Save Big on Coursera Plus. 7,000+ courses at $160 off. Limited Time Only! Grab it Explore a mathematical seminar from the Joint IAS/PU Groups and Dynamics series where Omri Solan from Hebrew University of Jerusalem delves into the complex behavior of SL_2(R) action on Teichmuller dynamics. Learn about the nonhomogeneous example of SL_2(R) action on space H_g and its preservation of finite measure, particularly in relation to the moduli space of genus g curves. Examine McMullen's identification of SL_2(R).x orbits where x has infinitely generated SL_2(R)-stabilizers, and discover how these stabilizers are analyzed through their critical exponent. Understand the proof that demonstrates these stabilizers' critical exponent is uniformly bounded away from 1, establishing their uniform distance from being a lattice.