Teichmuller discs with completely degenerate Kontsevich-Zorich spectrum- David Aulicino

Conference Title: GEAR Retreat 2012 Theme: Dynamics on Moduli Spaces (4 of 5) Title: Teichmuller discs with completely degenerate Kontsevich-Zorich spectrum Speaker: David Aulicino, University of Maryland; Date and Time: Thursday August 9, 14:40 Description: We consider the Lyapunov exponents of the Kontsevich-Zorich cocycle over the moduli space of Abelian dfferentials with respect to SL(2,R)-invariant ergodic probability measures. Eskin-Kontsevich-Zorich asked for a classfication of all such measures whose Lyapunov spectrum is completely degenerate. We approach the problem by studying SL(2,R)-invariant sets called Teichmuller discs, and prove that their closures cannot support a measure with completely degenerate spectrum for g = 2 and g greater than or equal to 13. In genus three and four, we prove that the known examples are the only ones. Finally, if there are no square-tiled surfaces in genusfive whose orbit supports such a measure, then there are no such measures for g greater than or equal to5. Time permitting we discuss partial results (with Vincent Delecroix) toward showing that no such surfaces in genusfive exist. Sponsor: GEAR Network Local host: UIUC Department of Mathematics Funding provided by: National Science Foundation Research Networks in Mathematical Sciences programAbstract: David Aulicino, in this GEAR Retreat 2012 session on Dynamics on Moduli Spaces, will discuss the results of studying Teichmuller discs in relation to Lyapunov exponents of the Kontsevich-Zorich cocycle.