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Events for the weeks of October 4th – 16th

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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
Tue, Oct. 13 11am (350)	Number Theory Faculty & Postdoc Number Theory Open House
Tue, Oct. 13 1:30pm (Math 3…	Homotopy Theo Johnson-Freyd (Perimeter Institute for Theoretical Physics and Dalhousie University) X Abstract: Kitaev has argued that the spaces of n-dimensional invertible phases of matter, as n varies, fit together into the structure of an Omega-spectrum. It follows that each n-dimensional phase determines a (possibly trivial) character on the nth stable homotopy group of spheres. I will present an enforced-gaplessness theorem (conditional on some reasonable semisimplicity assumptions about the category of topological phases of matter): if this character is nontrivial, and not one of the six nontrivial Kervaire invariants, then the invertible phase is a topological insulator: a material all of whose boundary conditions have gapless conducting modes. This is joint work in progress with David Reutter. With six exceptions, nontrivial characters of spheres do not admit gappable boundary conditions Sponsored by the Meyer Fund
Tue, Oct. 13 1:30pm (Math350)	Math Phys Theo Johnson-Freyd (Perimeter Institute for Theoretical Physics and Dalhousie University) X Abstract: Kitaev has argued that the spaces of n-dimensional invertible phases of matter, as n varies, fit together into the structure of an Omega-spectrum. It follows that each n-dimensional phase determines a (possibly trivial) character on the nth stable homotopy group of spheres. I will present an enforced-gaplessness theorem (conditional on some reasonable semisimplicity assumptions about the category of topological phases of matter): if this character is nontrivial, and not one of the six nontrivial Kervaire invariants, then the invertible phase is a topological insulator: a material all of whose boundary conditions have gapless conducting modes. This is joint work in progress with David Reutter. With six exceptions, nontrivial characters of spheres do not admit gappable boundary conditions
Tue, Oct. 13 2:30pm (MATH 3…	Lie Theory Kelsey Brown (Colorado State University) TBD
Wed, Oct. 14 4:40pm (MATH 3…	Grad Student Seminar Alex Lajeunesse (CU Boulder) X TBD Tilting at Witt-mills: a Glimpse of Perfectoid Spaces
Thu, Oct. 15 11:15am (MATH …	Algebraic Geometry Jacob Cleveland (Colorado State University) X We show that birational toric Landau–Ginzburg models which are related by a crepant variation of GIT have isomorphic state spaces under mild assumptions, generalizing the state space LG/CY correspondence of Chiodo–Ruan. We prove that this isomorphism is canonical, and is induced by a Fourier–Mukai transform. In the special case that a toric LG model is a so-called geometric phase, we identify the LG state space with the cohomology of the associated hypersurface. The State Space Correspondence for Toric Landau-Ginzburg Models

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