HOME
RESEARCH
TEACHING
MATHEMATICS
PERSONAL

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 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.

Symplectic foliation of the Evens-Lu Poisson structure on the 2-sphere

Papers
Toric Poisson Structures, Moscow Math. J., 11 (2) 2011, pp. 205--229
Download: pdf 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
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
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.