Tamara Grava Homepage

Tamara Grava

Associate Professor of Mathematics

SISSA, via Bonomea 265, 34136, Trieste, Italy

Room number: 626

Phone number: (+39) 040 3787 445

Fax number: (+39) 040 3787 528

e-mail: grava@sissa.it

Research interests: theory of integrable systems in Mathematical Physics and Applied Mathematics

Highly oscillatory Hamiltonian PDEs, numerical treatment, asymptotic solutions

Theta-functions of Riemann surfaces and nonlinear waves

Random Matrix theory and orthogonal polynomials

Riemann-Hilbert problems

Upcoming events

Integrability and Physics, Conference in honour of Antonio Degasperis 70's birthday, La Sapienza, Rome, 25/03/2011.

Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory, The University of Georgia, Athens, US, April 3, 2011 - April 7, 2011.

Painleve Equations and related topics, Euler Institute (Saint Petersburg), 17-23 June, 2011.

Foundations of Computational Mathematics (FOCM '11), Budapest (Hungary), July 4-14, 2011.

Completely integrable systems and applications, Erwin Schrodinger Institute, Vienna, Austria, 3-8 July 2011.

Formal and Analytic Solutions of Differential and Difference Equations, Bedlewo, Poland, August 8-13, 2011.

Conference in honour of Franco Magri's 65th birthday, Milan, 27th of September to 1st October 2011.

National and international research and training networks:

Italian MUR Research Project: Geometric methods in the theory of nonlinear waves and their applications. Co-investigator. National Coordinator: B. Dubrovin

ESF Research Network MISGAM. Project coordinator.

Marie Curie RTN ENIGMA. Co-proponent and Participant.

European Research Council Advanced Grant FroM-PDE (Frobenius Manifolds and Hamiltonian Partial Differential Equations) 2009-2013. Team member. P.I.: B. Dubrovin

IRSES project RIMMP, Random and Integrable Models in Mathematical Physics. From 01/12/2010 to 30/11/2013. Proponent and coordinator.

Teaching 2010/2011

Master Course: Istituzioni di Fisica Matematica
Ph.D. Course: Riemann surfaces and theta-functions
Cycle of seminars on random matrices

Recent publications

Highly oscillatory PDEs and asymptotic solutions, numerics with spectral methods

B.Dubrovin, T.Grava, C.Klein Numerical Study of breakup in generalized Korteweg-de Vries and Kawahara equations

S. Abenda, T. Grava, C. Klein, Numerical Solution of the Small Dispersion Limit of the Camassa-Holm and Whitham Equations and Multiscale Expansions. SIAM J. Appl. Math. vol 70, p 2797-2821, 2010.

B.Dubrovin, T.Grava, C.Klein, On universality of critical behaviour in the focusing nonlinear Schroedinger equation, elliptic umbilic catastrophe and the tritronquee solution to the Painleve-I equation. J. Nonlinear Sci. 19 (2009), no. 1, 57--94.

T.Grava, C.Klein, Numerical study of a multiscale expansion of the Korteweg de Vries equation and Painleve-II equation, Proc. R. Soc. A (2008) n.464, 733- 757.

T. Grava, C.Klein, Numerical solution of the small dispersion limit of Korteweg - de Vries and Whitham equations, Communications on Pure and Applied Mathematics, 60, (2007), n.11, 1623-1664.

Asymptotic Analysis and Riemann-Hilbert methods

T.Claeys, T.Grava The KdV hierarchy: universality and a Painleve transcendent

T.Claeys, T.Grava, Solitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit. SIAM J. Math. Analysis, vol 42, p. 2132-2154, 2010.

T.Claeys, T.Grava, Painleve II Asymptotics near the Leading Edge of the Oscillatory Zone for the Korteweg de Vries Equation in the Small-Dispersion Limit. Comm. Pure and Appl. Math. 63, (2010) p. 203- 232.

T.Claeys and T.Grava, Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach. Comm. Math. Phys. 286 (2009), no. 3, 979--1009.

Modulation equations in integrable systems and random matrices

T. Grava, V.U.Pierce, Fei-Ran Tian, Initial value problem of the Whitham equations for the Camassa-Holm equation. Physica D, 238, (2009) 1, 55--66.

T.Grava, Fei-Ran Tian, Large parameter behavior of equilibrium measures. Commun. Math. Sci. 4 (2006), no. 3, 551--573.

T.Grava, Partition function for multi-cut matrix models J. Phys. A: Math. Gen. 39 No 28 (2006) 8905-8919.

Riemann Surfaces

S. Abenda and T. Grava, Reciprocal transformations and flat metrics on Hurwitz spaces J. Phys. A: Math. Theor. 40 No 35 (2007) 10769-10790.

V. Z.Enolski, T.Grava, Thomae type formulae for singular Z_N curves. Lett. Math. Phys. 76 (2006), no. 2-3, 187--214.