Algebraic Geometry Seminar
Please see the following for more related talks:
- Friday, September 20, 2019, 3:15pm, 119 Physics, Algebraic Geometry Seminar
The Moduli Space of Matroids
Matt Baker (Georgia Tech, Mathematics)
- I will begin with an introduction to hyperfields (originally introduced by Krasner for number-theoretic reasons), and then discuss a far-reaching generalization, Oliver Lorscheid’s theory of ordered blueprints. Two key examples are the sign hyperfield S and the tropical hyperfield T. I will discuss a common generalization, in this language, of Descartes' Rule of Signs (which involves polynomials over S) and the theory of Newton Polygons (which involves polynomials over T). I will then give a quick introduction to matroids and explain how the theory of ordered blueprints and ordered blue schemes allow us to construct a "moduli space of matroids", which can be viewed as an enhancement of the usual Grassmannian variety in algebraic geometry. This is joint work with Oliver Lorscheid.
- Friday, September 27, 2019, 3:15pm, 119 Physics, Algebraic Geometry Seminar
Moduli of symmetric cubic fourfolds and nodal sextic curves
Chenglong Yu (U Penn)
- Period map is a powerful tool to study geometric objects related to K3 surfaces and cubic 4-folds. In this talk, we focus on moduli of cubic 4-folds and sextic curves with specified symmetries and singularities. We identify the geometric (GIT) compactifications with the Hodge theoretic (Looijenga, mostly Baily-Borel) compactifications of locally symmetric varieties. As a corollary, the algebra of GIT invariants is identified with the algebra of automorphic forms on the corresponding period domains. One of the key inputs is the functorial property of semi-toric compactifications of locally symmetric varieties. Our work generalizes results of Matsumoto-Sasaki-Yoshida, Allcock-Carlson-Toledo, Looijenga-Swierstra and Laza-Pearlstein-Zhang. This is joint work with Zhiwei Zheng.
- Friday, October 4, 2019, 3:15pm, 119 Physics, Algebraic Geometry Seminar
Rigidity of Schubert varieties in rational homogeneous manifolds of Picard number one
Jaehyun Hong (Korea Institute for Advanced Study)
- Given a rational homogeneous manifold S=G/P of Picard number one and a Schubert variety S_0 of S, the pair (S,S_0) is said to be homologically rigid if any subvariety of S having the same homology class as S_0 must be a translate of S_0 by G. The pair (S,S_0) is said to be Schur rigid if any subvariety of S with homology class equal to a multiple of the homology class of S_0 must be a sum of translates of S_0. In this talk we use the theory of minimal rational curves to get homological rigidity and apply a refined form of transversality to reduce Schur rigidity to homological rigidity, proving that (S,S_0) exhibits Schur rigidity whenever S_0 is a non-linear smooth Schubert variety. This is joint work with N. Mok.
- Friday, November 1, 2019, 3:15pm, 119 Physics, Algebraic Geometry Seminar
- Friday, November 8, 2019, 3:15pm, 119 Physics, Algebraic Geometry Seminar
Sarah J Frei (U Oregon)
- Friday, November 15, 2019, 3:15pm, Physics 119, Algebraic Geometry Seminar
- Friday, November 22, 2019, 3:15pm, Physics 119, Algebraic Geometry Seminar
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