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Events happening on February 21, 2017

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Feb. 21, 2017 11am (MATH 350)	Number Theory Arthur Baragar (University of Nevada Las Vegas) X The Apollonian circle and sphere packings are well known classical objects. The four dimensional analog, though, has long been thought to not exist, owing to a perceived obstruction. In this talk, we describe the four dimensional analog and the obstruction. Most of the talk will be geometrical, requiring little background, and with only a little emphasis on the connection to number theory. Near the end of the talk, if time permits, we will describe how all these objects can be thought of as ample cones for elliptic K3 surfaces. Apollonian packings in higher dimensions and ample cones on K3 surfaces
Feb. 21, 2017 12:10pm (Math …	Kempner Peter Elliott (CU Boulder) X A short history of key theorems and their methodology will be given , leading to more recent results and an open ended problem that appears disarmingly simple. Asymptotic estimates for mean values of multiplicative functions, then and now
Feb. 21, 2017 1pm (MATH 220)	Jeffrey Shriner (CU Boulder) X For a fixed finite algebra A, the subpower membership problem is the decision problem which asks, given tuples a_1,...,a_n,b of A^m, is b in the subalgebra generated by a_1,...,a_n? We are interested in classifying the complexity of this problem, which is dependent on the algebra A. Much work has been done towards this goal, though there are still large unanswered questions, particularly within congruence modular varieties. We present an example of an algebra with a Taylor term whose subpower membership problem is NP-hard, and show how this example extends to other examples of interest within congruence modular varieties. NP-hardness Results for the Subpower Membership Problem, Part 1
Feb. 21, 2017 2pm (MATH 220)	Jakub Bulin (CU) X The aim of this talk series is to present Zhuk's technique of untangling primitive positive definitions of essential relations into formulas of tree shape. This technique was successfully applied to obtain several important results about finitely related algebras. Most recently, Barto's proof of the Valeriote conjecture: In a congruence modular variety, all finitely related algebras have few subpowers. Blockers, loop lemmata and tree formulas, 1
Feb. 21, 2017 3pm (Math 220)	Functional Analysis Alex Kumjian (University of Nevada, Reno) X Let $G$ be an amenable locally compact groupoid, and let $A$ be a closed subgroup of a locally compact abelian group $B$ . Given a $B/A$ -valued $1$ -cocycle $ϕ$ on $G$ , there is a central extension $Σ_{ϕ}$ of $G$ by $A$ that is trivial iff $ϕ$ lifts to a $B$ -valued cocycle. We prove that $C(Σφ)$ is isomorphic to the induced algebra of the natural action of $B/A$ on $C(G)$ . We also consider a simple class of examples arising from Cech $1$ -cocycles. This is joint work with Marius Ionescu. Obstructions to Lifting Cocycles on Groupoids and the Associated $C^{*}$ -Algebras (Part III)
Feb. 21, 2017 3pm (Math 350)	Algebraic Geometry Graeme Wilkin (NUS) X Title: The reverse Yang-Mills-Higgs flow in the neighbourhood of a critical point Abstract: The Yang-Mills-Higgs flow was originally studied by Simpson in the context of constructing Hermitian-Einstein metrics on Higgs bundles. Methods of Donaldson and Simpson show that the Yang-Mills-Higgs flow resembles a nonlinear heat equation on the space of Hermitian metrics on the bundle and therefore the downwards flow is well-behaved with respect to existence and uniqueness, and it also has nice smoothing properties. On the other hand, the reverse flow is ill- posed and therefore even existence of solutions is problematic. In this talk I will describe a new method to construct long-time solutions to the reverse Yang-Mills-Higgs flow that converge to a given critical point. The methods naturally lead to an algebraic criterion for two critical points to be connected by a flow line and a geometric condition to distinguish between broken and unbroken flow lines in terms of secant varieties of the underlying curve. If time permits I will talk about work in progress to describe the compactification of the space of flow lines in terms of the geometry of secant varieties. The reverse Yang-Mills-Higgs flow in the neighbourhood of a critical point Sponsored by the Meyer Fund
Feb. 21, 2017 4pm (MATH 350)	Topology Andy Riddle (CU Boulder) Thom Spectra and the Pontryagin-Thom Theorem

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