.edu
SUMMARY:Fitting ellipsoids to random points
DESCRIPTION:Probability Seminar \nSpeaker: Antoine Maillard (ETH Zürich) \nTitle: Fitting ellipsoids to random points \nAbstract: We consider the problem of exactly fitting an ellipsoid (centered at 0) to n standard Gaussian random vectors in dimension d\, for very large n and d. This problem has connections to questions in statistical learning and theoretical computer science\, and is conjectured to undergo a sharp transition: with high probability\, it has a solution if n < d^2/4\, while it is not satisfiable if n > d^2/4. In this talk we will discuss the origin of this conjecture\, and highlight some recent progress\, in three different directions: \n\nA proof that the problem is feasible for n < d^2 / C\, for some (large) constant C\, significantly improving over previously-known bounds.\nA non-rigorous characterization of the conjecture\, as well as significant generalizations\, using analytical methods of statistical physics.\nA rigorous proof of a satisfiability transition exactly at n = d^2 / 4 in a slightly relaxed version of the problem\, the first rigorous result characterizing the expected phase transition in ellipsoid fitting. The proof is inspired by the non-rigorous characterization discussed above.\n\nThis talk is based on the three manuscripts: arXiv:2307.01181\, arXiv:2310.01169\, arXiv:2310.05787\, which are joint works with A. Bandeira\, Tim Kunisky\, Shahar Mendelson and Elliot Paquette.
URL:https://cmsa.fas.harvard.edu/event/probability-11823/
LOCATION:Virtual
CATEGORIES:Probability Seminar
END:VEVENT
END:VCALENDAR