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X-WR-CALDESC:Events for CMSA
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230926T123000
DTEND;TZID=America/New_York:20230926T133000
DTSTAMP:20240223T081646Z
CREATED:20240223T081626Z
LAST-MODIFIED:20240223T081646Z
UID:10002835-1695731400-1695735000@cmsa.fas.harvard.edu
SUMMARY:CMSA Q and A Seminar 9/26/2023
DESCRIPTION:CMSA Q and A Seminar \nSpeakers: Michael Douglas (CMSA) and Mayuko Yamashita (Kyoto University) \nTopics: \nMichael Douglas: “What is non-commutative field theory?”\n\nMayuko Yamashita: “What is differential cohomology?”
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_92623/
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:20230927T140000
DTEND;TZID=America/New_York:20230927T150000
DTSTAMP:20240227T082824Z
CREATED:20240227T082824Z
LAST-MODIFIED:20240227T082824Z
UID:10002872-1695823200-1695826800@cmsa.fas.harvard.edu
SUMMARY:Transformers for maths\, and maths for transformers
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: François Charton\, Meta AI \nTitle:  Transformers for maths\, and maths for transformers \nAbstract: Transformers can be trained to solve problems of mathematics. I present two recent applications\, in mathematics and physics: predicting integer sequences\, and discovering the properties of scattering amplitudes in a close relative of Quantum ChromoDynamics. \nProblems of mathematics can also help understand transformers. Using two examples from linear algebra and integer arithmetic\, I show that model predictions can be explained\, that trained models do not confabulate\, and that carefully choosing the training distributions can help achieve better\, and more robust\, performance. \n  \n  \n 
URL:https://cmsa.fas.harvard.edu/event/nt-92723/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-09.27.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230929T120000
DTEND;TZID=America/New_York:20230929T130000
DTSTAMP:20240223T112516Z
CREATED:20240223T112516Z
LAST-MODIFIED:20240223T112516Z
UID:10002863-1695988800-1695992400@cmsa.fas.harvard.edu
SUMMARY:Moduli of vector bundles on curve and semiorthogonal decomposition
DESCRIPTION:Member Seminar \nSpeaker: Kai Xu (CMSA) \nTitle: Moduli of vector bundles on curve and semiorthogonal decomposition \nAbstract: In this talk we construct semiorthogonal decompositions of moduli of vector bundles on a curve into its symmetric powers. The essential ingredients in the proof include Borel-Weil-Bott theory for loop groups\, derived Schur-Weyl duality for current groups and derived Θ-stratification. \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-92923/
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:20231002T163000
DTEND;TZID=America/New_York:20231002T173000
DTSTAMP:20240227T095159Z
CREATED:20240227T095159Z
LAST-MODIFIED:20240227T095159Z
UID:10002874-1696264200-1696267800@cmsa.fas.harvard.edu
SUMMARY:Gravitational Instantons
DESCRIPTION:Speaker: Yu-Shen Lin (Boston University) \nTitle: Gravitational Instantons \nAbstract: Gravitational instantons were introduced by Hawking as building blocks of his Euclidean quantum gravity theory back in the 1970s. These are non-compact Calabi-Yau surfaces with L2 curvature and thus can be viewed as the non-compact analogue of K3 surfaces. K3 surfaces are 2-dimensional Calabi-Yau manifolds and are usually the testing stone before conquering the general Calabi-Yau problems. The moduli space of K3 surfaces and its compactification on their own form important problems in various branches in geometry. In this talk\, we will discuss the Torelli theorem of gravitational instantons\, how the cohomological invariants of a gravitational instanton determine them. As a consequence\, this leads to a description of the moduli space of gravitational instantons.
URL:https://cmsa.fas.harvard.edu/event/colloquium-10223/
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-10.02.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231003T123000
DTEND;TZID=America/New_York:20231003T133000
DTSTAMP:20240223T082622Z
CREATED:20240223T082622Z
LAST-MODIFIED:20240223T082622Z
UID:10002836-1696336200-1696339800@cmsa.fas.harvard.edu
SUMMARY:CMSA Q and A Seminar 10/3/2023
DESCRIPTION:CMSA Q and A Seminar \nSpeakers: Dan Freed (Harvard Math & CMSA) and Dan Berwick-Evans (University of Illinois at Urbana-Champaign)\n\nTopics:\nDan Freed: What is framing anomaly? How is it different from other anomalies?\nDan Berwick-Evans: What is Atiyah-Singer index theorem?
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_10323/
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:20231006T120000
DTEND;TZID=America/New_York:20231006T130000
DTSTAMP:20240223T105621Z
CREATED:20240223T105546Z
LAST-MODIFIED:20240223T105621Z
UID:10002854-1696593600-1696597200@cmsa.fas.harvard.edu
SUMMARY:Random matrices and large deviations 
DESCRIPTION:Member Seminar \nSpeaker: Benjamin McKenna \nTitle: Random matrices and large deviations \nAbstract: We give a generalist overview of random matrices and their (a)typical behaviors. In recent years\, classical results have been complemented by a variety of new ones\, in both the math and physics literatures\, whose proofs leverage connections with special integrals over matrix groups. Some of these models exhibit interesting transition points\, whose motivating relationships to eigenvector (de)localization are not yet fully understood. Based on joint work with Jonathan Husson. \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-10623/
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:20231010T123000
DTEND;TZID=America/New_York:20231010T133000
DTSTAMP:20240223T103936Z
CREATED:20240223T091026Z
LAST-MODIFIED:20240223T103936Z
UID:10002842-1696941000-1696944600@cmsa.fas.harvard.edu
SUMMARY:CMSA Q and A Seminar 10/10/23
DESCRIPTION:CMSA Q and A Seminar \nSpeakers: Dan Freed (Harvard Math and CMSA) and Sunghyuk Park (CMSA) \nTopics: \nDan Freed: What is Dijkgraaf-Witten theory? \nSunghyuk Park: What happened at the Clay Math Institute Workshop?
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_101023/
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:20231011T140000
DTEND;TZID=America/New_York:20231011T150000
DTSTAMP:20240223T114336Z
CREATED:20240223T114336Z
LAST-MODIFIED:20240223T114336Z
UID:10002868-1697032800-1697036400@cmsa.fas.harvard.edu
SUMMARY:LeanDojo: Theorem Proving with Retrieval-Augmented Language Models
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Alex Gu\, MIT Dept. of EE&CS \nTitle: LeanDojo: Theorem Proving with Retrieval-Augmented Language Models \nAbstract: Large language models (LLMs) have shown promise in proving formal theorems using proof assistants such as Lean. However\, existing methods are difficult to reproduce or build on\, due to private code\, data\, and large compute requirements. This has created substantial barriers to research on machine learning methods for theorem proving. We introduce LeanDojo: an open-source Lean playground consisting of toolkits\, data\, models\, and benchmarks. LeanDojo extracts data from Lean and enables interaction with the proof environment programmatically. It contains fine-grained annotations of premises in proofs\, providing valuable data for premise selection: a key bottleneck in theorem proving. Using this data\, we develop ReProver (Retrieval-Augmented Prover): the first LLM-based prover that is augmented with retrieval for selecting premises from a vast math library. It is inexpensive and needs only one GPU week of training. Our retriever leverages LeanDojo’s program analysis capability to identify accessible premises and hard negative examples\, which makes retrieval much more effective. Furthermore\, we construct a new benchmark consisting of 96\,962 theorems and proofs extracted from Lean’s math library. It features a challenging data split requiring the prover to generalize to theorems relying on novel premises that are never used in training. We use this benchmark for training and evaluation\, and experimental results demonstrate the effectiveness of ReProver over non-retrieval baselines and GPT-4. We thus provide the first set of open-source LLM-based theorem provers without any proprietary datasets and release it under a permissive MIT license to facilitate further research. \n 
URL:https://cmsa.fas.harvard.edu/event/nt-101123-2/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-10.11.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231013T120000
DTEND;TZID=America/New_York:20231013T130000
DTSTAMP:20240223T105527Z
CREATED:20240223T105131Z
LAST-MODIFIED:20240223T105527Z
UID:10002852-1697198400-1697202000@cmsa.fas.harvard.edu
SUMMARY:On the Breakdown of Einstein's Gravity
DESCRIPTION:Member Seminar \nSpeaker: Puskar Mondal (CMSA) \nTitle: On the Breakdown of Einstein’s Gravity \nAbstract: It is important to understand under which conditions\, the solutions of non-linear hyperbolic PDEs break down in finite time. In the context of Einstein’s gravity\, this is very closely tied to naked singularity formation and Penrose’s weak cosmic censorship conjecture. In this talk\, I will give sharp estimates on the relevant geometric entities that allow one to continue the solutions of Einstein’s equations indefinitely in the future in a ‘time’ direction without forming a naked singularity.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-101323/
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:20231016T163000
DTEND;TZID=America/New_York:20231016T173000
DTSTAMP:20251026T063911Z
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:20231018T140000
DTEND;TZID=America/New_York:20231018T150000
DTSTAMP:20240223T114049Z
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:20231020T120000
DTEND;TZID=America/New_York:20231020T130000
DTSTAMP:20240223T110405Z
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:20231023T163000
DTEND;TZID=America/New_York:20231023T173000
DTSTAMP:20240223T092904Z
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:20231024T123000
DTEND;TZID=America/New_York:20231024T133000
DTSTAMP:20240223T083135Z
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:20240223T105453Z
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:20231027T120000
DTEND;TZID=America/New_York:20231027T130000
DTSTAMP:20240223T110834Z
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:20240223T084547Z
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:20231103T120000
DTEND;TZID=America/New_York:20231103T130000
DTSTAMP:20240227T113702Z
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:20231106T163000
DTEND;TZID=America/New_York:20231106T173000
DTSTAMP:20240223T083208Z
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:20231107T123000
DTEND;TZID=America/New_York:20231107T133000
DTSTAMP:20240223T083628Z
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:20231108T140000
DTEND;TZID=America/New_York:20231108T150000
DTSTAMP:20240222T095919Z
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:20231113T163000
DTEND;TZID=America/New_York:20231113T173000
DTSTAMP:20240223T081522Z
CREATED:20240223T081522Z
LAST-MODIFIED:20240223T081522Z
UID:10002834-1699893000-1699896600@cmsa.fas.harvard.edu
SUMMARY:Koszul duality in QFT
DESCRIPTION:Speaker: Brian Williams (Boston University) \nTitle: Koszul duality in QFT \nAbstract: We will describe appearances of the algebraic phenomena of Koszul duality in the context of boundary conditions and defects in quantum field theory. Primarily motivated by topological string theory\, this point of view was pioneered by Costello and Li in their proposal for a twisted version of the AdS/CFT correspondence. Since then\, many important examples of (twisted) holographic dualities in string and M-theory have been studied in work of Costello\, Gaiotto\, Paquette and many others. I will survey some of these examples and some current work with Raghavendran and Saberi which uses this formalism to predict exceptional symmetries present in M-theory. \n 
URL:https://cmsa.fas.harvard.edu/event/colloquium-111323/
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-11.13.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231115T140000
DTEND;TZID=America/New_York:20231115T150000
DTSTAMP:20240222T095355Z
CREATED:20240222T094758Z
LAST-MODIFIED:20240222T095355Z
UID:10002797-1700056800-1700060400@cmsa.fas.harvard.edu
SUMMARY:On the Power of Forward pass through Transformer Architectures
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Abhishek Panigrahi\, Dept. of Computer Science\, Princeton University \nTitle: On the Power of Forward pass through Transformer Architectures \nAbstract: Highly trained transformers are capable of interesting computations as they infer for an input. The exact mechanism that these models use during forward passes is an interesting area of study. This talk studies two interesting phenomena. \nIn the first half\, we explore how and why pre-trained language models\, specifically BERT of moderate sizes\, can effectively learn linguistic structures like parse trees during pre-training. Specifically\, using synthetic data through PCFGs\, we show how moderate-sized transformers can perform forward-backward parsing\, also known as the inside-outside algorithm\, during inference. We further understand the role of the pre-training loss for the model to learn to parse during pre-training. \nIn the second half\, we consider in-context learning of large language models\, where they learn to reason on the fly. An ongoing hypothesis is that transformers simulate gradient descent at inference to perform in-context learning. We propose the Transformer in Transformer (TinT) framework\, which creates explicit transformer architectures that can simulate and fine-tune a small pre-trained transformer model during inference. E.g. a 1.3B parameter TINT model can simulate and fine-tune a 125 million parameter model in a single forward pass. This framework suggests that large transformers might execute intricate sub-routines during inference\, and provides insights for enhancing their capabilities through intelligent design considerations. \n 
URL:https://cmsa.fas.harvard.edu/event/nt-111523/
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-11.15.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231117T120000
DTEND;TZID=America/New_York:20231117T130000
DTSTAMP:20240227T113251Z
CREATED:20240227T113236Z
LAST-MODIFIED:20240227T113251Z
UID:10002879-1700222400-1700226000@cmsa.fas.harvard.edu
SUMMARY:A quasi-local mass in general relativity
DESCRIPTION:Member Seminar \nSpeaker: Aghil Alaee \nTitle: A quasi-local mass in general relativity \nAbstract: One of the fundamental open problems in geometric analysis and mathematical relativity is constructing a (universal) energy/mass quantity to compute the energy/mass of a finite region of spacetime\, which can include a star\, black hole\, or galaxy. We define a new gauge-independent quasi-local mass and energy with respect to the Minkowski spacetime\, and show its relation to the Brown-York Hamilton-Jacobi analysis. A quasi-local proof of the positivity\, based on spacetime harmonic functions\, is given for admissible closed spacelike 2-surfaces which enclose an initial data set satisfying the dominant energy condition.  Rigidity is also established in that vanishing energy implies that the 2-surface arises from an embedding into Minkowski space\, and conversely\, the mass vanishes for any such surface. This is joint work with M. Khuri and S.T. Yau. \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-111723/
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:20231120T163000
DTEND;TZID=America/New_York:20231120T173000
DTSTAMP:20240223T080617Z
CREATED:20240223T080617Z
LAST-MODIFIED:20240223T080617Z
UID:10002833-1700497800-1700501400@cmsa.fas.harvard.edu
SUMMARY:The analytical challenges of connectomics
DESCRIPTION:Speaker: Jeff W. Lichtman (Harvard University) \nTitle: The analytical challenges of connectomics \nAbstract: Recent progress in generating synapse-level maps of brains\, a field known as connectomics\, brings both opportunities and challenges. The upside is that the biophysical instantiation of memories\, behaviors\, and knowledge will soon be before us. The downside is that no one knows exactly how to make sense of this data. I will show what connectomics data sets are and attempt to explain why it is so difficult to unravel their meaning.
URL:https://cmsa.fas.harvard.edu/event/colloquium-112023/
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-11.20.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231127T163000
DTEND;TZID=America/New_York:20231127T173000
DTSTAMP:20240223T080018Z
CREATED:20240223T080018Z
LAST-MODIFIED:20240223T080018Z
UID:10002831-1701102600-1701106200@cmsa.fas.harvard.edu
SUMMARY:What do topological dynamics\, combinatorics\, and model theory have in common?
DESCRIPTION:Speaker: Dana Bartosova (University of Florida) \nTitle: What do topological dynamics\, combinatorics\, and model theory have in common? \nAbstract: A striking correspondence between dynamics of automorphism groups of countable first order structures and Ramsey theory of finitary approximation of the structures was established in 2005 by Kechris\, Pestov\, and Todocevic. Since then\, their work has been generalized and applied in many directions. It also struck a fresh wave of interest in finite Ramsey theory.  Many classes of finite structures are shown to have the Ramsey property by encoding their problem in a known Ramsey class and translating a solution back. This is often a case-by-case approach and naturally there is a great need for abstracting the process. There has been much success on this front\, however\, none of the tools captures every situation. We will discuss one such encoding via a model-theoretic notion of semi-retraction introduced by Lynn Scow in 2012. In a joint work\, we showed that a semi-retraction transfers the Ramsey property from one class of structures to another under quite general conditions. We compare semi-retractions to a category-theoretical notion of pre-adjunction revived by Mašulović in 2016. If time permits\, I will mention a transfer theorem of the Ramsey property from a class of finite structures to their uncountable ultraproducts\, which is an AIMSQuaRE project with Džamonja\, Patel\, and Scow.
URL:https://cmsa.fas.harvard.edu/event/colloquium-112723/
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-11.27.2023_Page_1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231201T120000
DTEND;TZID=America/New_York:20231201T130000
DTSTAMP:20240227T112731Z
CREATED:20240227T112716Z
LAST-MODIFIED:20240227T112731Z
UID:10002878-1701432000-1701435600@cmsa.fas.harvard.edu
SUMMARY:An introduction to mixture of experts in deep learning
DESCRIPTION:Member Seminar \nSpeaker: Samy Jelassi \nTitle: An introduction to mixture of experts in deep learning \nAbstract: Scale has opened new frontiers in natural language processing – but at a high cost. Mixture-of-Experts (MoE) have been proposed as a path to even larger and more capable language models. They select different parameters for each incoming example. By doing so\, the parameter count is decoupled from the compute per example leading to very large\, but efficient models. In this talk\, I will review the concept of mixture of experts\, provide a basic description of the Switch Transformers model\, characterize some of their behaviors and conclude by highlighting some open problems in the field. This talk is mainly based on the following papers: https://arxiv.org/pdf/2101.03961.pdf\, https://arxiv.org/pdf/2209.01667.pdf .
URL:https://cmsa.fas.harvard.edu/event/member-seminar-12123/
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:20231204T163000
DTEND;TZID=America/New_York:20231204T173000
DTSTAMP:20240223T075301Z
CREATED:20240223T075301Z
LAST-MODIFIED:20240223T075301Z
UID:10002830-1701707400-1701711000@cmsa.fas.harvard.edu
SUMMARY:Analysis of ALH* gravitational instantons
DESCRIPTION:Speaker: Xuwen Zhu (Northeastern) \nTitle: Analysis of ALH* gravitational instantons \nAbstract: Gravitational instantons are non-compact Calabi-Yau metrics with L^2 bounded curvature and are categorized into six types. We will discuss one such type called ALH* metrics which has a non-compact end modelled by the Calabi ansatz with inhomogeneous collapsing near infinity. Such metrics appeared recently in the works on SYZ conjecture\, as well as the scaling bubble limits for codimension-3 collapsing of K3 surfaces\, where the study of its Laplacian played a central role. In this talk I will talk about the Fredholm mapping property and L^2 cohomology of such metrics. This is ongoing work joint with Rafe Mazzeo.
URL:https://cmsa.fas.harvard.edu/event/colloquium-12423/
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-12.04.2023.docx-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231205T123000
DTEND;TZID=America/New_York:20231205T133000
DTSTAMP:20240223T084615Z
CREATED:20240223T084615Z
LAST-MODIFIED:20240223T084615Z
UID:10002841-1701779400-1701783000@cmsa.fas.harvard.edu
SUMMARY:CMSA Q and A Seminar 12/5/2023
DESCRIPTION:CMSA Q and A Seminar \nSpeakers: Mike Douglas (Harvard CMSA) and Anurag Anshu (Harvard Computer Science) \nTopics:  \nMike Douglas: What are scaling laws in deep learning? \nAnurag Anshu: What’s the difference between classical information theory and quantum information theory (or classical computation vs quantum computation)? \n 
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_12523/
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:20231208T120000
DTEND;TZID=America/New_York:20231208T130000
DTSTAMP:20240227T112426Z
CREATED:20240227T112413Z
LAST-MODIFIED:20240227T112426Z
UID:10002877-1702036800-1702040400@cmsa.fas.harvard.edu
SUMMARY:Open Problems in Physics and Novel Solutions from Math
DESCRIPTION:Member Seminar \nSpeaker: Juven Wang \nTitle: Open Problems in Physics and Novel Solutions from Math \n  \nAbstract: (1) How do neutrinos obtain tiny mass and oscillate between e\, \mu\, \tau three flavors? What consists of Dark Matter? What causes leptogenesis and baryogenesis? \n(2) Why the Parity Symmetry is violated in the weak interaction? How do we quantum mechanically regularize and numerically simulate the Standard Model (chiral fermion/gauge theory) on the lattice in 3+1 spacetime dimensions? \n(3) Strong CP problem: Why is the neutron electric dipole moment nearly zero and QCD respects the CP = T symmetry? \n(4) Family/Generation problem: Why are there three families/generations of quarks and leptons? \nIn my talk\, I will sketch and propose novel solutions to these challenging open problems in physics based on my own work (available on arXiv\, some jointly with my collaborators). \nI will show that the eclectic cross-disciplinary fertilization of ideas between the Math-Physics geometry and topology\, Quantum Condensed Matter\, and High-Energy Physics (theory\, pheno\, lattice) can help solving these big problems. \nThe (1) answer relates to Ultra Unification: a Z_{16} class Atiyah-Patodi-Singer eta invariant (Baryon – Lepton)-protected topological superconductor and a symmetry-extended anomalous topological quantum field theory. \nThe (2) and (3) answers relate to a trivial cobordism class and Symmetric Mass Generation\, and disordering and removing the Pecci-Quinn axions. \nThe (4) answer has to do with the Hirzebruch signature and Atiyah-Singer index theorem\, gravitational Chern-Simons theory\, and 3 E8 quantum Hall states. \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-12823/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
END:VCALENDAR