Martin J Schmoll

Position:
Visiting Assistant Professor of Mathematical Sciences

Education:
PhD, Dynamical Systems, TU Berlin
MS, Dynamical Systems, Ergodic Therory, U. Goettingen

Professional Interests:
I study the Teichmueller geodesic flow motivated by questions on polygonal billiards. More precisely I look at the SL(2,R) action on families of Riemann surfaces equipped with a quadratic differential. Important questions are to classify SL(2,R)-orbit closures in moduli space (of quadratic differentials). More elaborate and related to the former is to prove Ratner Theorems with respect to the action of unipotent subgroups of SL(2,R). Significant progress has been made in the subject during the last 8 years by many mathematicians including medal decorated fellows such as C. T. McMullen, M. Kontsevich and A. Okounkov.

Professional Activities:
Invited: Dynamics of Lie group actions on parameter spaces. Sede Boqer, Israel. January 2-7 2007

Selected Publications:

• Schmoll, Martin Spaces of elliptic differentials. Algebraic and topological dynamics, 303--320, Contemp. Math., 385, Amer. Math. Soc., Providence, RI, 2005.
• Eskin, Alex; Masur, Howard; Schmoll, Martin Billiards in rectangles with barriers. Duke Math. J. 118 (2003), no. 3, 427--463.
• Schmoll, M. On the asymptotic quadratic growth rate of saddle connections and periodic orbits on marked flat tori. Geom. Funct. Anal. 12 (2002), no. 3, 622--649.

Related Web Sites:
Homepage.
Department of Mathematical Sciences.