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| Allen Back |
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| Senior Lecturer of Mathematics |
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Web Site Contact Information
Courses & Office Hours |
Education
Ph.D. (1977) University of California at Berkeley
Research Area: Differential geometry, dynamical systems
My original training was primarily in differential geometry and secondarily in topology. The most interesting portion of my earlier work was related to the role of compact Lie group actions in differential geometry, especially curvature realizability questions. I've been impressed by a variety of recent progress in this area (e.g. Einstein metrics and positive Ricci curvature on many cohomogeniety one manifolds) and have been working on what further directions may now be fruitful.
Besides equivariant differential geometry, other areas of past work and interest include transformation groups, homotopy theory, dynamical systems, some parts of mathematical physics, geometric modeling and robotics. My work as director of the Instructional Computing Lab has also meshed with a long-standing interest in the use of computers for mathematical enrichment.
Selected Publications
Rational Pontryagin classes and killing forms, J. Differential Geom. 16 no. 2 (1981), 191–193.
Pontryagin forms on homogeneous spaces, Comment. Math. Helv. 57 no. 3 (1982), 349–355.
Equivariant geometry and Kervaire spheres (with Wu Yi Hsiang), Trans. AMS 304 no. 1 (1987), 207–227.
dstool: Computer assisted exploration of dynamical systems (with J. Guckenheimer, M. Myers, F.J. Wicklin and P. Worfolk), Notices AMS 39 (1992), 303–309.
Mathematics and tensegrity (with R. Connelly), American Scientist March-April (1998), 142–151.
Last modified: June 6, 2005