- 2017 Class of Fellows of AMS

- Plenary Speaker, International Society of Porous Media, May 2015

- 45 minute Invited Talk, International Congress of Mathematicians, South Korea, 2014 (the article in SCIENCE, TAMU)

- Plenary talk, SIAM Geosciences 2011.

- QRI Scolar, 2011

- Fraunhofer Bessel Award (Alexander von Humboldt Foundation), 2010

- The young researcher fellowship of Sixth U.S. National Congress on Computational Mechanics, August 2001

- W. P. Carey Prize for outstanding thesis work in applied mathematics, California Institute of Technology, 1999

- Saul Kaplun Memorial Fellowship, California Institute of Technology, 1995-1996

- Honors Diploma in Moscow State University, 1993

- Second Degree Diploma (shared the second place) in the USSR Mathematics Competition, 1988