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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231002T163000
DTEND;TZID=America/New_York:20231002T173000
DTSTAMP:20260730T190807
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:20260730T190807
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:20260730T190807
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:20260730T190807
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:20260730T190807
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:20260730T190807
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:20260730T190807
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:20260730T190807
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:20260730T190807
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:20260730T190807
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:20260730T190807
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:20260730T190807
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:20260730T190807
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:20260730T190807
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
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