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DTSTART;TZID=America/New_York:20270215T080000
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UID:10003888-1802678400-1810400400@cmsa.fas.harvard.edu
SUMMARY:Stable Homotopy Theory and Arithmetic Geometry
DESCRIPTION:Stable Homotopy Theory and Arithmetic Geometry \nDates: Feb 15–May 15\, 2027 \nLocation: Harvard CMSA\, 20 Garden St\, Cambridge MA \nThis program will focus on interactions between stable homotopy theory and arithmetic geometry. In recent years\, ideas from homotopy theory have begun to play an important role in areas such as p-adic cohomology\, prismatic methods\, and aspects of the Langlands program\, while techniques from arithmetic geometry have led to new insights and computations in chromatic homotopy theory. Despite this growing overlap\, researchers in the two areas often use different languages and tools. A central goal of the program is to make these ideas more accessible across fields and to encourage collaborations around shared problems. \nThe program will run from February 15 to May 15 and will be built around research and informal collaboration. It will begin with a short introductory bootcamp\, followed by two focused workshops (one near the start and one toward the end)\, a weekly seminar with broadly accessible talks\, and a weekly open-problem session. Most of the time will be left open for discussion and joint work among participants\, aiming to spark new projects and longer-term connections between the two communities. \nThe program will include: \n(1) a bootcamp during the week Feb. 22–26\, consisting of introductory lectures on both subjects;\n(2) two research workshops—one during Mar. 1–5 and one during May 3–7—highlighting current developments\, especially those at the interface of the two areas;\n(3) a weekly seminar featuring talks of broad relevance to participants; and\n(4) a weekly open-problem seminar aimed at proposing and developing collaborative research directions\, both for the duration of the program and beyond. \nRegister Online \n  \nOrganizers: Tomer Schlank (Harvard)\, Jared Weinstein (Boston University)\, Mark Kisin (Harvard)\, Jeremy Hahn (MIT)\, Lucas Mann (Münster)
URL:https://cmsa.fas.harvard.edu/event/htag/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Programs
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UID:10003950-1819616400-1841158800@cmsa.fas.harvard.edu
SUMMARY:CMSA Quantum Field Theory Program
DESCRIPTION:CMSA Quantum Field Theory Program \nDates: August 30\, 2027 – May 5\, 2028 \nLocation: Harvard CMSA\, 20 Garden Street\, Cambridge MA \nQuantum field theory (QFT) has long been a subject with a large influence on mathematics\, yet there is still no unified mathematical framework that encompasses all viewpoints.  Constructive QFT and Algebraic QFT—typified by the Wightman and Haag-Kastler axiom systems\, respectively—have many achievements in relativistic and Euclidean QFT\, but they do not include Wick-rotated theories on compact manifolds and so miss many of the geometric\, topological\, and algebraic developments of the past several decades.  These developments include supersymmetric QFT and applications to geometry and topology\, generalized symmetries in QFT\, and a robust theory of topological QFTs.  The more recent Segal and Costello-Gwilliam axiom systems do accommodate some of these developments\, but they are largely disjoint from the analytic progress.  Techniques from probability theory and stochastic PDE have been used to advance traditional constructive and algebraic QFT; they have also been applied to obtain rigorous results in two-dimensional conformal field theory and Euclidean lattice gauge theories.  There has also been recent progress in quantum lattice systems\, revealing surprising new bridges between operator algebras and topology. \nThis special year at CMSA aims to shape the direction of the field by bringing the analytic and geometric threads of mathematical QFT into closer contact.  The program will gather a diverse group of mathematicians together with physicists who enjoy close interactions with mathematicians.  The year will be organized around the four focus areas listed below.  There will be several short courses and one workshop for each of these focus areas.  All lectures will be hybrid. \n  \nFOCUS AREAS \nFirst Semester \n\nAxiomatic approaches to QFT\nSymmetry\, anomalies\, and topology\n\nSecond Semester \n\nProbabilistic methods in QFT\nSupersymmetry\, geometry\, and moduli spaces\n\nOrganizers:  \n\nSourav Chatterjee (Stanford University)\nClay Cordova (University of Chicago)\nDan Freed (Harvard University)\nAnton Kapustin (Caltech)\nConstantin Teleman (University of California\, Berkeley)\n\n  \n 
URL:https://cmsa.fas.harvard.edu/event/cmsaqft_2027/
LOCATION:Hybrid – G10
CATEGORIES:Programs
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