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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231002T103000
DTEND;TZID=America/New_York:20231002T113000
DTSTAMP:20260503T043337
CREATED:20240222T084421Z
LAST-MODIFIED:20240222T084421Z
UID:10002791-1696242600-1696246200@cmsa.fas.harvard.edu
SUMMARY:Motivic decomposition of moduli space from brane dynamics
DESCRIPTION:Algebraic Geometry in String Theory Seminar \n\n\nPre-talk Speaker: Kai Xu (CMSA): 10:00-10:30 am \n\nSpeaker: Kai Xu (CMSA) \nTitle: Motivic decomposition of moduli space from brane dynamics \nAbstract: Supersymmetric gauge theories encode deep structures in algebraic geometry\, and geometric engineering gives a powerful way to understand the underlying structures by string/M theory. In this talk we will see how the dynamics of M5 branes tell us about the motivic and semiorthogonal decompositions of moduli of bundles on curves.
URL:https://cmsa.fas.harvard.edu/event/agst-10223/
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-10.02.2023.docx-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231002T163000
DTEND;TZID=America/New_York:20231002T173000
DTSTAMP:20260503T043337
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:20231003T110000
DTEND;TZID=America/New_York:20231003T120000
DTSTAMP:20260503T043337
CREATED:20240223T054715Z
LAST-MODIFIED:20240223T054715Z
UID:10002820-1696330800-1696334400@cmsa.fas.harvard.edu
SUMMARY:A Smooth Horizon without a Smooth Horizon
DESCRIPTION:General Relativity Seminar \nSpeaker: Chethan Krishnan (IISc Bangalore) \nTitle: A Smooth Horizon without a Smooth Horizon \nAbstract: I will talk about some work that is about to appear\, where we note one precise way in which the stretched horizon can simulate a smooth horizon. I will also make an effort to put things in some perspective (brickwalls\, fuzzballs\, Type I algebras\,…)
URL:https://cmsa.fas.harvard.edu/event/gr_10323/
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231003T123000
DTEND;TZID=America/New_York:20231003T133000
DTSTAMP:20260503T043337
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:20231004T103000
DTEND;TZID=America/New_York:20231004T113000
DTSTAMP:20260503T043337
CREATED:20240221T111722Z
LAST-MODIFIED:20240221T111849Z
UID:10002779-1696415400-1696419000@cmsa.fas.harvard.edu
SUMMARY:Dipolar and modulated symmetry protected topological phases
DESCRIPTION:Topological Quantum Matter Seminar \nSpeaker: Ho Tat Lam\, MIT \nTitle: Dipolar and modulated symmetry protected topological phases \nAbstract: Modulated symmetries are symmetries whose symmetry generators exhibit spatial modulations. We will discuss one-dimensional symmetry protected topological (SPT) phases protected by modulated symmetries. We will present a simple recipe for constructing modulated SPT models by generalizing the concept of decorated domain walls. We will then focus on the simplest modulated SPT protected by dipolar symmetries\, classify them using matrix product states and construct their response field theories using twisted finite tensor gauge theories.
URL:https://cmsa.fas.harvard.edu/event/tqms_10423/
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-10.04.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231006T120000
DTEND;TZID=America/New_York:20231006T130000
DTSTAMP:20260503T043337
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:20231010T110000
DTEND;TZID=America/New_York:20231010T120000
DTSTAMP:20260503T043337
CREATED:20240223T054233Z
LAST-MODIFIED:20240223T054233Z
UID:10002819-1696935600-1696939200@cmsa.fas.harvard.edu
SUMMARY:Tidal Squeezing of Black Holes
DESCRIPTION:General Relativity Seminar \nSpeaker: Maria Rodriguez (Utah) \nTitle: Tidal Squeezing of Black Holes \nAbstract: Recent developments indicate that Kerr black holes do not deform when perturbed by a static external gravitational field. Relying on hidden symmetries\, compelling progress has been achieved to explain that Love numbers for Kerr black holes vanish. How does the phenomenon of tidal squeezing manifest in broader contexts? An elementary presentation of dynamical tidal squeezing of Kerr black holes will be given.
URL:https://cmsa.fas.harvard.edu/event/gr_101023/
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-10.10.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231010T123000
DTEND;TZID=America/New_York:20231010T133000
DTSTAMP:20260503T043337
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:20260503T043337
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:20231011T163000
DTEND;TZID=America/New_York:20231011T180000
DTSTAMP:20260503T043337
CREATED:20240222T060902Z
LAST-MODIFIED:20240222T060902Z
UID:10002785-1697041800-1697047200@cmsa.fas.harvard.edu
SUMMARY:Non-invertible symmetries\, leptons\, quarks\, and why multiple generations
DESCRIPTION:Quantum Matter Seminar \nSpeaker: Seth Koren (Notre Dame) \nTitle: Non-invertible symmetries\, leptons\, quarks\, and why multiple generations \nAbstract: Generalized global symmetries are present in theories of particle physics\, and understanding their structure can give insight into these theories and UV completions thereof. After discussing the generalized symmetries of the Standard Model\, we will go Beyond and show that the identification of a non-invertible symmetry of Z’ models of L_µ – L_τ reveals the existence of non-Abelian horizontal gauge theories which naturally produce exponentially small Dirac neutrino masses. Next we will uncover a subtler non-invertible symmetry in horizontal gauge theories of the quark sector which will lead us to a massless down-type quarks solution to strong CP in color-flavor unification. Intriguingly\, this theory works by virtue of the SM having the same numbers of colors and generations.
URL:https://cmsa.fas.harvard.edu/event/qm_101123/
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-10.11.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231012T130000
DTEND;TZID=America/New_York:20231012T140000
DTSTAMP:20260503T043337
CREATED:20240223T072135Z
LAST-MODIFIED:20240223T072135Z
UID:10002826-1697115600-1697119200@cmsa.fas.harvard.edu
SUMMARY:Contractility\, structure formation and fluctuations in active gels\, with and without molecular motors
DESCRIPTION:Active Matter Seminar\n\n\nSpeaker: Fred MacKintosh (Rice University) \nTitle: Contractility\, structure formation and fluctuations in active gels\, with and without molecular motors \nAbstract: Various processes in living cells depend on contractile forces that are often generated by myosin motors in concert with polar actin filaments. A textbook example of this is the actomyosin contractile ring that forms during cell division. Recent evidence\, however\, has begun to suggest alternate or redundant mechanisms that do not depend on myosin. Experiments on simplified\, reconstituted systems also point to contractility and structure formation in disordered\, apolar arrays of filaments. We propose a motor-free mechanism that can generate contraction in biopolymer networks without the need for motors such as myosin or polar filaments such as actin. This mechanism is based on active binding and unbinding of cross-linkers that breaks the principle of detailed balance\, together with the asymmetric force-extension response of semiflexible biopolymers. We discuss the resulting force-velocity relation and other implications of this\, as well as possible evidence for non-motor force generation.
URL:https://cmsa.fas.harvard.edu/event/am-101223/
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-10.12.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231013T120000
DTEND;TZID=America/New_York:20231013T130000
DTSTAMP:20260503T043337
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:20231016T100000
DTEND;TZID=America/New_York:20231016T113000
DTSTAMP:20260503T043337
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:20260503T043337
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:20260503T043337
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:20260503T043337
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:20260503T043337
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:20260503T043337
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:20260503T043337
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:20260503T043337
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:20260503T043337
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:20260503T043337
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:20260503T043337
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:20260503T043337
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:20260503T043337
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:20260503T043337
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:20260503T043337
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:20260503T043337
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:20260503T043337
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:20260503T043337
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
END:VCALENDAR