Homepage of Jayadev Athreya

Contact information

Teaching

I am teaching Math 202 (Linear Algebra) this semester (Spring 2008). You can find a pdf version of my teaching statement here. For course information, please see the Blackboard site.

Research interests

My research interests are in geometry and dynamical systems

My primary area of research is the study of dynamics of Lie group actions on various parameter spaces. In particular, I study the dynamics of the SL(2, R) action on moduli spaces of abelian and quadratic differentials, as well as dynamics on the space of lattices, both over the reals and over fields of positive characteristic.

These subjects lie at the intersection of low-dimensional topology, ergodic theory, dynamics of group actions, and diophantine approximation.

For more information, you can see the full text of my Research Statement (pdf). (this needs to be updated, but should have mostly correct information)

Relevant publications and preprints

1. Deviation of ergodic averages for rational polygonal billiards (joint with Giovanni Forni), to appear in Duke Mathematical Journal.
2. Quantitative recurrence and large deviations for Teichmuller geodsic flow, Geometriae Dedicata, April 2006
3. Lattice point asymptotics and volume growth on Teichmuller space, (joint with Sasha Bufetov, Alex Eskin, and Maryam Mirzakhani)
4. Diophantine approximation and Borel-Cantelli laws in positive characteristic (joint with Anish Ghosh and Amri Prasad), see the announcement
5. Rectangular billiards and quadratic differentials (joint with Alex Eskin and Anton Zorich), work in progress
6. Logarithm laws for unipotent flows (joint with Gregory Margulis), work in progress
7. Logarithm laws for unipotent flows on spaces of quadratic differentials (joint with Yair Minsky), work in progress

Other publications and preprints

1. Number theory, balls in boxes, and the asymptotic uniqueness of maximal discrete order statistics, with L. Fidkowski, INTEGERS: Electronic Journal of Combinatorial Number Theory, volume 0, 2000.
2. On the asymptotics of discrete order statistics, with S. Sethuraman, Statistics and Probability Letters, v. 54, issue 3, 2001, pp. 243-249
3. More methods of lion-hunting that every graduate student should know. This is joint with Apoorva Khare (University of Chicago).
   
   
   

Conferences

Anish Ghosh, David Ellwood, Dmitry Kleinbock, and I are organizing a workshop on Shrinking Target Properties, from Jan 31-Feb 3 2008 at Brandeis University and the Clay Mathematics Institute. More details can be found here.