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| Research |
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I am in interested in mathematics and its interaction with
all sciences, and education at the collegiate level. My view
on the sciences is through the mathematical windows of differential
geometry, analysis, and mathematical physics. Currently, I
am conducting research in the following sub-classes of these
general areas of mathematics:
- Geometry:
algebraic and differential Poisson geometry, Lie theory
- Analysis:
spectral theory of operators on manifolds
- Mathematical Physics:
constructive quantum field theory, generalized field theories in topology
With regards to education, I have worked extensively on the
development of ancillary materials and pedagogy for honors calculus/analysis and vector
calculus and I am very interested in the development of online
instructional tools and materials for the teaching of mathematics.
Within this section of my site, you can find some of my lecture
notes, download copies of my papers, follow links to brief video summaries
of their content, and download slides from selected lectures.
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Symplectic foliation of the Evens-Lu Poisson structure on the 2-sphere
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| Papers |
| Toric Poisson Structures, accepted: Moscow Mathematics Journal, arXiv:0910.0229
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| Download: pdf,
ps |
Video Summary |
| with Doug Pickrell, Homogeneous
Poisson structures on symmetric spaces, Int. Math. Res. Not. IMRN 2009, no. 1, Art. ID rnn126, 98--140, arXiv:0710.4484
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| Download: pdf,
ps |
Video Summary |
| Compact symmetric
spaces, triangular factorization, and Poisson geometry, J. Lie Theory 18 (2008), no. 2, 273--294,
arXiv:math.SG/0608454 |
| Download: pdf,
ps |
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| Poisson Structures
on U/K and Applications, Dissertation -- University
of Arizona |
| Download: pdf
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| Notes |
| Supersymmetric Euclidean Field Theories and Generalized Cohomology, Spring 2009, Lecture Notes from a topics course by Stephan Stolz |
| Download: pdf, ps , Last Updated: June 15, 2009 |
| C*-algebras and the GNS Construction, Summer 2010, Notes for a 2 hour survey lecture I gave for the ND Math/Physics seminar |
| Download: pdf, ps , Last Updated: July 16, 2010 |
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| Slides |
| Toric Poisson Structures, 20 November, 2009, Lie Theory Seminar, Cornell University. |
| Toric Poisson Structures, 24 October, 2009, Special Session on Integrable Systems and Related Areas, Eastern Sectional Meeting of the AMS, Penn State University. |
| Perspectives from Poisson Geometry, 29 February 2008, Colloquium: University College Cork, Ireland. |
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