Advisor: Matilde Marcolli

Research Interests

• Noncommutative geometry, particularly noncommutative Riemannian geometry via spectral triples.
• Applications of noncommutative geometry to mathematical physics.

Teaching

• Spring 2013 - TA for Ma Ma 1c Practical (Vector Calculus).
• Winter 2013 - Lead TA for Ma 1b Practical (Linear Algebra).
• Fall 2012 - TA for Ma 2a Analytic (Differential Equations).
• Winter 2012 - Grader for Ma 108b (Classical Analysis).
• Fall 2011 - Grader for Ma 110a (Analysis I).
• Spring 2011 - TA for Ma 4c (Fractal Geometry and Chaos Theory), Ma 148c (Quantum Physics for Mathematicians).
• Winter 2011 - TA for Ma 1b Analytic (Linear Algebra).
• Fall 2010 - TA for Ma 1a (Calculus).
• Spring 2010 - TA for Ma 1c Practical (Vector Calculus).
• Winter 2010 - TA for Ma 1b Practical (Linear Algebra).
• Fall 2009 - TA for Ma 1a (Calculus).

Preprints

• A reconstruction theorem for toric noncommutative manifolds (in preparation).

Publications

• Real structures on almost-commutative spectral triples, to appear in Letters in Mathematical Physics.
• Coupling of gravity to matter, spectral action and cosmic topology (with Matilde Marcolli and Kevin Teh), to appear in Journal of Noncommutative Geometry.
• A reconstruction theorem for almost-commutative spectral triples, Lett. Math. Phys. 100 (2012), no. 2, 181-202. (Erratum, June 2012, incorporated into the latest arXiv version)
• Moduli spaces of Dirac operators for finite spectral triples, in Quantum Groups and Noncommutative Spaces: Perspectives on Quantum Geometry (eds. M. Marcolli, D. Parashar), Vieweg Verlag, 2010.