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DTSTART;TZID=America/New_York:20241017T160000
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CREATED:20240927T150813Z
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SUMMARY:Math Science Lectures in Honor of Raoul Bott: Andrew Neitzke
DESCRIPTION:Speaker: Andrew Neitzke\, Yale University \nLocation: Harvard University Science Center Hall D & via Zoom webinar \nDates: October 16 & 17\, 2024 \nTime: 4:00 pm \n  \n \nWednesday\, Oct. 16\, 2024 \nTitle: Abelianization in analysis of ODEs \nAbstract: I will describe the exact WKB method for asymptotic analysis of families of ODEs in one variable\, and its interpretation as a kind of abelianization procedure\, which replaces GL(N)-connections over a Riemann surface by GL(1)-connections over an N-fold branched cover. This abelianization procedure connects exact WKB to various subjects in geometry (cluster algebras\, moduli of Higgs bundles\, enumerative geometry). One application is a conjectural description of Hitchin’s hyperkahler metric on the moduli of Higgs bundles; I will review some recent progress on these conjectures. \n  \n \nThursday\, Oct. 17\, 2024 \nTitle: Abelianization in quantum topology \nAbstract: I will describe new applications of abelianization to various related subjects: perturbative Chern-Simons invariants\, skein algebras\, and conformal blocks. The aim is to explain how abelianization gives a unifying perspective on constructions familiar in each of these subjects (e.g. dilogarithmic formulas for Chern-Simons invariants\, vertex models for computing quantum invariants of links\, and iterated-fusion constructions of conformal blocks for the Virasoro algebra)\, and also suggests various extensions\, which are just beginning to be explored. \n\n  \nRaoul Bott (9/24/1923 – 12/20/2005) is known for the Bott periodicity theorem\, the Morse–Bott functions\, and the Borel–Bott–Weil theorem. 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/mathscibott_1024-2/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Event,Math Science Lectures in Honor of Raoul Bott,Public Lecture,Special Lectures
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DTSTART;TZID=America/New_York:20241028T090000
DTEND;TZID=America/New_York:20241030T170000
DTSTAMP:20241106T191859Z
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SUMMARY:Mathematics and Machine Learning Closing Workshop
DESCRIPTION:Mathematics and Machine Learning Closing Workshop \nDates: October 28 – Oct. 30\, 2024 \nLocation: Room G10\, CMSA\, 20 Garden Street\, Cambridge MA \nThe closing workshop will provide a forum for discussing the most current research in these areas\, including work in progress and recent results from program participants. We will devote one day to frontier topics in interactive theorem proving\, such as mathematical library development and AI for mathematical search and theorem proving. \n  \nYoutube Playlist \n \nOrganizers \n\nFrancois Charton (Meta AI)\nMichael R. Douglas (Harvard CMSA)\nMichael Freedman (Harvard CMSA)\nFabian Ruehle (Northeastern)\nGeordie Williamson (Univ. of Sydney)\n\nSpeakers \n\nAnkit Anand\, Google Deepmind Montreal\nJeremy Avigad\, Carnegie Mellon University\nAngelica Babei\nMatej Balog\, Deepmind\nGergely Bérczi\, Aarhus University\nTristan Buckmaster\, New York University\nGiorgi Butbaia\, University of New Hampshire\nEdgar Costa\, MIT\nAlex Davies\, DeepMind\nBin Dong\, Beijing International Center for Mathematical Research\nKit Fraser-Taliente\, University of Oxford\nJavier Gomez-Serrano\, Brown University\nJim Halverson\, Northeastern University\nThomas Harvey\, MIT\nAmaury Hayat\, Ecole des Ponts Paristech\nYang-Hui He\, City University of London\nJürgen Jost\, Max Planck Institute for Mathematics in the Sciences\nPetros Koumoutsakos\, Harvard University\nKyu-Hwan Lee\, University of Connecticut\nDavid Lowry-Duda\, ICERM\nStephane Mallat\, Flatiron/College de France\nAbbas Mehrabian\, Google Deepmind Montreal\nCengiz Pehlevan\, Harvard University\nFabian Ruehle\, Northeastern University\nEric Vanden-Eijnden\, Courant/NYU\nAdam Wagner\, Worcester Polytechnic Institute\nMelanie Matchett Wood\, Harvard University\n\n  \nSchedule (download PDF) \nMonday Oct. 28\, 2024 \n9:00–9:30 amMorning refreshments \n9:30–9:45 amIntroductions \n9:45–10:45 amJürgen Jost\, Max Planck Institute for Mathematics in the Sciences \nTitle: Data visualization with category theory and geometry \nAbstract: While data often come in a high-dimensional feature space\, they typically exhibit intrinsic constraints and regularities\, and they can therefore often be represented on a lower-dimensional\, but possibly highly curved Riemannian manifold. Still\, for visualization purposes\, that dimension still needs to be lowered to 2 or 3. We present the mathematical foundations for such schemes\, in particular UMAP\, and describe an improved such method. \n10:45–11:00 amBreak \n11:00 am–12:00 pmAnkit Anand\, Google Deepmind Montreal\, Abbas Mehrabian\, Google Deepmind Montreal \nTitle: From Theorem Proving to Disproving: Modern machine learning versus classical heuristic search in automated theorem proving and extremal graph theory \nAbstract: Machine learning is widely believed to outperform classical methods\, but this is not always the case. Firstly\, we describe how we adapted the idea of hindsight experience replay from reinforcement learning to the automated theorem proving domain\, so as to use the intermediate data generated during unsuccessful proofs. We show that provers trained in this way can outperform previous machine learning approaches and compete with the state-of-the-art heuristic-based theorem prover E in its best configuration\, on the popular benchmarks MPTP2078\, M2k and Mizar40. The proofs generated by our algorithm are also almost always significantly shorter than E’s proofs. Based on this paper\, which was presented at ICML 2022: https://proceedings.mlr.press/v162/aygun22a.html. Secondly\, we study a central extremal graph theory problem inspired by a 1975 conjecture of Erdős\, which aims to find graphs with a given size (number of nodes) that maximize the number of edges without having 3- or 4-cycles. We formulate this problem as a sequential decision-making problem and compare AlphaZero\, a neural network-guided tree search\, with tabu search\, a heuristic local search method. Using either method\, by introducing a curriculum—jump-starting the search for larger graphs using good graphs found at smaller sizes—we improve the state-of-the-art lower bounds for several sizes. Joint work with Tudor Berariu\, Joonkyung Lee\, Anurag Murty Naredla\, Adam Zsolt Wagner\, and other colleagues at Google DeepMind. Based on this paper\, which was presented at IJCAI 2024: https://arxiv.org/abs/2311.03583. \n12:00–1:30 pmLunch Break \n1:30–2:30 pmFabian Ruehle\, Northeastern University\, Giorgi Butbaia\, University of New Hampshire \nTitle: Rigorous results 
from ML using RL \nAbstract: We explain how to use Reinforcement Learning in Mathematics to obtain provably correct results. After a brief introduction to Reinforcement Learning\, I will illustrate the idea using an example from Number Theory\, where we solve a Diophantine Equation related to String Theory\, and two from Knot Theory. The first knot theory problem is to identify unknots\, while the second is concerned with identifying so-called ribbon knots. The latter play an important role in the search for counter-examples to the smooth Poincare conjecture. \n2:30–2:45 pmBreak \n2:45–3:45 pmCengiz Pehlevan\, Harvard University \nTitle: Solvable Models of Scaling and Emergence in Deep Learning \n3:45–4:00 pmBreak \n4:00–4:30 pmMatej Balog\, Deepmindvia Zoom \nTitle: FunSearch: Mathematical discoveries from program search with large language models \nAbstract: Large language models (LLMs) have demonstrated tremendous capabilities in solving complex tasks\, from quantitative reasoning to understanding natural language. However\, LLMs sometimes suffer from confabulations (or hallucinations)\, which can result in them making plausible but incorrect statements. This hinders the use of current large models in scientific discovery. We introduce FunSearch (short for searching in the function space)\, an evolutionary procedure based on pairing a pretrained LLM with a systematic evaluator. We demonstrate the effectiveness of this approach to surpass the best-known results in important problems\, pushing the boundary of existing LLM-based approaches. Applying FunSearch to a central problem in extremal combinatorics—the cap set problem—we discover new constructions of large cap sets going beyond the best-known ones\, both in finite dimensional and asymptotic cases. This shows that it is possible to make discoveries for established open problems using LLMs. We showcase the generality of FunSearch by applying it to an algorithmic problem\, online bin packing\, finding new heuristics that improve on widely used baselines. In contrast to most computer search approaches\, FunSearch searches for programs that describe how to solve a problem\, rather than what the solution is. Beyond being an effective and scalable strategy\, discovered programs tend to be more interpretable than raw solutions\, enabling feedback loops between domain experts and FunSearch\, and the deployment of such programs in real-world applications. \n4:30–5:00 pmEdgar Costa\, MIT \nTitle: Machine learning L-functions \nAbstract: We report on multiple experiments related to L-functions data. L-functions are complex functions that encode significant information about number theory and algebraic geometry\, playing a crucial part in the Langlands program\, a foundational set of conjectures connecting number theory with other mathematical domains. We focused on two L-function datasets. The first includes about 250k rational L-functions of small arithmetic complexity with diverse origins. Multiple dimensionality reduction techniques were used to analyze invariants and behavioral trends\, focusing on how differing origins impact the results. The second dataset is composed of L-functions associated with Maass forms. Although these L-functions are non-rational\, they also share the low arithmetic complexity of the first dataset. The crux of our investigation here is determining whether this set manifests similar characteristics to the first one. Based on this exploration\, we propose a simple heuristic method to deduce their Fricke sign\, an unknown invariant for 40% of the data. This is joint work with: Joanna Biere\, Giorgi Butbaia\, Alyson Deines\, Kyu-Hwan Lee\, David Lowry-Duda\, Tom Oliver\, Tamara Veenstra\, and Yidi Qi. \n  \n  \nTuesday Oct. 29\, 2024  \n9:15–9:45 amMorning refreshments \n9:45–10:45 amYang-Hui He\, London Institute for Mathematical Sciences Via Zoom \nTitle: AI assisted mathematics \nAbstract: We argue how AI can assist mathematics in three ways: theorem-proving\, conjecture formulation\, and language processing. Inspired by initial experiments in geometry and string theory in 2017\, we summarize how this emerging field has grown over the past years\, and show how various machine-learning algorithms can help with pattern detection across disciplines ranging from algebraic geometry to representation theory\, to combinatorics\, and to number theory.  At the heart of the program is the question how does AI help with theoretical discovery\, and the implications for the future of mathematics. \n10:45–11:00 amBreak \n11:00 –11:30Angelica Babei \nTitle: Learning Euler factors of elliptic curves with transformers \nAbstract: The L-function of an elliptic curve is at the core of the BSD conjecture\, and its Euler factors encode important arithmetic information about the curve. For example\, understanding these Euler factors using machine learning techniques has recently led to discovering the phenomenon of murmurations. In this talk\, we present some results on learning Euler factors based on 1. other nearby factors\, and 2. the Weierstrass equation of the curve.  \n11:30–12:00 pmDavid Lowry-Duda\, ICERM \nTitle: Exploring patterns in number theory with deep learning: a case study with the Möbius and squarefree indicator functionsAbstract: We report on experiments using neural networks and Int2Int\, the integer sequence to integer sequence transformer made by François Charton for this CMSA program. We initially study the Möbius function. This function appears as the coefficients of the reciprocal of the Riemann zeta function and is famously hard to understand. Predicting the Möbius function is closely related to predicting the squarefree indicator function\, leading us to perform similar experiments there. Finally\, we’ll discuss how varying the input representation and model affects the strength of the predictions and allows us to explain most (but not all) of the predictive strength and behavior. \n12:00–1:30 pmLunch \n1:30–2:30 pmAmaury Hayat\, Ecole des Ponts Paristech\, Melanie Matchett Wood\, Harvard University\, Alex Davies\, DeepMind\, Jeremy Avigad\, Carnegie Mellon University \nTitle: Machine learning and theorem proving \nAbstract: Recent successes in machine learning have raised hopes that neural networks could one day assist mathematicians in proving theorems. This raises the question of an appropriate setting to apply machine learning methods to theorem proving. Formal languages\, such as Lean\, provide automatic verification of mathematical proofs and thus offer a natural environment. Nevertheless\, some challenges emerge\, particularly because these languages are often designed to verify correctness rather than find a solution\, while mathematicians often perform reasoning steps to do both at the same time. This talk will present recent applications of machine learning methods to theorem proving in Lean\, highlight current challenges\, and explore what these developments might mean for the future of mathematics. \n  \n2:30–2:45 pmBreak \n2:45–3:45 pmAdam Wagner\, Worcester Polytechnic Institute\, Kit Fraser-Taliente\, University of Oxford\, Gergely Bérczi\, Aarhus University\, Thomas Harvey\, MIT \nTitle: Sparse subgraphs of the d-cube with diameter d \nAbstract: Erdos et al studied spanning subgraphs of the $d$-cube which have the same diameter $d$ as the cube itself. They asked the following natural question: what is the maximum number of edges one can delete from the $d$-dimensional hypercube\, without increasing its diameter? We will discuss how we can use PatternBoost\, a simple machine learning algorithm that alternates local and global optimization steps\, to find good constructions for this problem \n3:45–4:00 pmBreak \n4:00–4:30 pmPetros Koumoutsakos\, Harvard University \n4:30–5:00 pm \nStéphane Mallat\,  Flatiron/College de France \nTitle: Image Generation by Score Diffusion and the Renormalisation Group \nAbstract: Score based diffusions generate impressive models of images\, sounds and complex physical systems. Are they generalising or memorising? How can deep network estimate high-dimensional scores without curse of dimensionality? This talk shows that generalisation does occur for deep network estimation of scores\, with enough training data.  The ability to avoid the curse of dimensionality seems to rely on multiscale properties revealed by a renormalisation group decomposition coming from statistical physics. Applications to models of turbulences will be introduced and discussed. \n  \nWednesday Oct. 30\, 2024 \n9:15–9:45 amMorning refreshments \n9:45–10:45 amBin Dong\, Beijing International Center for Mathematical Research(via Zoom)  \nTitle: AI for Mathematics: From Digitization to Intelligentization \nAbstract: This presentation explores the synergistic relationship between AI and mathematics\, beginning with a brief historical overview of their mutually beneficial interactions. It then examines notable existing work in AI for mathematics\, highlighting their achievements and limitations.  Next\, I will share preliminary findings from the ongoing AI4M research project at Peking University\, including our work on creating high-quality mathematical datasets through formalization (digitization)\, and our future plans for developing intelligent applications using these datasets. The presentation concludes with a forward-looking perspective on the opportunities and challenges within this exciting interdisciplinary field. \n10:45–11:00 am Break \n11:00 am–12:00 pm Eric Vanden-Eijnden\, Courant/NYUvia Zoom \nTitle: Generative modeling with flows and diffusions\, with applications to scientific computing. \nAbstract: Generative models based on dynamical transport have recently led to significant advances in unsupervised learning. At mathematical level\, these models are primarily designed around the construction of a map between two probability distributions that transform samples from the first into samples from the second.  While these methods were first introduced in the context of image generation\, they have found a wide range of applications\, including in scientific computing where they offer interesting ways to reconsider complex problems once thought intractable because of the curse of dimensionality. In this talk\, I will discuss the mathematical underpinning of generative models based on flows and diffusions\, and show how a better understanding of their inner workings can help improve their design. These results indicate how to structure the transport to best reach complex target distributions while maintaining computational efficiency\, both at learning and sampling stages.  I will also discuss applications of generative AI in scientific computing\, in particular in the context of application with models and no data (as opposed to the more standard data andno model)\, such as Monte Carlo sampling\, with applications to the statistical mechanics and Bayesian inference\, as well as the numerical integration and interpretation of random dynamical systems driven out of equilibrium. \n12:00–1:30 pm Lunch \n1:30–2:30 pm Kyu-Hwan Lee\, University of Connecticut \nTitle: Discovering New Mathematical Structures with Machine Learning \nAbstract: Can machine learning help discover new mathematical structures? In this talk\, I will present two case studies: murmurations in number theory and loadings of partitions related to Kronecker coefficients in representation theory and combinatorics. The focus will be on the paradigm of examining mathematical objects collectively\, rather than individually\, to create datasets suitable for machine learning experiments and interpretations. \n2:30–2:45 pm Break \n2:45–3:45 pm James Halverson\, Northeastern University \nTitle: Learning the Topological Invariance of Knots \nAbstract: This talk focuses on using machine learning for the defining problem in knot theory\, the classification of knots up to ambient space isotopy. We will train transformers and convolutional neural networks to distinguish topologically inequivalent knots\, given only representatives of the classes and no a priori knowledge of topological invariants. In this scheme\, we find that equivalent knots are well-clustered in the embedding space of the neural network\, and a trained decoder maps effectively from the embedding space back to knot space. Preliminary results will be presented on a new approach to resolving the Jones unknot conjecture. \n3:45–4:00 pmBreak \n4:00–5:00 pm Tristan Buckmaster\, New York University\, Javier Gomez-Serrano\, Brown Universityvia Zoom \n  \n  \nImage by Sue Side. https://www.sueside.com/\n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/mmlworkshop_1024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Workshop
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/ML_Closing-workshop_v3-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241121T090000
DTEND;TZID=America/New_York:20241121T103000
DTSTAMP:20241203T144846Z
CREATED:20240923T152934Z
LAST-MODIFIED:20241203T144846Z
UID:10003528-1732179600-1732185000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:CMSA/Tsinghua Math-Science Literature Lecture: Bjorn Poonen\, MIT
DESCRIPTION:CMSA/Tsinghua Math-Science Literature Lecture \nDate: November 21\, 2024 \nTime: 9:00 – 10:30 am ET \nLocation: CMSA G10\, 20 Garden Street\, Cambridge MA & via Zoom \nSpeaker: Bjorn Poonen\, MIT \nTitle: Ranks of elliptic curves \nAbstract: Elliptic curves are simplest varieties whose rational points are not fully understood\, and they are the simplest projective varieties with a nontrivial group structure.  In 1922 Mordell proved that the group of rational points on an elliptic curve is finitely generated.  We will survey what is known and what is believed about this group. \n  \n\nBeginning in Spring 2020\, the CMSA began hosting a lecture series on literature in the mathematical sciences\, with a focus on significant developments in mathematics that have influenced the discipline\, and the lifetime accomplishments of significant scholars.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/mathscilit2024_bp/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Math Science Literature Lecture Series
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/Mathlit_Poonen_11x17.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250121T090000
DTEND;TZID=America/New_York:20250124T170000
DTSTAMP:20250213T211311Z
CREATED:20240710T140404Z
LAST-MODIFIED:20250213T211311Z
UID:10003397-1737450000-1737738000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Workshop on Symmetries and Gravity
DESCRIPTION:Workshop on Symmetries and Gravity \nDates: January 21-24\, 2025 \nLocation: Harvard CMSA\, 20 Garden Street\, Cambridge\, MA 02138 \nOrganizers: Ibrahima Bah (Johns Hopkins University)\, Patrick Jefferson (Johns Hopkins University)\, Yiming Chen (Stanford University) \nDescription: There is a widespread belief\, that has its origins in work from the 70s\, that a theory of quantum gravity cannot admit global symmetries. Traditionally\, this was seen only as a qualitative statement about ordinary symmetries\, but there have since been a number of developments that have both widened its scope and sharpened its implications. Recent work has greatly broadened the definition of global symmetries\, and characterizes them in terms of topological operators in quantum systems. Concurrently\, insights from quantum gravity have suggested ways to quantify the extent of global symmetry violation. Additionally\, advances in the swampland program\, along with amplitudes and bootstrap techniques\, have shown ways to turn high-energy statements into constraints on low-energy effective field theories. In string theory\, there are more concrete statements on charge violation in gravity\, with proofs in limited context. In general\, however\, “no global symmetries in quantum gravity” continues to be an open conjecture with broad implications on the nature of quantum gravity and low-energy effective field theory. The main goal of the meeting is to bring together experts in the various arenas of research above\, to reassess and develop new strategies for making progress on this long-standing open problem. Some objectives include understanding the violation of various generalized and categorical symmetries in gravity more cohesively\, and putting concrete bounds on global charge-violating amplitudes at low energies. \nPartially funded by the Simons Collaboration on Global Categorical Symmetries. \n  \nConfirmed Participants \n\nTom Banks\, Rutgers\nFederico Bonetti\, Durham University\nChristian Copetti\, Oxford\nHector Parra De Freitas\, Harvard\nDamian van de Heisteeg\, Harvard CMSA\nMatilda Delgado\, IFT\nMichele Del-Zotto\, Uppsala University\nMuldrow Etheredge\, UMass Amherst\nIñaki Garcia-Etxebarria\, Durham University\nEduardo Garcia-Valdecasas\, SISSA\, Trieste\nNaomi Gendler\, Harvard\nKelian Haring\, CERN\nDaniel Harlow\, MIT\nJonathan Heckman\, University of Pennsylvania\nBen Heidenreich\, UMass Amherst\nAidan Herderschee\, IAS\nMax Huebner\, Uppsala University\nJesús Huertas\, Instituto de Física Teórica\nTheo Johnson-Freyd\, Dalhousie University\nHo Tat Lam\, MIT\nAdam Levine\, MIT\nYue-Zhou Li\, Princeton\nJacob McNamara\, Caltech\nRuben Minasian\, Institute of Theoretical Physics Saclay\nAmineh Mohseni\, Harvard\nMiguel Montero\, IFT\nGregory Moore\, Rutgers\nLeonardo Rastelli\, Stony Brook\nMatt Reece\, Harvard University\nGrant Remmen\, New York University\nDiego Rodriguez-Gomez\, University of Oviedo\nKonstantinos Roumpedakis\, Johns Hopkins\nTom Rudelius\, Durham University\nVivek Saxena\, Stony Brook and Rutgers\nEdgar Shaghoulian\, UC Santa Cruz\nShu-Heng Shao\, Stony Brook and MIT\nAdar Sharon\, Simons Center for Geometry and Physics\, Stony Brook\nIrene Valenzuela\, IFT and CERN\nThomas Waddleton\, Johns Hopkins\nHao Xu\, University of Göttingen\nXingyang Yu\, Virginia Tech\n\n  \nSchedule  \nTuesday\, Jan. 21\, 2025 \n9:00 – 9:30 am\nBreakfast \n9:30 – 11:00 am\nReview\nLeonardo Rastelli\, Stony Brook University\nYoutube Video \n11:00 – 11:15 am\nBreak \n11:15 am– 12:00 pm\nKelian Haring\, CERN\nTitle: S-matrix bootstrap and black hole production\nAbstract: I will review the expected effects of black hole production in scattering amplitudes. I will consider both symmetry-breaking and elastic amplitudes. I will argue that\, in the elastic case\, this input can be computationally useful. Then\, I will discuss an example of a symmetry-breaking Wilson coefficient as a concrete target for the bootstrap.\nYoutube Video \n12:00 – 1:45 pm\nLunch Break \n1:45 – 2:30 pm\nHo Tat Lam\, MIT\nTitle: Global Aspects of Exactly Marginal Current-Current Deformations\nAbstract: Conformal field theories connected by exactly marginal deformations form conformal manifolds. In two dimensions\, a large class of conformal manifolds is generated by bilinears of currents\, known as current-current deformations. In this talk\, we will revisit these deformations and prove that a dense set of points on the conformal manifolds are related to the seed theory through discrete gauging. This perspective enables us to connect the topology of the conformal manifolds with the anomalies of the currents and to show that enhanced invertible symmetries reorganized into non-invertible symmetries away from the symmetry enhanced points. We will also discuss how current-current deformation can be understood from the recently proposed continuous abelian symmetry topological field theory.\nYoutube Video \n2:30 – 3:15 pm\nTom Banks\, Rutgers University\nTitle: Symmetries in the Hilbert Bundle Formulation of Quantum Gravity\nAbstract: Results of Jacobson\, Carlip and Solodukhin from the 1990s\, as extended by Banks and Zurek in 2021\, point to a solution of Einstein’s equations as a hydrodynamic approximation to a quantum gravitational system\, which determines the density matrix assigned to each subsystem corresponding to a hydrodynamic causal diamond in terms of the Virasoro generator of a cut off 1 + 1 dimensional CFT. The full quantum system can be viewed as a Hilbert bundle over the space of timelike geodesics on the hydrodynamic background. Isometries of the background generically map one fiber of the bundle to another and don’t act on a fixed Hilbert space. Time evolution along each geodesic is given by an analog of “one sided modular flow in QFT”\, which in this context is a sequence of unitary embeddings of smaller diamond Hilbert spaces into larger ones. A full unitary map on the entire Hilbert space of a fiber requires a “Quantum Principle of Relativity” equating the entanglement spectrum of the density matrix of the largest diamond in the overlap between diamonds on different geodesics. In principle\, this implies asymptotic symmetries for spacetimes which have them. For the case of asymptotically AdS space\, this can be worked out in a hand waving way by using the Tensor Network Renormalization Group of Evenbly and Vidal. For asymptotically flat space we probably require a better non-perturbative definition of the space of asymptotic states to understand the action of the Poincare group. For de Sitter space there is no sense in which the de Sitter group acts on any set of asymptotic observables. Ironically\, there IS an approximate de Sitter invariance of at least low point inflationary correlation functions\, but I will not have time to discuss that.\nYoutube Video \n3:15 – 3:45 pm\nBreak \n3:45 – 4:30 pm\nChristian Copetti\, Oxford University\nTitle: Non-Invertible Symmetries\, Generalized Gauging and Factorization\nAbstract: We analyze a toy model for low dimensional holography\, in which the dual theory is an ensemble over 2d RCFTs. This simple model lacks factorization on multi-boundary geometries and at the same time has a (generalized) bulk global symmetry. We show that both problems are solved if the path integral prescription is modified by a generalized gauging operation\, which can also be interpreted as the insertion of (topological) EOW branes.\nYoutube Video \n4:30 – 5:00 pm\nFree Discussion \nWednesday\, Jan. 22\, 2025 \n9:00 – 9:30 am\nBreakfast \n9:30 – 11:00 am\nReview\nDaniel Harlow\, MIT\nYoutube Video \n11:00 – 11:15 am\nBreak \n11:15 am– 12:00 pm\nJacob McNamara\, Caltech\nTitle: Conserved Charges of Closed Universes\nAbstract: In quantum gravity\, while our standard notions of symmetry operator become hard to define\, the notion of conserved charge continues to make sense. After a general discussion of conserved charges in quantum gravity\, I will present a new kinematic invariant of a gravitational path integral that refines the cobordism groups of quantum gravity: the (higher) category of closed universe charges. By categorifying an argument of Coleman\, Giddings\, and Strominger\, I will argue that conserved charges in quantum gravity of any form degree arise only due to a categorical version of ensemble holography.\nYoutube Video \n12:00 – 1:45 pm\nLunch Break \n1:45 – 2:30 pm\nFederico Bonetti\, Durham University\nTitle: Aspects of Categorical Symmetries for Branes\nYoutube Video \n2:30 – 3:15 pm\nKonstantinos Roumpedakis\, Johns Hopkins University\nTitle: Symmetry Operators and Gravity\nAbstract: It is widely believed that there are no conserved charges in a theory of gravity\, based on arguments involving black holes. Moreover\, the modern approach to study global symmetries is the language of topological operators. In this talk\, I will revisit the absence of global symmetries in a theory of gravity from the perspective of topological operators. More specifically\, I will argue that topological operators for continuous symmetries written in terms of currents need regularization\, which effectively gives them a small but finite width. The regulated operator is a finite tension object which fluctuates. In the zero-width limit these fluctuations freeze\, recovering the properties of a topological operator. When gravity is turned on\, the zero-width limit becomes ill-defined\, thereby prohibiting the existence of topological operators. This talk is based on work in collaboration with Ibrahima Bah\, Patrick Jefferson\, and Thomas Waddleton.\nYoutube Video \n3:15 – 3:45 pm\nBreak \n3:45 – 4:30 pm\nIñaki Garcia-Etxebarria\, Durham University\nTitle: Some aspects of symmetry descent\nAbstract: SymTFTs allow us to encode the symmetry structure of Quantum Field Theories in a convenient way. For those QFTs that arise in geometric engineering\, or holography\, we expect to be able to derive the SymTFT from the geometric data of the string background. This talk will describe some recent progress in this direction\, together with S. Hosseini and with F. Gagliano.\nYoutube Video \n4:30 – 5:00 pm\nFree Discussion \n6:00 pm\nDinner at Changsho Restaurant \nThursday\, Jan. 23\, 2025 \n9:00 – 9:30 am\nBreakfast \n9:30 – 11:00 am\nReview\nIrene Valenzuela\, IFT and CERN\nTitle: Breaking of Symmetries in Gravity\nAbstract: Global symmetries are expected to be broken (or gauged) in quantum gravity. However\, we can still learn a lot from understanding the mechanisms by which quantum gravity avoids them and quantifying their breaking. Remarkably\, several Swampland constraints can be reinterpreted as consequences of breaking global symmetries. I will first focus on quantifying the minimal symmetry violation of axionic shift symmetries\, and show how the bottom-up expectation based on black holes seems to hold in string theory examples. I will then discuss how this symmetry violation changes as we move in the moduli space\, implying a drop-off of the quantum gravity cut-off when the symmetry is approximate. Finally\, I will discuss the fate of non-invertible symmetries in string theory\, and how they are typically broken at loop level. Nevertheless\, these approximate non-invertible symmetries are still useful to fill in the gaps in the worldsheet proofs of some Swampland conjectures. \n11:00 – 11:15 am\nBreak \n11:15 am– 12:00 pm\nTom Rudelius\, Durham University\nTitle: A Symmetry-Centric Perspective on the Geometry of the Landscape and the Swampland\nAbstract: As famously observed by Ooguri and Vafa nearly twenty years ago\, scalar field moduli spaces in quantum gravity appear to exhibit various universal features. For instance\, they seem to be infinite in diameter\, have trivial fundamental group\, and feature towers of massive particles that become light in their asymptotic limits. In this talk\, I will explain how these features can be reformulated in more modern language using generalized notions of global symmetries. Such symmetries are ubiquitous in non-gravitational quantum field theories\, but it is widely believed that they must be either gauged or broken in quantum gravity. We will see that the observations of Ooguri and Vafa can be understood as consequences of such gauging or breaking. \n12:00 – 1:45 pm\nLunch Break \n1:45 – 2:30 pm\nMiguel Montero\, IFT\nTitle: Parity symmetry breaking and the membrane Weak Gravity Conjecture\nAbstract: Symmetries are expected to be broken or gauged in any consistent theory of quantum gravity\, and this also applies to spacetime symmetries such as parity. I will argue that\, in the context of 4d N=1 AdS vacua of string theory\, the Weak Gravity Conjecture for membranes case only holds if the vacuum has an exact (i.e. gauged) parity symmetry of Pin+ type. I will give top-down examples of M-theory vacua illustrating this\, and show that in the DGKT scenario (a putative massive IIA vacuum with scale separation\, whose full consistency is the subject of some debate in the literature) there is no parity symmetry\, and the membrane WGC is violated. Thus\, there is either a pathology in DGKT\, or the membrane WGC is wrong. Both possibilities would have interesting consequences\, and I will outline ongoing work to figure out which one is it. \n2:30 – 3:15 pm\nMatilda Delgado\, IFT\nTitle: Dualities\, Defects and Duality Defects\nAbstract: I will outline how duality symmetries in quantum gravity theories naturally predict the existence of defects associated with duality transformations. While some of these objects are well-understood and extensively studied\, others remain enigmatic; I will discuss this with examples. I will conclude by discussing the potential role of dualities in characterising the UV defects predicted by cobordism conjecture (and more generally by the no global symmetries conjecture). Based on: [2412.03640] \n3:15 – 3:45 pm\nBreak \n3:45 – 4:30 pm\nMax Hübner\, Uppsala University\nTitle: Metric Isometries\, Holography\, and Continuous Symmetry Operators\nAbstract: In the AdS/CFT correspondence\, a topological symmetry operator of the boundary CFT is dual to a dynamical brane in the gravitational AdS bulk. Said differently\, this predicts a dynamical brane for every global symmetry of the boundary CFT. We analyze this correspondence for continuous symmetries which arise from a consistent truncation of isometries on the “internal” factor X of AdS × X. We discuss how this perspective can be used to both derive properties of the topological symmetry operators and non-topological properties of their bulk duals. \n4:30 – 5:00 pm\nFree Discussion \n  \nFriday\, Jan. 24\, 2025 \n9:00 – 9:30 am\nBreakfast \n9:30 – 10:15 am\nJonathan Heckman\, University of Pennsylvania\nTitle: Cobordism Utopia\nAbstract: On general grounds one expects that global symmetries are absent in quantum gravity. We discuss some aspects of this issue\, focusing on the recently proposed Swampland Cobordism Conjecture\, and related conjectures connected with completeness of the spectrum of states charged under symmetries. In particular\, the U-dualities of M-theory provide an excellent arena both for testing aspects of these conjectures\, as well as predicting the existence of new dynamical objects. We also comment on how this approach connects to related top down and holographic approaches to constructing and studying gauging and breaking symmetries in quantum gravity. Based on joint work to appear with Braeger\, Debray\, Dierigl\, and Montero. \n10:15 – 11:00 am\nNaomi Gendler\, Harvard University \n11:00 – 11:15 am\nBreak \n11:15 am – 12:00 pm\nDiego Rodriguez-Gomez\, University of Oviedo\nTitle: Non-BPS branes as holographic symmetry operators\nAbstract: We propose a holographic description of the operators implementing continuous global symmetries that are dual to superstring gauge fields in terms of non-BPS D- branes\, and consider some possible further extensions. \n12:00 – 12:45 pm\nGreg Moore\, Rutgers University\nTitle: Summing Over Bordisms In 2d TQFT: Déjà Vu\nAbstract: This is basically a rerun of a talk I gave on zoom for the CMSA on March 16\, 2022. I will review the contents of a paper I wrote with Anindya Banerjee 2201.00903\, but including a few minor updates. I will describe a construction in Topological Field Theory (TFT) which was motivated by developments in the quantum gravity community. The goal is to provide an interpretation of a model discussed by D. Marolf and H. Maxfield 2002.08950 aimed at fitting their model within the functorial framework of Quantum Field Theory (QFT). Given a TFT one can consider – formally – the sum over all bordisms between fixed ingoing and outgoing spatial slices (with appropriate weight factors for the bordisms) of the amplitudes associated to the bordism by the TFT. This construction leads to convergent sums in d\leq 2 dimensions\, at least for for generic parameters of the TFT. I will describe a curious splitting property satisfied by the total amplitude. I view the splitting property as an alternative to ensemble-type interpretations. There will be a cameo appearance of a very interesting paper by Daniel Friedan 2306.00019 which purports to give an axiomatic framework for Euclidean Quantum Gravity (EQG) analogous to the functorial formalism of QFT. I will also note\, in passing\, that these extremely simple\, low-dimensional\, baby baby baby models of EQG admit global symmetries and continuous parameters. \n1:00 pm\nFarewell Lunch \n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/symmetries/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:Workshop
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/Poster_Workshop-on-Symmetries-and-Gravity_2.png
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250130T160000
DTEND;TZID=America/New_York:20250130T173000
DTSTAMP:20241218T212836Z
CREATED:20240710T194728Z
LAST-MODIFIED:20241218T212836Z
UID:10003399-1738252800-1738258200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:CMSA/MATH Welcome Back Gathering
DESCRIPTION:Thursday\, Jan. 30\, 2025 \n4:00 pm \nAll CMSA and Math affiliates are invited. \n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/cmsa-math_13025/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:Event
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250213T160000
DTEND;TZID=America/New_York:20250213T170000
DTSTAMP:20250328T150436Z
CREATED:20240708T151711Z
LAST-MODIFIED:20250328T150436Z
UID:10003396-1739462400-1739466000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:2025 Ding Shum Lecture: Irit Dinur\, IAS: Expanders from local to global
DESCRIPTION:  \n \nOn February 13\, 2025 the CMSA hosted the sixth annual Ding Shum Lecture\, given by Irit Dinur\, Institute for Advanced Study. \nLocation: Harvard Science Center  Hall A & via Zoom Webinar \nSpeaker: Irit Dinur\, Institute for Advanced Study \n\n\n\nTitle: Expanders from local to global \nAbstract: Imagine a network—like a social network\, a transportation system\, or even a biological system—where every part of the network is robustly connected to the rest. Expander graphs are the mathematical idealization of such networks. They are structures where any small group of points (nodes) has many connections to the rest of the graph\, ensuring that no part is isolated and information (or influence) spreads efficiently throughout.\nWe will begin by surveying expander graphs\, their discovery and construction\, and some fascinating applications such as error-correcting codes\, pseudorandomness\, and probabilistically checkable proofs (PCPs)\, highlighting their role as a foundation for many breakthroughs in theoretical computer science. Then\, we will shift focus to an exciting new kind of expanders called high dimensional expanders (HDXs). While expanders are well-understood and widely applied\, HDXs remain enigmatic\, with potential that we are only starting to uncover. We will talk about a fascinating local to global feature that HDXs have\, and some applications. \n\n \n\n\n\n\nThis event is made possible by the generous funding of Ding Lei and Harry Shum.\n\n\n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/2025_dingshum/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Ding Shum Lecture,Event,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/DIngShum_21325.png
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250324T090000
DTEND;TZID=America/New_York:20250524T170000
DTSTAMP:20250514T204248Z
CREATED:20240228T180801Z
LAST-MODIFIED:20250514T204248Z
UID:10002883-1742806800-1748106000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Program on Classical\, quantum\, and probabilistic integrable systems - novel interactions and applications
DESCRIPTION:Program on Classical\, quantum\, and probabilistic integrable systems – novel interactions and applications \nDates: March 24–May 24\, 2025  \nLocation: CMSA\, 20 Garden Street\, Cambridge MA 02138 \nExactly solvable models have played pivotal roles in mathematics and physics throughout their history. The program is dedicated to exploring and developing a more recent wave of their influence in stochastic models together with accompanying combinatorial\, classical\, and quantum integrable systems. Topics will include: \n\nColored and uncolored interacting particle systems with associated vertex models and line ensembles\nYang-Baxter integrability and its applications in algebraic combinatorics\, quantum systems\, and conformal field theory\nQuantum stochastic models\, quantum exclusion processes\, and free probability\nEmerging new aspects of classical and quantum integrable systems – hydrodynamics\, large deviations of stochastic models\, and random surface models\n\nOrganizers: \n\nAmol Aggarwal\, Columbia University & Clay Mathematics Institute\nGuillaume Barraquand\, École normale supérieure\, Paris\nAlexei Borodin\, MIT\nIvan Corwin\, Columbia University\nPierre Le Doussal\, École normale supérieure\, Paris\nMichael Wheeler\, University of Melbourne\n\nParticipants \n\nDenis Bernard\, Ecole Normale Supérieure Paris\nAlexey Bufetov\, University of Leipzig\nPasquale Calabrese\, SISSA Trieste\nSylvie Corteel\, UC Berkeley\nCesar Cuenca\, Ohio State University\nJan De Gier\, University of Melbourne\nAndrea De Luca\, CNRS\, Cergy Paris University\nBenjamin Doyon\, King’s College London\nPatrik Ferrari\, University of Bonn\nVadim Gorin\, UC Berkeley\nTamara Grava\, SISSA\nJimmy He\, Ohio State University\nJiaoyang Huang\, University of Pennsylvania\nKurt Johansson\, KTH Stockholm\nRichard Kenyon\, Yale\nAlexandre Krajenbrink\, Cambridge Quantum Computing & Quantinuum\nAtsuo Kuniba\, University of Tokyo\nMatteo Mucciconi\, National University of Singapore\nGreta Panova\, University of Southern California\nLeonid Petrov\, University of Virginia\nSylvain Prolhac\, Université Paul Sabatier\, Toulouse\nTomaž Prosen\, University of Ljubljana\nTomohiro Sasamoto\, Tokyo Institute of Technology\nHerbert Spohn\, Technical University of Munich\nLi-Cheng Tsai\, University of Utah\n\nSchedule \nWeek 1\nMonday\, March 24th \n11:00am – 12:00pm Room G-10\, Lecture 1 of 4: Denis Bernard\, École normale supérieure de Paris: Quantum Exclusion Processes for (and by) Amateurs \n12:00 – 2:00pm Common Room: Program Lunch \n4:00 – 4:30pm Common Room: CMSA colloquium tea \n4:30 – 5:30pm Common Room\, CMSA colloquium: Amol Aggarwal\, Columbia University: The Toda Lattice as a Soliton Gas \n  \nTuesday\, March 25th \n3:30 – 4:00pm Common Room: Program tea \n4:00 – 5:00pm Room G-10\, Seminar: Patrik Ferrari\, Universität Bonn: Decoupling and decay of two-point functions in a two-species TASEP \n  \nWednesday\, March 26th \n11:00am – 12:00pm Room G-10\, Lecture 1 of 3: Atsuo Kuniba\, University of Tokyo: Multispecies ASEP and t-PushTASEP on a ring and a strange five vertex model \n3:00 – 4:00pm Room G-10\, Lecture 2 of 4: Denis Bernard\, École