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Combinatorics and geometry of the amplituhedron

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Colloquium Speaker: Lauren Williams, Harvard University Title: Combinatorics and geometry of the amplituhedron Abstract: 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, […]

BPS Algebras in Landau-Ginzburg Models

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Speaker: Ahsan Khan (CMSA) Title: BPS Algebras in Landau-Ginzburg Models Abstract: 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 […]

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Periodic pencils of flat connections and their p-curvature

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Colloquium Speaker: Pavel Etingof (MIT) Title: Periodic pencils of flat connections and their p-curvature  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 […]

Mathematics around Twisted Holography

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Geometry and Quantum Theory Seminar Speaker: Keyou Zeng (CMSA) Title: Mathematics around Twisted Holography Abstract: 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 […]

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Symmetry groups in infinite dimensions

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Colloquium Speaker: Lisa Carbone, Rutgers University Title: Symmetry groups in infinite dimensions Abstract: 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 […]

Symplectic duality in examples

Science Center Hall E 1 Oxford Street, Cambridge, MA, United States

Geometry and Quantum Theory Seminar Speaker: Vasily Krylov, Harvard CMSA & Math Title: Symplectic duality in examples Abstract: 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, […]

Topological Invariants of gapped states through cosheaves

Science Center Hall E 1 Oxford Street, Cambridge, MA, United States

Geometry and Quantum Theory Seminar Speaker: Bowen Yang, Harvard CMSA Title: Topological Invariants of gapped states through cosheaves Abstract: We provide a proper mathematical framework for the constructions of topological invariants of gapped quantum states and interpret topological invariants of gapped states as lattice analogs of ’t Hooft anomalies in Quantum Field Theory. Our secondary […]

Local complexity measures in modern parameterized function classes for supervised learning

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Colloquium Speaker: Elisenda Grigsby, Boston College Title: Local complexity measures in modern parameterized function classes for supervised learning Abstract: The parameter space for any fixed architecture of neural networks serves as a proxy during training for the associated class of functions - but how faithful is this representation? For any fixed feedforward ReLU network architecture, it […]

Skein traces and curve counting

Science Center Hall E 1 Oxford Street, Cambridge, MA, United States

Geometry and Quantum Theory Seminar Speaker: Sunghyuk Park, Harvard CMSA Title: Skein traces and curve counting Abstract: Skein modules are vector space-valued invariants of 3-manifolds describing the space of line defects modulo skein relations (determined by a choice of a ribbon category). When the 3-manifold is S x I for some surface S, the skein […]