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Events happening on September 25, 2018

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Sep. 25, 2018 11am (MATH 350)	Number Theory Robert Hines (CU Boulder) X We consider approximation of vectors $z∈ F⊗R≅Rr×Cs$ by elements of a number field $F$ and construct examples of badly approximable vectors. These examples come from compact subspaces of $SL2(OF) SL2(F⊗R)$ naturally associated to (totally indefinite, anisotropic) $F$ -rational binary quadratic and Hermitian forms, a generalization of the well-known fact that quadratic irrationals are badly approximable over $ℚ$ . Examples of badly approximable vectors over number fields
Sep. 25, 2018 1pm (MATH 220)	Peter Mayr X We show that if a constraint language does not have a WNU polymorphism, then its CSP is NP-complete. Then we discuss various kinds of local consistency checks and in particular (2,3)-minimal instances. CSP hardness and bounded width
Sep. 25, 2018 1pm (MATH 350)	Ulam V. Baranovsky (UC Irvine) X Let (X, w) be a complex projective manifold with a holomorphic symplectic form w. Assume for simplicity that the space of holomorphic 2-forms on X is one-dimensional. Then it is known that (symplectic) deformations of the pair (X, w) are described by the Beauville-Bogomolov quadric Q in the second complex cohomology H2(X, C). The goal of the talk is to understand Q in terms of algebraic deformation theory and the fact that the Koszul bracket on the de Rham complex of X is homotopy abelian. Joint work with D. Kaledin. L-infinity morphisms and the Beauville-Bogomolov quadric
Sep. 25, 2018 2pm (MATH 350)	Lie Theory Michael Strayer (University of North Carolina at Chapel Hill) X R.M. Green axiomatically defined full heaps and used them to build minuscule-like representations of many affine Kac-Moody algebras. Two other classes of colored posets, namely minuscule and d-complete posets, have also been used in many applications to Lie theory; for instance, they correspond to “dominant minuscule” elements of Kac-Moody Weyl groups. We present new poset coloring properties that unify the above three classes of colored posets and characterize various Kac-Moody (sub)algebra representations. These include the full heap representations of Green, the minuscule representations of semisimple Lie algebras, and Demazure modules of dominant minuscule Weyl group elements. We will give the classifications of colored posets satisfying the two most important sets of these properties. Minuscule Kac-Moody settings unified by new poset coloring properties Sponsored by the Meyer Fund
Sep. 25, 2018 2pm (MATH 220)	Michael Wheeler (CU Boulder) The regular and good ultrapowers, Part 1
Sep. 25, 2018 3pm (Math 350)	Algebraic Geometry Leo Herr (University of Colorado, Boulder) X We will introduce a variant of Gromov-Witten Theory for log smooth curves, and compare invariants of a product of log smooth varieties with the invariants of each. To make this possible, we will give brief introductions to both Gromov-Witten Theory (curve counting) and Log Geometry. This variant of the theory originated in the work of M. Gross and B. Siebert, and we offer a new perspective on it, accompanied by new theorems. The Log Gromov-Witten Product Formula
Sep. 25, 2018 4pm (MATH 350)	Topology Robin Deeley (CU Boulder) X I will begin with a discussion on the basic properties of C-algebras with an emphasis on examples. Next the notions of essentially self-adjoint and essentially normal operator will be defined and relationship between these operators and K-homology with be developed. The talk will very much be an introduction and hence accessible to a wide audience. An introduction to C-algebras and K-homology

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