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Events happening on April 3, 2018

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Apr. 03, 2018 11am (MATH 350)	Number Theory Bill Duke (UCLA) X This is joint with Nick Andersen. We introduce some analogues of the Markov spectrum defined in terms of modular billiards and consider the problem of characterizing that part of the spectrum below the lowest limit point. Markov spectra for modular billiards
Apr. 03, 2018 2pm (MATH 350)	Lie Theory Jieru Zhu (Oklahoma) X The hyperoctahedral group is the wreath product between the cyclic group of order 2 and the symmetric group. In 1997, Green defined the hyperoctahedral Schur algebra as the centralizer of the hyperoctahedral group acting on a tensor space. This action commutes with a Levi Lie subalgebra of the general linear Lie algebra, where the two actions fully centralize each other, and the Schur algebra is a quotient of the tensor product of quantum groups. This leads to two presentations of the Schur algebra, and is also true when the cyclic group has higher orders, when the centralizer is called the cyclotomic Schur algebra. One presentation implies a categorification of the cyclotomic Schur algebra, following the categorification of the quantum groups by Khovanov-Lauda-Rouquier. Presenting and categorifying cyclotomic Schur algebras Sponsored by the Meyer Fund
Apr. 03, 2018 3pm (MATH 350)	Algebraic Geometry Dawei Chen (Boston College) X An abelian differential induces a flat metric such that the underlying Riemann surface can be realized as a plane polygon. Varying the shape of such polygons induces a GL(2,R)-action on the moduli space of abelian differentials. The corresponding GL(2,R)-orbit closures are called affine invariant submanifolds, where "affine" refers to the locally linear structure under the period coordinates. In this talk we explore the amusing question whether affine invariant submanifolds are affine varieties in the sense of algebraic geometry. Are affine invariant submanifolds affine? Sponsored by the Meyer Fund
Apr. 03, 2018 4pm (MATH 220)	Topology Katharine Adamyk (CU Boulder) X Abstract: In this talk, we will consider stable model categories (under some conditions) with a set of compact generators. A theorem of Schwede and Shipley describes an equivalence between the homotopy categories of such a model category and the endomorphism category of the set of generators. In particular, we will see that an equivalence can be given by replacing the model category with an appropriate category of symmetric spectra. Some familiarity with model categories and their homotopy categories will be assumed, but there will be a brief overview of these topics, as well as an introduction to symmetric spectra. Classification of Stable Model Categories
Apr. 03, 2018 4pm (MATH 350)	Algebraic Geometry Matt Grimes (Boston College) X Title: Contracting the Weierstrass locus with variation of GIT Abstract: A fundamental problem in the study of moduli spaces is constructing quotient spaces under a group action. The solution of Geometric Invariant Theory is to select a subspace for which the group action is well-behaved. In general, there can be many such subspaces, which leads to variation of GIT. The goal of the talk is to discuss recent work in which VGIT allows us to construct several related moduli spaces of marked genus two curves. Along the way, we will emphasize accessibility and background by discussing the ideas behind GIT as well as important examples. Contracting the Weierstrass locus with variation of GIT Sponsored by the Meyer Fund

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