Advisor: Matilde Marcolli

Research Interests

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

Teaching

• 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

• Coupling of gravity to matter, spectral action and cosmic topology (with Matilde Marcolli and Kevin Teh), June 2011.

Publications

• A reconstruction theorem for almost-commutative spectral triples, Lett. Math. Phys. 100 (2012), no. 2, 181-202.
• 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.