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Research 
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 subclasses 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.

Symplectic foliation of the EvensLu Poisson structure on the 2sphere

Papers 
Toric Poisson Structures, Moscow Math. J., 11 (2) 2011, pp. 205229

Download: pdf

Video Summary 
with Doug Pickrell, Homogeneous
Poisson structures on symmetric spaces, Int. Math. Res. Not. IMRN 2009, no. 1, Art. ID rnn126, 98140, arXiv:0710.4484

Download: pdf,
ps 
Video Summary 
Compact symmetric
spaces, triangular factorization, and Poisson geometry, J. Lie Theory 18 (2008), no. 2, 273294,
arXiv:math.SG/0608454 
Download: pdf,
ps 

Poisson Structures
on U/K and Applications, Dissertation  University
of Arizona 
Download: pdf



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 

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. 


