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DTSTART;TZID=America/New_York:20240924T161500
DTEND;TZID=America/New_York:20240924T181500
DTSTAMP:20260505T024535
CREATED:20240907T180814Z
LAST-MODIFIED:20240924T145311Z
UID:10003455-1727194500-1727201700@cmsa.fas.harvard.edu
SUMMARY:Symplectic duality in examples
DESCRIPTION:Geometry and Quantum Theory Seminar \nSpeaker: Vasily Krylov\, Harvard CMSA & Math \nTitle: Symplectic duality in examples \nAbstract: Over the past twenty years\, mathematicians and physicists have shown increasing interest in studying certain Poisson varieties\, known as “symplectic singularities.” Many of these objects naturally arise as Higgs or Coulomb branches of certain TQFTs and\, therefore\, fall within the framework of 3D mirror symmetry\, also known as symplectic duality. The first part of the talk will provide a gentle introduction to the theory of symplectic singularities\, with an emphasis on various examples. In the second part\, we will discuss how the symplectic duality works in examples\, beginning with the simplest cases. We will then discuss a particular phenomenon called the Hikita-Nakajima conjecture\, which predicts a deep and nontrivial relationship between dual varieties. It is particularly intriguing that this conjecture was formulated by mathematicians and still requires further understanding from a physical perspective.
URL:https://cmsa.fas.harvard.edu/event/quantumgeo_92424/
LOCATION:Science Center Hall E\, 1 Oxford Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Geometry and Quantum Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Geometry-Quantum-Theory-09.24.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240923T163000
DTEND;TZID=America/New_York:20240923T173000
DTSTAMP:20260505T024535
CREATED:20240903T194207Z
LAST-MODIFIED:20240918T190927Z
UID:10003431-1727109000-1727112600@cmsa.fas.harvard.edu
SUMMARY:Symmetry groups in infinite dimensions
DESCRIPTION:Colloquium \nSpeaker: Lisa Carbone\, Rutgers University \nTitle: Symmetry groups in infinite dimensions \nAbstract: The study of many physical theories requires an understanding of symmetries of infinite dimensional Lie algebras. The construction of groups of automorphisms for infinite dimensional Lie algebras is challenging\, but there is well established theory for the class of Kac-Moody algebras. A generalization of Kac-Moody algebras known as Borcherds algebras arise in string theory models\, but the methods for constructing Kac-Moody groups break down for this more general class. We discuss the challenges that arise and describe several approaches to constructing groups for Borcherds algebras. Our main example is the Monster Lie algebra which plays an important role in the solution of Monstrous Moonshine and which is a symmetry algebra of a model of the compactified Heterotic String.
URL:https://cmsa.fas.harvard.edu/event/colloquium-92324/
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-09.23.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240917T160000
DTEND;TZID=America/New_York:20240917T180000
DTSTAMP:20260505T024535
CREATED:20240907T170124Z
LAST-MODIFIED:20240916T162843Z
UID:10003411-1726588800-1726596000@cmsa.fas.harvard.edu
SUMMARY:Mathematics around Twisted Holography
DESCRIPTION:Geometry and Quantum Theory Seminar \nSpeaker: Keyou Zeng (CMSA) \nTitle: Mathematics around Twisted Holography \nAbstract: The holography principle is an important idea in physics and has been widely studied since the 90s. Twisted holography offers a way to simplify physical holography models through the procedure called twisting. In the first part of the talk\, I’ll introduce some of the mathematical structures underlying this twisted version of holography\, such as Koszul duality. \nIn the second part\, I’ll discuss the concept of vertex algebras in symmetric monoidal categories\, specifically in Deligne category. This framework will serve as a tool to rigorously define the “large N” algebra that emerges from twisted holography. \n 
URL:https://cmsa.fas.harvard.edu/event/quantumgeo_91724/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Geometry and Quantum Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Geometry-Quantum-Theory-09.17.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240916T163000
DTEND;TZID=America/New_York:20240916T173000
DTSTAMP:20260505T024535
CREATED:20240903T193540Z
LAST-MODIFIED:20240916T163127Z
UID:10003430-1726504200-1726507800@cmsa.fas.harvard.edu
SUMMARY:Periodic pencils of flat connections and their p-curvature
DESCRIPTION:Colloquium \nSpeaker: Pavel Etingof (MIT) \nTitle: Periodic pencils of flat connections and their p-curvature \n A periodic pencil of flat connections on a smooth algebraic variety  is a linear family of flat connections  \, where  are local coordinates on  and  are matrix-valued regular functions. A pencil is periodic if it is generically invariant under the shifts  up to isomorphism. I will explain that periodic pencils have many remarkable properties\, and there are many interesting examples of them\, e.g. Knizhnik-Zamolodchikov\, Dunkl\, Casimir connections and equivariant quantum connections for conical symplectic resolutions with finitely many torus fixed points. I will also explain that in characteristic \, the -curvature operators  of a periodic pencil  are isospectral to the commuting endomorphisms \, where  is the Frobenius twist of . This allows us to compute the eigenvalues of the -curvature for the above examples\, and also to show that a periodic pencil of connections always has regular singularites. This is joint work with Alexander Varchenko. \n(Abstract link (pdf)
URL:https://cmsa.fas.harvard.edu/event/colloquium_91624/
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-09.16.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240910T160000
DTEND;TZID=America/New_York:20240910T180000
DTSTAMP:20260505T024535
CREATED:20240905T130004Z
LAST-MODIFIED:20240910T150123Z
UID:10003443-1725984000-1725991200@cmsa.fas.harvard.edu
SUMMARY:BPS Algebras in Landau-Ginzburg Models
DESCRIPTION:Speaker: Ahsan Khan (CMSA) \nTitle: BPS Algebras in Landau-Ginzburg Models \nAbstract: The study of BPS states in supersymmetric quantum field theory has been a fruitful source of both mathematical and physical insights. In particular their study often leads to rich algebraic structures – from the “Algebra of the Infrared” of Gaiotto-Moore-Witten to the “Cohomological Hall Algebras” of Kontsevich-Soibelman. In this talk\, I will provide an overview of some of these algebraic constructions\, with a particular emphasis on BPS states in two-dimensional Landau-Ginzburg models. In the second half of the talk\, I will discuss how these algebraic structures can be extended to more general Landau-Ginzburg models defined by closed holomorphic one-forms.
URL:https://cmsa.fas.harvard.edu/event/geometry-and-quantum-theory-seminar_91024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Geometry and Quantum Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Geometry-Quantum-Theory-09.10.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240909T163000
DTEND;TZID=America/New_York:20240909T173000
DTSTAMP:20260505T024535
CREATED:20240827T200454Z
LAST-MODIFIED:20240903T152309Z
UID:10003406-1725899400-1725903000@cmsa.fas.harvard.edu
SUMMARY:Combinatorics and geometry of the amplituhedron
DESCRIPTION:Colloquium \nSpeaker: Lauren Williams\, Harvard University \nTitle: Combinatorics and geometry of the amplituhedron \nAbstract: The amplituhedron is a geometric object introduced by Arkani-Hamed and Trnka to compute scattering amplitudes in N=4 super Yang Mills theory. It generalizes interesting objects such as cyclic polytopes and the positive Grassmannian. It has connections to tropical geometry\, cluster algebras\, and combinatorics (plane partitions\, Catalan numbers). I’ll give a gentle introduction to the amplituhedron\, then survey some recent progress on some of the main conjectures about the amplituhedron: the Magic Number Conjecture\, the BCFW tiling conjecture\, and the Cluster Adjacency conjecture.  Based on joint works withEvan-Zohar\, Lakrec\, Parisi\, Sherman-Bennett\, and Tessler.
URL:https://cmsa.fas.harvard.edu/event/colloquium_9924/
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-09.09.2024.png
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