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From Grand Canyon to Yosemite: Lessons learned from the development and assessment of digital geoscience field trips for mobile smart devices
How geoscience apps are enhancing students' understanding of the geology of places such as Grand Canyon and Yosemite national parks
Bimodule deformations, Picard groups and contravariant connections
We study deformations of invertible bimodules and the behavior of Picard
groups under deformation quantization. While K_0-groups are known to be stable
under formal deformations of algebras, Picard groups may change drastically. We
identify the semiclassical limit of bimodule deformations as contravariant
connections and study the associated deformation quantization problem. Our main
focus is on formal deformation quantization of Poisson manifolds by star
products.Comment: 32 pages. Minor corrections in Sections 5 and 6, typos fixed. Revised
version to appear in K-theor
Algebraic Rieffel Induction, Formal Morita Equivalence, and Applications to Deformation Quantization
In this paper we consider algebras with involution over a ring C which is
given by the quadratic extension by i of an ordered ring R. We discuss the
*-representation theory of such *-algebras on pre-Hilbert spaces over C and
develop the notions of Rieffel induction and formal Morita equivalence for this
category analogously to the situation for C^*-algebras. Throughout this paper
the notion of positive functionals and positive algebra elements will be
crucial for all constructions. As in the case of C^*-algebras, we show that the
GNS construction of *-representations can be understood as Rieffel induction
and, moreover, that formal Morita equivalence of two *-algebras, which is
defined by the existence of a bimodule with certain additional structures,
implies the equivalence of the categories of strongly non-degenerate
*-representations of the two *-algebras. We discuss various examples like
finite rank operators on pre-Hilbert spaces and matrix algebras over
*-algebras. Formal Morita equivalence is shown to imply Morita equivalence in
the ring-theoretic framework. Finally we apply our considerations to
deformation theory and in particular to deformation quantization and discuss
the classical limit and the deformation of equivalence bimodules.Comment: LaTeX2e, 51pages, minor typos corrected and Note/references adde
Lie groupoids and the Frolicher-Nijenhuis bracket
The space of vector-valued forms on any manifold is a graded Lie algebra with
respect to the Frolicher-Nijenhuis bracket. In this paper we consider
multiplicative vector-valued forms on Lie groupoids and show that they
naturally form a graded Lie subalgebra. Along the way, we discuss various
examples and different characterizations of multiplicative vector-valued forms.Comment: 16 pages. Appeared in special volume of the Bull. Braz. Math. Society
in 2013 (IMPA 60 years
A Tear in the Iron Curtain: The Impact of Western Television on Consumption Behavior
This paper examines the impact of exposure to foreign media on the economic behavior of agents in a totalitarian regime. We study private consumption choices focusing on former East Germany, where differential access to Western television was determined by geographic features. Using data collected after the transition to a market economy, we find no evidence of a significant impact of previous exposure to Western television on aggregate consumption levels. However, exposure to Western broadcasts affects the composition of consumption, biasing choices in favor of categories of goods with high intensity of pre-reunification advertisement. The effects vanish by 1998
The characteristic classes of Morita equivalent star products on symplectic manifolds
In this paper we give a complete characterization of Morita equivalent star
products on symplectic manifolds in terms of their characteristic classes: two
star products and on are Morita equivalent if and
only if there exists a symplectomorphism such that
the relative class is 2 \pi \im-integral. For star
products on cotangent bundles, we show that this integrality condition is
related to Dirac's quantization condition for magnetic charges.Comment: 22 pages. A few corrections made to Sections 3.2 and 3.
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