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  • Amplituhedra, Cluster Algebras, and Positive Geometry

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

    Amplituhedra, Cluster Algebras, and Positive Geometry Dates: May 29-31, 2024 Location: Harvard CMSA, 20 Garden Street, Cambridge MA 02138 & via Zoom In recent years, a remarkable paradigm shift has occurred in understanding quantum observables in particle physics and cosmology, revealing their emergence from underlying novel mathematical objects known as positive geometries. The conference will […]

  • 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, […]

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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 […]

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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 […]

  • 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 […]

  • Higher Vapnik–Chervonenkis theory

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

    Colloquium Speaker: Artem Chernikov, University of Maryland Title: Higher Vapnik–Chervonenkis theory Abstract: Finite VC-dimension, a combinatorial property of families of sets, was discovered simultaneously by Vapnik and Chervonenkis in probabilistic learning theory, and by Shelah in model theory (where it is called NIP). It plays an important role in several areas including machine learning, combinatorics, mathematical […]

  • The mathematics of evolution

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

    Colloquium Speaker: Martin Nowak (Harvard) Title: The mathematics of evolution Abstract: All living systems are guided by evolutionary dynamics. Evolution is a search process which occurs in populations of reproducing individuals. The three fundamental forces of evolution are mutation, selection and cooperation. I will present basic ideas in the mathematical description of evolutionary dynamics, including quasi-species theory, evolutionary […]