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DTSTART;TZID=America/New_York:20240205T090000
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DTSTAMP:20260430T155348
CREATED:20240103T173754Z
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UID:10001104-1707123600-1711731600@cmsa.fas.harvard.edu
SUMMARY:Arithmetic Quantum Field Theory Program
DESCRIPTION:Arithmetic Quantum Field Theory Program\nDates: Feb. 5–Mar. 29\, 2024 \nLocation: Harvard CMSA\, 20 Garden Street\, Cambridge MA 02138 \nArithmetic Quantum Field Theory Program Youtube Playlist \nOrganizers: \n\nDavid Ben-Zvi (University of Texas Austin)\nSolomon Friedberg (Boston College)\nNatalie Paquette (University of Washington Seattle)\nBrian Williams (Boston University)\n\nThis program features a weekly seminar series\, workshops\, and a conference. \nThe object of the program is to develop and disseminate exciting new connections emerging between quantum field theory and algebraic number theory\, and in particular between the fundamental invariants of each: partition functions and L-functions. \nOn one hand\, there has been tremendous progress in the past decade in our understanding of the algebraic structures underlying quantum field theory as expressed in terms of the geometry and topology of low-dimensional manifolds\, both on the level of states (via the Atiyah-Segal / Baez-Dolan / Lurie formalism of extended\, functorial field theory) and on the level of observables (via the Beilinson–Drinfeld / Costello–Gwilliam formalism of factorization algebras). On the other hand\, Weil’s Rosetta Stone and the Mazur–Morishita–Kapranov–Reznikov arithmetic topology (the “knots and primes” dictionary) provide a sturdy bridge between the topology of 2- and 3-manifolds and the arithmetic of number fields. Thus\, one can now port over quantum field theoretic ideas to number theory\, as first proposed by Minhyong Kim with his arithmetic counterpart of Chern-Simons theory. Most recently\, the work of Ben-Zvi–Sakellaridis–Venkatesh applies an understanding of the Langlands program as an arithmetic avatar of electric-magnetic duality in four-dimensional gauge theory to reveal a hidden quantum mechanical nature of the theory of $L$-functions. \nThe program will bring together a wide range of mathematicians and physicists working on adjacent areas to explore the emerging notion of arithmetic quantum field theory as a tool to bring quantum physics to bear on questions of interest for the theory of automorphic forms\, harmonic analysis and L-functions. Conversely\, we will explore potential geometric and physical consequences of arithmetic ideas\, for example\, the Langlands correspondence theory of L-functions for 3-manifolds. \n\nSchedule \nThe first week of the program will feature several lecture series aimed at a broad local community of mathematicians and physicists\, aiming to introduce the main ideas underlying our program and help establish a common reference point. \nThe program will host a weekly seminar series on Fridays. \nThe speakers will be selected with the aim of covering a wide panorama of the subjects over the course of the program. \nThe program will conclude with a week-long Conference on Arithmetic Quantum Field Theory March 25–29\, 2024. \n\nAQFT Youtube Playlist \nLecture series \nAll lectures take place in Room G10\, Harvard CMSA\, 20 Garden Street Cambridge. \nWeek 1: Feb. 5–9\, 2024 \nAbstract: In this lecture series we will introduce some of the themes underlying the CMSA program on Arithmetic Quantum Field Theory taking place this winter and the upcoming conference March 25-29\, 2024. \nSome of the themes we plan to discuss include: \nStructures in QFT (like factorization for observables and functorial QFT for states and their relation to geometric / deformation quantization) that are sufficiently algebraic and formal to allow for arithmetic analogs. \nThe setup of arithmetic topology as a bridge between the background of QFT to that of arithmetic (both “global” and “local”)\, including the “middle realm” of positive characteristic function fields. \nQuestions and structures in arithmetic that have been / might be amenable to inspiration from QFT\, in particular the theory of L-functions and the Langlands program. \nSchedule \n\n\n\nMonday\, Feb. 5\, 2024\n \n \n\n\n11:00 am – 12:00 pm\n Minhyong Kim\nArithmetic topology and field theory\nVideo\n(Slides part 1 pdf)\n\n\n1:30 – 2:30 pm\nBrian Williams\nAlgebraic quantum field theory\nVideo\n(Lecture Notes)\n\n\n2:30 – 3:30 pm\nDavid Ben-Zvi\nThe Langlands program via arithmetic QFT\nVideo\n\n\nWednesday\, Feb. 7\, 2024\n \n \n\n\n11:00 am – 12:00 pm\nMinhyong Kim\nArithmetic topology and field theory\nVideo\n(Slides part 2 pdf)\n\n\n2:30 – 3:30 pm\nBrian Williams\nAlgebraic quantum field theory\nVideo\n(Lecture Notes)\n\n\nThursday\, Feb.8\, 2024\n \n \n\n\n2:30 – 3:30 pm\nMinhyong Kim\nArithmetic topology and field theory\nVideo\n(Slides part 3 pdf)\n\n\n4:00 – 5:00 pm\nDavid Ben-Zvi\nThe Langlands program via arithmetic QFT\nVideo\n\n\nFriday\, Feb. 9\, 2024\n \n \n\n\n1:00 – 2:00 pm\nBrian Williams\nAlgebraic quantum field theory\nVideo\n(Lecture Notes)\n\n\n2:00 – 3:00 pm\nDavid Ben-Zvi\nThe Langlands program via arithmetic QFT 1\nVideo\n\n\n3:30 – 4:30 pm\nDavid Ben-Zvi\nThe Langlands program via arithmetic QFT 2\nVideo\n\n\nMonday\, Feb. 26\, 2024\n\n\n\n\n1:00 – 2:00 pm\nOmer Offen (Brandeis)\nPeriod integrals of automorphic forms and the residue method\nVideo\n\n\nTuesday\, Feb. 27\, 2024\n\n\n\n\n2:00 – 3:00 pm\nWei Zhang (MIT)\nShtuka special cycles and their generating series\nVideo\n\n\nFriday\, March 1\, 2024\n\n\n\n\n11:00 am – 12:00 pm\nChen Wan (Rutgers Newark)\nSome examples of the relative Langlands duality\nVideo\n\n\n2:00 – 3:00 pm\nPeng Shan (Tsinghua)\nSkein algebras and quantized Coulomb branches\nVideo\n\n\nThursday\, March 7\, 2024\n\n\n\n\n1:30 – 2:30 pm\nAn Huang (Brandeis)\nTate’s thesis and p-adic strings\nVideo\n\n\n3:00 – 4:00 pm\nJohn Francis (Northwestern)\nIntegrating braided categories over 3-manifolds\nVideo\n\n\nFriday\, March 8\, 2024\n\n\n\n\n1:00 – 2:00 pm\nDihua Jiang (U Minnesota)\nShalika Periods: Functoriality and Arithmetic\nVideo\n\n\nFriday\, March 15\, 2024\n\n\n\n\n11:45 – 1:00 pm\nBaiying Liu (Purdue)\nRecent progress on certain problems related to local Arthur packets of classical groups\nVideo\n\n\n2:15 – 3:30 pm\nTasho Kaletha (Michigan)\nCovers of reductive groups and functoriality\nVideo\n\n\nMonday\, March 18\, 2024\n\n\n\n\n1:00 – 3:00 pm\nXinwen Zhu (Stanford)\nThe tame categorical local Langlands correspondence\nVideo\n\n\n4:30 – 5:30 pm\nNatalie Paquette (U Washington)\nKoszul duality & twisted holography for asymptotically flat spacetimes\n\n\nWednesday\, March 20\, 2024\n\n\n\n\n11:00 – 12:15 pm\nStephen D. Miller (Rutgers)\nWhat 4-graviton scattering amplitudes had to say about the unitary dual\n\n\nFriday\, March 22\, 2024\n\n\n\n\n1:45 – 3:00 pm\nJayce Getz (Duke)\nThe Poisson summation conjecture and the fiber bundle method\nVideo\n\n\n\n\n\n\n\n\n\nProgram Visitors \n\nMina Aganagic\, University of California\, Berkeley\nAnne-Marie Aubert\, Institut de Mathématiques de Jussieu-Paris Rive Gauche\, March 15-29\nClark Barwick\, University of Edinburgh\, February 19-March 15\nAlexander Braverman\, Perimeter Institute\nAlejandra Castro\, Cambridge University\, March 25-29\nYoungJu Choie\, Pohang University of Science and Technology\, February 12-16; March 22-28\nJohn Francis\, Northwestern University\, March 1-14\nDavid Gaiotto\, Perimeter Institute\, March 25-29\nJayce Getz\, Duke University\, March 18-22\nEzra Getzler\, Northwestern University\, March 11-22\nSam Gunningham\, Montana State University\, February 9-12\nSarah Harrison\, Northeastern University\nDihua Jiang\, University of Minnesota\, February 29-March 9\nTasho Kaletha\, University of Michigan\, March 12-20\nMinhyong Kim\, University of Edinburgh\, February 1-29\nAxel Kleinschmidt\, Max Planck Institute for Gravitational Physics\, Potsdam\, March 18-28\nKim Klinger-Logan\, Kansas State University\, March 25-29\nKobi Kremnitzer\, Oxford University\, March 25-29\n\nBaiying Liu\, Purdue University\, March 13-16\n\n\nSteven Miller\, Rutgers University\n\nGreg Moore\, Rutgers University\, February 5-9\nDavid Nadler\, University of California\, Berkeley\, March 17-30\nBảo Châu Ngô\, University of Chicago\, March 25-29\nGeorge Pappas\, Michigan State University\, March 25-29\nDaniel Persson\, Chalmers Institute of Technology\, March 25-29\nSam Raskin\, Yale University\, March 26-29\nYiannis Sakellaridis\, Johns Hopkins University\, March 18-22\nPeng Shan\, Tsinghua University\, February 12-April 14\nAkshay Venkatesh\, Institute for Advanced Study\nRoberto Volpato\, University of Padova\, February 4-10\nChen Wan\, Rutgers University\, February 29-March 9\nFei Yan\, Brookhaven National Laboratory\, March 18-29\nXinwen Zhu\, Stanford University\n\n  \n 
URL:https://cmsa.fas.harvard.edu/event/aqft2024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Programs
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Poster_AQFT-Program_letter-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240209T093000
DTEND;TZID=America/New_York:20240209T110000
DTSTAMP:20260430T155348
CREATED:20240205T162614Z
LAST-MODIFIED:20240207T184606Z
UID:10001506-1707471000-1707476400@cmsa.fas.harvard.edu
SUMMARY:Quantum Algorithms to Recognize Phases of Matter and Exactly Solvable 2D Models with Anomalous Entanglement Entropy
DESCRIPTION:Quantum Matter in Mathematics and Physics Seminar \nSpeaker: Soonwon Choi (MIT) \nTitle: Quantum Algorithms to Recognize Phases of Matter and  Exactly Solvable 2D Models with Anomalous Entanglement Entropy \nAbstract: In this talk\, I will report my two recent results at the intersection of quantum information and strongly interacting phases of matters. \nIn the first half of the talk\, we describe exact quantum algorithms that recognize a class of 1D gapped phases\, namely symmetry protected topological phases or spontaneous symmetry breaking phases protected by abelian internal symmetry. The key idea is to observe the conceptual similarity between renormalization group (RG) flow and error correction\, and to implement the latter as unitary circuits emulating the RG flow. Our algorithm guarantees faithful recognition of a target phase with a small number of input quantum state samples. \nIn the second half\, we present a class of 2D Hamiltonians\, where the exact ground state wavefunctions can be exactly evaluated and shown to exhibit anomalous entanglement properties. One class of our models exhibit area-law scaling entanglement entropy\, but this is mostly due to non-local correlation: one finds that the topological entanglement entropy also scales with the size of subsystem choices. By making simple modifications\, we can also devise 2D models with volume-law scaling bipartite entanglement entropy. Our results can be understood as a generation of the 1D Motzkin model to 2D systems. \nBased on work done with Ethan Lake and Shankar Balasubramanian \nhttps://arxiv.org/abs/2211.09803 \nhttps://arxiv.org/abs/2305.07028
URL:https://cmsa.fas.harvard.edu/event/qm-2924/
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-02.09.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240209T120000
DTEND;TZID=America/New_York:20240209T130000
DTSTAMP:20260430T155348
CREATED:20240208T143028Z
LAST-MODIFIED:20240208T143041Z
UID:10000669-1707480000-1707483600@cmsa.fas.harvard.edu
SUMMARY:The spectrum of some nonlinear random matrices
DESCRIPTION:CMSA Member Seminar \nSpeaker: Benjamin McKenna (Harvard) \nTitle: The spectrum of some nonlinear random matrices \nAbstract: Modern data science often requires one to consider “nonlinear random matrices\,” a broad term for random-matrix models whose construction involves a nonlinear function applied entrywise. Such models are typically far from classical random matrix theory\, and in principle entrywise nonlinearities can affect the eigenvalues in a complicated way. However\, recent years have seen a number of results on nonlinear models whose spectrum is surprisingly simple. We give one such result\, emphasizing general random-matrix techniques like free probability and orthogonal polynomials. Joint work with Sofiia Dubova\, Yue M. Lu\, and Horng-Tzer Yau.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-2924/
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:20240209T130000
DTEND;TZID=America/New_York:20240209T140000
DTSTAMP:20260430T155348
CREATED:20240125T174316Z
LAST-MODIFIED:20240209T183618Z
UID:10001359-1707483600-1707487200@cmsa.fas.harvard.edu
SUMMARY:AQFT Lecture Series | Brian Williams
DESCRIPTION:Arithmetic Quantum Field Theory Program Lecture Series\nSpeaker: Brian Williams\, Boston University \nTopic: Algebraic quantum field theory \nAbstract: Questions and structures in arithmetic that have been / might be amenable to inspiration from QFT\, in particular the theory of L-functions and the Langlands program.
URL:https://cmsa.fas.harvard.edu/event/aqft-lecture-series-brian-williams-2924/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:AQFT Lecture Series,Colloquia & Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240209T140000
DTEND;TZID=America/New_York:20240209T150000
DTSTAMP:20260430T155348
CREATED:20240125T175054Z
LAST-MODIFIED:20240207T211016Z
UID:10001362-1707487200-1707490800@cmsa.fas.harvard.edu
SUMMARY:AQFT Lecture Series | David Ben-Zvi
DESCRIPTION:Arithmetic Quantum Field Theory Program Lecture Series\nSpeaker: David Ben-Zvi \nTopic: The Langlands program via arithmetic QFT \nAbstract: Structures in QFT (like factorization for observables and functorial QFT for states and their relation to geometric / deformation quantization) that are sufficiently algebraic and formal to allow for arithmetic analogs.
URL:https://cmsa.fas.harvard.edu/event/aqft-lecture-series-david-ben-zvi-2924/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:AQFT Lecture Series,Colloquia & Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240209T153000
DTEND;TZID=America/New_York:20240209T163000
DTSTAMP:20260430T155348
CREATED:20240125T175133Z
LAST-MODIFIED:20240207T210956Z
UID:10001363-1707492600-1707496200@cmsa.fas.harvard.edu
SUMMARY:AQFT Lecture Series | David Ben-Zvi
DESCRIPTION:Arithmetic Quantum Field Theory Program Lecture Series\nSpeaker: David Ben-Zvi \nTopic: The Langlands program via arithmetic QFT \nAbstract: Structures in QFT (like factorization for observables and functorial QFT for states and their relation to geometric / deformation quantization) that are sufficiently algebraic and formal to allow for arithmetic analogs.
URL:https://cmsa.fas.harvard.edu/event/aqft-lecture-series-david-ben-zvi-2924_pm/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:AQFT Lecture Series,Colloquia & Seminar
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