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Events happening on November 15, 2016

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Nov. 15, 2016 10am (MATH 220)	Number Theory Robert Hines (University of Colorado, Boulder) X We consider a pair of dynamical systems on the complex plane inspired by the action of the super-Apollonian group, realized here as reflections in the sides of a right-angled ideal hyperbolic octahedron. These systems are “reflective” versions of Asmus Schmidt’s continued fraction algorithms over Q(i). We study aspects of the dynamics including the natural extension, invariant measure, action on rational points, and restriction to the real line. Super-Apollonian Continued Fractions
Nov. 15, 2016 10am (MATH 350)	Geometry/Analysis Taylor Joseph Klotz (CU Boulder) X The famous Inverse Scattering Transform (IST) is a powerful method for finding solutions to so called Integrable Systems. It is considered to be a nonlinear analog of the Fourier Transform technique. By looking at the "scattering data" for two associated linear problems, we can reconstruct the solution to the nonlinear problem in question. We'll focus on what this method is, its inspiration, and work through an explicit example. Either the classic KdV (Korteweg de-Vries) equation or the NLS (nonlinear Schrodinger) equation. Focusing on the Inverse Scattering Transform
Nov. 15, 2016 12:10pm (MATH …	Kempner Youri Davydov (Université des Sciences et Technologies de Lille) X It is well known that the transformations of symmetrization introduced by Steiner for the proof of Isoperimetric Theorem play an important role in geometry and its applications. Another important transformation is the Minkowski (sometimes called Blaschke) symmetrization. In the talk, the asymptotic behavior of random sequences of successive Steiner and Minkowski symmetrizations is investigated. In the case of independent directions, we prove the almost sure convergence of successive symmetrizations at exponential rate for Minkowski, and at rate $-c n$ , with $c > 0$ , for Steiner. Random symmetrizations of convex bodies
Nov. 15, 2016 1pm (MATH 220)	Zak Mesyan (CU Colorado Springs) X Let V be an arbitrary vector space over a field K, and let End(V) be the ring of all K-linear transformations of V. We characterize the diagonalizable linear transformations in End(V), as well as the (simultaneously) diagonalizable subalgebras of End(V), generalizing results from classical finite-dimensional linear algebra. These characterizations are formulated in terms of a natural topology on End(V), which reduces to the discrete topology when V is finite-dimensional. (Based on joint work with Miodrag Iovanov and Manuel Reyes.) Infinite-Dimensional Diagonalization
Nov. 15, 2016 2pm (MATH 350)	Lie Theory Mandi Schaeffer-Fry (Metro State) X As a consequence to his Galois-McKay conjecture, G. Navarro has conjectured a necessary and sufficient condition for a finite group $G$ to have a self-normalising Sylow $2$ -subgroup, which is given in terms of the ordinary irreducible characters of $G$ . I will discuss this conjecture and my reduction to (quasi) simple groups. Then I’ll discuss the specific case of Type A. Galois Automorphisms and Self-Normalizing Sylow $2$ Subgroups
Nov. 15, 2016 2pm (MATH 220)	Mark Pulllins (CU) Bad groups, 3
Nov. 15, 2016 3pm (MATH 350)	Topology Leo Herr (CU Boulder) Grothendieck's Six Operations

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