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Events for the weeks of September 27th – October 9th

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Tue, Sep. 29 2:30pm (MATH 3…	Lie Theory Katrina Barron (Notre Dame University) X We recall some aspects of the representation theory for Lie algebras and how some number theory makes an appearance through characters for modules. We motivate why this occurs by putting this in the setting of vertex operator algebras which are the algebras that naturally arise from the geometry of Conformal Field Theory (or string theory). We discuss how analytic properties can be proved in certain settings by the construction of a modular linear differential equation, including recently in a new setting through joint work with Florencia Orosz Hunziker and Gaywalee Yamskulna. Why should we expect number theoretic properties to arise in Lie theory and group theory? Sponsored by the Meyer Fund
Tue, Sep. 29 3:30pm (MATH 3…	Topology Emily Montelius (CU Boulder) Introduction to Topological Data Analysis and seminar organization
Wed, Sep. 30 2:30pm (Math350)	Math Phys Markus J. Pflaum (CU Boulder) State spaces in quantum mechanics Part 3: Invariant Theory
Wed, Sep. 30 4:30pm (Math 2…	Homotopy Jesse Keyes (University of Kentucky) X Using the Hill-Hopkins-Ravenel norm, one can produce a G-equivariant analog N_{C_2}^{G} MU_R of the Real bordism spectrum for any group G containing a cyclic group of order two. In the case that G is a cyclic 2-group, the slice spectral sequence associated to N_{C_2}^{C_{2^k}} MU_R was a critical component in the resolution of the Kervaire-invariant one problem by Hill-Hopkins-Ravenel. We focus on the case that G is the quaternion group Q_8 and give an identification of the zero slice of N_{C_2}^{Q_8} MU_R, highlighting a computational technique for determining objects like this. Further, we give a computation of a portion of the RO(Q_8)-graded homotopy of this zero slice. The Zero Slice of Quaternionic Real Bordism Sponsored by the Meyer Fund
Thu, Oct. 1 11:15pm (MATH …	Algebraic Geometry Sachi Hashimoto X Let X be a curve of genus at least 2. By Faltings’ theorem, we know that X has finitely many rational points, but how can we actually determine this set in practice? Around 40 years before Faltings’ proof, Chabauty proved this finiteness theorem for certain curves by studying the embedding of X inside an abelian variety, the Jacobian variety of X. In the first part of my talk, I will explain Chabauty’s original method and the modern day extension “Geometric linear Chabauty” that makes this effective. In the second part of my talk, I will describe recent progress to extend Chabauty’s method to a broader class of curves by studying line bundles over the Jacobian (arising from pullbacks of the Poincare bundle). The math in these talks arises out of work of Edixhoven and Lido, and also reflects joint work with Spelier, Lido, Lombardo, Mascot, and Parent. Geometric methods for determining rational points on curves I and II
Fri, Oct. 2 1:25pm (Math 3…	A. I. TBA TBA
Wed, Oct. 7 4:40pm (MATH 3…	Grad Student Seminar Colin Jackson (CU Boulder) X Some numbers are rational, a few more are algebraic, but most are transcendental. We will briefly cover some definitions, investigate some special cases of numbers, and finally look at some positive results in transcendental number theory. Rational, Algebraic, or Transcendental?
Thu, Oct. 8 11:15am (MATH …	Algebraic Geometry Sachi Hashimoto X Let X be a curve of genus at least 2. By Faltings’ theorem, we know that X has finitely many rational points, but how can we actually determine this set in practice? Around 40 years before Faltings’ proof, Chabauty proved this finiteness theorem for certain curves by studying the embedding of X inside an abelian variety, the Jacobian variety of X. In the first part of my talk, I will explain Chabauty’s original method and the modern day extension “Geometric linear Chabauty” that makes this effective. In the second part of my talk, I will describe recent progress to extend Chabauty’s method to a broader class of curves by studying line bundles over the Jacobian (arising from pullbacks of the Poincare bundle). The math in these talks arises out of work of Edixhoven and Lido, and also reflects joint work with Spelier, Lido, Lombardo, Mascot, and Parent. Geometric methods for determining rational points on curves I and II
Fri, Oct. 9 1:25pm (Math 3…	A. I. Zak Miller TBA

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