Homepage of Jayadev Athreya

Contact information

Teaching

This semester (Spring 2012) I am teaching Math 428, the Honors Capstone Course. For course information, please see the course wiki.

Outreach

I direct the Illinois Geometry Lab, a new initiative to involve undergraduate students in research and outreach projects involving geometry and visualization.

I recently wrote a piece on Apollonian circle packings for the Indian children's science magazine Brainwave.

In Fall 2011, I worked with Anne Sautmann, the director of education at the Krannert Art Museum on a workshop on the interactions between art and mathematics for high school teachers.

In Summer 2011, I worked with students and teachers at the Chirag School, in the Indian state of Uttarakhand, to develop curriculum focusing on geometry and pattern recognition.

Research interests

My research interests are in geometry and dynamical systems, andy 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 \(SL(2, \mathbb R)\) 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.

Awards and Support

My research has been supported by a NSF Postdoctoral Fellowship (DMS 0603636), and currently I am the holder of an NSF PI grant (DMS 1069153), and am also supported by the University of Illinois Campus Research Board. I am also a member of the GEometric structures And Representation varieties (GEAR) NSF Research Network. For further information, please see my CV.

Publications

(In reverse chronological order)

1. The distribution of gaps for saddle connection directions, (joint with Jon Chaika), to appear in Geometric and Functional Analysis.
2. Lattice point asymptotics and volume growth on Teichmuller space, (joint with Sasha Bufetov, Alex Eskin, and Maryam Mirzakhani), to appear in Duke Mathematical Journal.
3. Ultrametric Logarithm Laws, II (joint with Anish Ghosh and Amritanshu Prasad), to appear in Monat. Math.
4. Logarithm laws and shrinking target properties, Proceedings of the Indian Academy of Sciences, volume 119, number 4, pages 541-559, November 2009
5. Logarithm laws for unipotent flows, I (joint with Gregory Margulis), Journal of Modern Dynamics, volume 3, number 3, pages 359-378, July 2009
6. Ultrametric Logarithm Laws, I (joint with Anish Ghosh and Amritanshu Prasad), Discrete and Continuous Dynamical Systems - Series S, volume 2, number 2, pages 337-348, June 2009.
7. Deviation of ergodic averages for rational polygonal billiards (joint with Giovanni Forni), Duke Mathematical Journal, volume 144, number 2, pages 285-319, August 2008.
8. Quantitative recurrence and large deviations for Teichmuller geodsic flow, Geometriae Dedicata, volume 119, number 1, pages 121-140, April 2006
9. On the asymptotics of discrete order statistics, with S. Sethuraman, Statistics and Probability Letters, volume 54, number 3, pages 243-249, October 2001
10. 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.

Preprints

1. Cusp excursions on parameter spaces, submitted to London Math Society

Conferences

Chris Leininger, Steve Bradlow, and I are serving as local organizers for the first GEometric structures And Representation varieties (GEAR) Network Retreat, August 6-10, 2012, in Champaign-Urbana.

Yitwah Cheung, Anton Zorich, and I organized a special session on Lie group actions, Teichmüller Flows and Number Theory, at the American Mathematical Society Western Section Meeting, April 25-26, 2009, in San Francisco. Details can be found here.

Anish Ghosh, David Ellwood, Dmitry Kleinbock, and I organized 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.

Lion Hunting

More methods of lion-hunting that every graduate student should know. This is joint with Apoorva Khare (Stanford University).