Either mathematics is too big for the human mind or the human mind is more than a machine.

K. Godel

I am a member of the School of Math at the Institute for Advanced Study, and an assistant professor of Mathematics at Washington University. I am interested in problems in dynamics, spectral geometry, and differential equations. I tend to work on physically motivated problems, and those where the tools of analysis are useful.

Now I am working on bifurcation theory and spectral geometry of integrable systems with Laurent Charles, Tudor Ratiu and San Vu Ngoc. I am also incorporating probabilistic methods into symplectic dynamics with Fraydoun Rezakhanlou, and working on type theory for integrable systems, with Vladimir Voevodsky, and Michael Warren.

I have taught algebra, calculus, geometry and analysis, at both the undergraduate and graduate levels.

Announcements:

• November 2011: solution to isospectral problem for quantum toric integrable systems posted in Publications
• July 2011: Plenary Lecture at Congress of the Belgian, Royal Spanish and Luxembourg Mathematical Societies (announced)
• April 2011: NSF CAREER Award is official
• March 2011: Honorary position at Spanish National Research Council
• February 2011: Ceremony for the Rubio de Francia Prize 2010
  
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