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Events happening on April 9, 2019

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Apr. 09, 2019 12:10pm (MATH …	Kempner Adam Sikora (State University of New York at Buffalo) X The Jones polynomial is simple to define, yet a mysterious invariant of links in R^3. It extends to links in thickened surfaces, leading to the notion of the skein algebra of a surface, which turns out to be a quantization of the Teichmuller space. We will study some fundamental properties of these algebras using the theory of measured foliations and pseudo-Anosov diffeomorphisms of surfaces. From the Jones polynomial to Quantum Teichmuller Theory
Apr. 09, 2019 1pm (Math 245)	Thesis Defenses Jon Belcher (CU Boulder) X The connection between Hochschild and cyclic cohomologies with generalized De Rham homology and index theories for arbitrary algebras has long been established by the work of Connes, Karoubi, Loday, Feigin, Tsygan, et al. Here we generalize these cohomology theories even further, essentially creating a theory that establishes a step-wise bridge between the two. Motivation for this construction comes from trying to generalize the Hochschild-Kostant-Rosenberg-Connes theorem to manifolds with boundary, and applications in tracial constructions in certain classes of pseudo-differential operators. Further geometric and topological interests of this theory include extending Chern-Weil theory to manifolds with boundary via pairings between bridge cohomology and higher K-theories. Bridge Cohomology
Apr. 09, 2019 1pm (MATH 220)	Thesis Defenses Steven Weinell (CU Boulder) X This thesis characterizes the potential behaviors of higher commutators in a simple algebra. On the Descending Central Series of Higher Commutators
Apr. 09, 2019 1pm (MATH 220)	Steven Weinell (CU Boulder) X This thesis characterizes the potential behaviors of higher commutators in a simple algebra. On the Descending Central Series of Higher Commutators (Thesis defense)
Apr. 09, 2019 2pm (MATH 350)	Lie Theory Farid Aliniaeifard (University of Colorado Boulder) X The theory of $P$ -partitions was introduced by Stanley, and a $P$ -partition can be viewed as a generalization of the tableaux. Stembridge introduced enriched $P$ -partitions, and these combinatorial objects are a generalization of the shifted Young tableaux. The polynomials corresponding to the enriched $P$ -partitions produce the peak algebra. We introduce and develop a theory of colored $P$ -partitions and colored enriched $P$ -partitions, and this theory give us tools to define the peak algebra in non-commutating variables. In the end, we generalize the peak algebra to an arbitrary combinatorial Hopf algebra. This is joint work with Shu Xiao Li. Hopf structures in algebra and combinatorics: The peak algebra
Apr. 09, 2019 2pm (MATH 220)	Steven Weinell (CU Boulder) On the Descending Central Series of Higher Commutators (Thesis defense)
Apr. 09, 2019 4pm (MATH 350)	Topology Michael Hermele (CU Boulder) Extended Topological Field Theories and the Cobordism Hypothesis

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