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Uri Shapira
ETH Zürich, Departement Mathematik
Rämistrasse 101
8092 Zürich
Switzerland

Phone: +41 44 632 4388
Room: HG J 16.5
Email: ushapira@gmail.com

I have a joint postdoc position at ETH math department and EPFL math department. I am physically at ETH and mainly working with Manfred Einsiedler. I finished my Ph.D at the Hebrew University of Jerusalem and my advisers were Hillel Furstenberg and Barak Weiss.
My areas of interest are Homogeneous Dynamics, Ergodic Theory, and applications to Number Theory (especially to Diophantine approximations and the geometry of numbers).

I recently updated my CV which can be found here and wrote a research statement which can be found here. Also, since the 14th of March 2012 I am trying to solve the following divine equation.

Publications:

1. Measure Theoretical Entropy of Covers. Israel Journal of math. 158(2007), (1) p 225-247.
2. On a generalization of Littlewood's conjecture. Journal of Modern Dynamics Volume 3, No. 3, 2009. Updated on 24/7/2009.
3. A solution to a problem of Cassels and Diophantine properties of cubic numbers. Annals of Mathematics Volume 173 (2011), no. 1, pages 543-557. Updated on 1/11/2010.
4. Diophantine approximations on fractals. Joint work with M. Einsiedler and L. Fishman. Geometric and Functional Analysis, Volume 21, Number 1, 14-35. Updated on 1/12/2010.
5. Homogeneous orbit closures and applications. Joint work with E. Lindenstrauss. To appear in Erg. The. and Dyn. Sys. A volume in memory of Dan Rudolph. Updated on 29/11/2010.
6. Grids with dense values. To appear in Commentarii Mathematici Helvetici. Updated on 4/4/2011.
7. On the evolution of continued fraction expansions in a fixed quadratic field. Updated and corrected on 28.9.2011. Joint work with Menny Aka. Submitted.

Forthcoming papers:

8. On Minkowski's conjecture and stable lattices. Joint with Barak Weiss. In preparation.
9. Two remarks on Euclidean minima. Joint with Zhiren Wang. In preparation.
10. On the decimal expansion of 3^{-n}. Joint with Manfred Einsiedler. In preparation.