I work on the interface between continuum mechanics and the theory of partial differential equations. In recent years, my research has focused on nonlinear hyperbolic systems of conservation laws, whose solutions spontaneously develop singularities that propagate as shock waves. I am interested in the interplay between thermodynamics and analysis, in the theory of these systems, and have been striving to elucidate the fundamental role of entropy, as a stabilizing agent.

Over the past three years, I have been involved in the following research projects:

(1) Uniqueness and stability of solutions to hyperbolic systems of conservative laws, arising in elastodynamics and electromagnetism, which are endowed with involutions, a polyconvex entropy and a set of contingent entropies.

(2) Continuous solutions of hyperbolic balance laws with applications to the Hunter-Saxton equation.

(3) Irrotational sonic-subsonic gas flow via the method of compensated compactness.

NSF Grant # DMS-020288 (Hyperbolic Conservation Laws in Continuum Physics)

NSF Grant # DMS-0244295 (FRG Collaborative Research: Multi-Dimensional Problems for the Euler Equations)

Fellow American Academy of Arts and Sciences, 2001-.
Correspondent Member, Academy of Athens, 1988-.
Honorary Professor, Academia Sinica, China, 2004-.
Foreign Member, Accademia Nazionale dei Lincei, Roma 2011-.
Member, Board of Governors, Weizmann Institute of Science (Israel), 1995-.
Fellow, SIAM, 2009-.
Fellow, AMS 2013-.
Fellow, Society of Scholars, Johns Hopkins University.
Chairman, Society for Natural Philosophy, 1977-78.
Secretary, International Society for the Interaction of Mathematics and Mechanics, 1984-86.
Ordway Chair, University of Minnesota, 1985.
Keeley Fellowship, Wadham College, Oxford, 2001.
Honorary Doctorate, University of Athens, 1987.
Honorary Doctorate, National Technical University (Greece), 1991.
Honorary Doctorate, University of Crete, 2001.
SIAM W.T. and Idalia Reid Prize, 2000.
Cataldo e Angiola Agostinelli Prize, 2011.
GALILEO Medal, City of Padua, 2012.
ISIMM Prize, 2014.
AMS Norbert Weiner Prize, 2016.
Elected to the National Academy of Sciences, 2016.

Editorial Board of following publications:

Quarterly of Applied Mathematics, Associate Managing Editor
Acta Mathematica Scientia, Chief Co-Editor
Annali di Matematica Pura ed Applicata
Archive for Rational Mechanics and Analysis
Mathematics Applied in Science and Technology
Communications in Applied Analysis
Proceedings of the Royal Society of Edinburgh
Ricerche di Matematica
Revista Matematica Complutense
Bulletin of Greek Mathematical Society
Journal of Dynamics and Differential Equations
Journal of Hyperbolic Differential Equations

Member, Board of Governors and Scientific and Academic Advisory Committee, Weizmann Institute of Science, Israel
Member, National Committee on Research and Technology, Greece
Member, Advisory Board, Institute of Mathematics, Academy of Sciences, Czech Republic
Member, Scientific Advisory Board, Archimedes Center, Crete, Greece
Member, Scientific Advisory Panel, IRIMA, University of Wales, U.K.
Member, Institute of Numerical Analysis, Crete, Greece
Member, Scientific Committee, XIV International Conference on Nonlinear Hyperbolic PDE, Padova, Italy
Member, Scientific Committee, Workshop, Crete, Greece
Cochairman, Scientific Committee, International Conference in memory of Guoping Li, Wuhan, China
Member, Scientific Committee, EUROCONFERENCES, Crete
Member, Scientific Committee, WASCOM 2011
Member, Scientific Committee, International Conference on Conservation Laws, Tata Institute, Bangalore, India
Member, Jury for habilitation thesis, Université Pierre et Marie Curie, Paris.
Member, Promotion Committee, University of Crete, Greece