Modular spaces of Riemann surfaces; Teichmuller Theory

researched Teichmuller theory hyperbolic geometry ergodic theory & symplectic geometry; found that a property of the modulus space corresponds to the number of simple closed geodesics of the hyperbolic surface; developed a simple proof for the theorem of Schur; proved William Thurston's earthquake flow on Teichmuller space is ergodic; 2014 with Alex Eskin & input from Amir Mohammadi proved complex geodesics & their closures in moduli space are surprisingly regular rather than irregular or fractal; made several contributions to the theory of moduli spaces of Riemann surfaces

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Category:
Mathematics

Completion Status:
yes

Patent Number:
N/A

Co-Inventor:
none