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Events happening on November 11, 2014

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Nov. 11, 2014 11am (MATH 350)	Number Theory Leonhard Summerer (University of Vienna) X In this talk I want to introduce a method based on the geometry of numbers and in particular on the study of the successive minima functions with respect to a certain lattice and a suitable one-parameter family of convex bodies. This approach leads to the definition of some new approximation constants and in turn to some new transference inequalities. The related geometric picture in conjunction with some recent results of D. Roy motivates some best possible bounds in the case of simultaneous approximation of several real numbers. Geometry of Numbers and simultaneous Approximation
Nov. 11, 2014 12:10pm (MATH …	Kempner Anca Radulescu (SUNY New Paltz) X The behavior of orbits for iterated logistic maps has been widely studied since the dawn of discrete dynamics as a research field. Existing results refer not only to the family of real polynomials $f : ℝ \to ℝ$ , $fμ(x) =μ x(1-x)$ , for $μ >0$ , but also to the context of complex maps $f : ℂ \to ℂ$ , parametrized as $fc(z)=z2+c$ , with $c ∈ C$ . However, little is is known about orbit behavior if the map changes along with the iterations. \\ \noindent We investigate how the theory changes if the dynamical scheme involves two functions, $f0$ and $f1$ , iterated according to a prescribed binary sequence of $0$ s and $1$ s. In particular, we observe the effects of the structure of the symbolic sequence (periodicity, complexity, etc) on the complexity of the resulting system and (visually) on the topological structure of its Julia set.\\ \noindent This direction is of potential interest to a variety of applications (including genetic and neural coding), since it investigates how an occasional or a reoccurring error in a replication or learning algorithm may affect the outcome. Real and complex dynamics for symbolic sequences of logistic maps
Nov. 11, 2014 2pm (MATH 350)	Lie Theory Derek Wise (University of Erlangen) X While groups formalize the notion of symmetry, "2-groups" include also the idea that symmetries might be related to each other by symmetries of their own. I will explain 2-groups, which are categories equipped with a group-like multiplication, and discuss their representation theory. Just as groups have representations on vector spaces, 2-groups have representations on "2-vector spaces", which are categories analogous to vector spaces. For a simple reason that I will explain, the most interesting representations of Lie 2-groups are all infinite-dimensional. I will describe Lie 2-group representations on an appropriate kind of infinite-dimensional 2-vector space, and show that these can be nicely understood in terms of objects familiar from ordinary group representation theory and geometry. Higher Symmetry: Lie 2-Groups and their Representations Sponsored by the Meyer Fund
Nov. 11, 2014 11pm (Math 220)	Noncomm Geometry Josh Frinak X If $u:E0→ E1$ is morphism of complex vector bundles over a smooth manifold $M$ which is an isomorphism over a subset $A$ , then $u$ determines a class in the relative $K$ -group $K(M,A)$ . I intend to present Quillen's construction of the Chern character which involves the use of a $Z2$ -graded variant of the concept of a connection called a superconnection. Given a convenient choice of superconnection $𝔸$ we are interested in the curvature $θ=A2$ . It will turn out that the super trace of $e^{θ}$ will represent the Chern character, $ch E0-ch E1$ , in de Rham cohomology. Chern character via superconnections.

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