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Events happening on September 22, 2015

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Sep. 22, 2015 10am (Math350)	Ryan Rosenbaum (Colorado) X TBD Lie groups?
Sep. 22, 2015 11am (MATH 350)	Number Theory Jayadev Athreya (University of Washington) X Given an Apollonian Circle Packing $𝒫$ and a circle $C0 = ∂ B(z0, r0)$ in $𝒫$ , color the set of disks in $𝒫$ tangent to $C0$ red. What proportion of the concentric circle $Cε = ∂ B(z0, r0 + ε)$ is red, and what is the behavior of this quantity as $ε → 0$ ? Using equidistribution of closed horocycles on the modular surface $H2/SL(2, Z)$ , we show that the answer is $3/π = 0.9549$ We also describe an observation due to Alex Kontorovich connecting the rate of this convergence in the Farey-Ford packing to the Riemann Hypothesis. For the analogous problem for Soddy Sphere packings, we find that the limiting radial density is $3/2VT=0.853$ , where $V_{T}$ denotes the volume of an ideal hyperbolic tetrahedron with dihedral angles $π/3$ . Radial Density in Apollonian Packings
Sep. 22, 2015 12:10pm (MATH …	Kempner Piotr Hajac (Polish Academy of Sciences and University of New Brunswick) X In terms of multipullback C-algebras, we construct a noncommutative deformation of odd-dimensional spheres that preserves the natural partition of the (2n+1)-dimensional sphere into (n+1)-many solid tori. The aim of this talk is to explain in an elementary way basic ideas proving that the noncommutative line bundles associated to the multipullback quantum (2n+1)-dimensional sphere are pairwise stably non-isomorphic. In particular, we conclude that the tautological line bundles over the multipullback quantum complex projective spaces are not stably trivial. First, we use the technology of higher-rank graph C-algebras to prove that our multipullback C*-algebras are universal for commuting isometries satisfying a sphere equation. Furthermore, by finding a strong connection, we show that the natural U(1)-action on our quantum (2n+1)-dimensional sphere is free. This puts us in the framework of Chern-Galois theory which, combined with the aforementioned universal presentation, reduces the pairwise non-isomorphism problem from dimension 2n+1 to dimension 3. The latter case is handled by an index pairing computation thus completing the proof. By very ample references to the standard geometry of odd-dimensional spheres thought of as U(1)-principal bundles over complex projective spaces, the talk will be accessible to non-experts. (Based on joint work with David Pask, Aidan Sims and Bartosz Zielinski.) Multidimensional line bundles associated to multipullback quantum odd spheres
Sep. 22, 2015 1pm (MATH 220)	Peter Mayr (CU Boulder) X The subpower membership problem (SMP) for a fixed finite algebra A has as input tuples a_1,...a_k and b in A^n. The question is whether b belongs to the subalgebra of A^n that is generated by a_1,...a_k. The SMP arises from the question whether relations (subalgebras of powers) can be efficiently represented by generators. We consider the complexity of the problem for various algebras. Introduction to the Subpower Membership Problem
Sep. 22, 2015 1pm (Math350)	Stephen Preston Riemannian geometry overview, part 3 of 3
Sep. 22, 2015 2pm (MATH 350)	Lie Theory Jon Lamar (CU) X Let G be a group and let SCT(G) be the set of all supercharacter theories of G. We can endow SCT(G) with a natural partial order, which in fact gives this set the structure of a lattice. From this jumping-off point, we can study the interplay between the combinatorics of SCT(G) and the algebra of G. In this talk, I will summarize what is already known about the lattice of supercharacter theories of a group, as well as present some new results and open problems along these directions. Poset Theory of Supercharacters
Sep. 22, 2015 2pm (MATH 220)	Keith Kearnes (CU) Tame Congruence Theory
Sep. 22, 2015 3pm (Math 350)	Markus Pflaum (CU Boulder) Foundations of Deformation Quantization (continued)
Sep. 22, 2015 4pm (Math 350)	Alexander Nita (CU Boulder) Fedosov's Deformation Quantization

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