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ANDRE SOBOLEVSKI I I

Personal Data Mail Address. Quantum Statistics and Field Theory Division, Physics Department, M. V. Lomonossov Moscow State University, 119992 Moscow, Russia. Phone. 7 495 2425366. Email. ansobol@obs-nice.fr (preferred means of communication). Date and Place of Birth. July 15, 1974, Moscow. Languages Spoken. Russian (mother tongue), English (fluent), French. Education Ph.D.. 1999, Moscow State University. "Generalized variational principles and the method of vanishing viscosity for some quasilinear equations and systems of equations." Advisors: Prof. Ya. G. Sinai, Prof. Yu. M. Loskutov. Diploma (M.Sc.). 1996, Physics Department, Moscow State University. Advisor: Prof. Ya. G. Sinai Employment M. V. Lomonossov Moscow State University. (Moscow, Russia). Associate Professor since January 2005. 20002004: Assistant Professor 19992000: Junior Research Fellow MITP RAN. (International Institute for Earthquake Prediction Theory and Mathematical Geophysics of the Russian Academy of Sciences, Moscow, Russia) 2000Present: Research Fellow (part-time). 19972000: Junior Research Fellow (part-time). Postdo ctoral Position. Observatoire de la Cote d'Azur. (Nice, France). ^ 2003: Henri Poincarґ Fellowship. e Visiting Positions. Observatoire de la Cote d'Azur. (Nice, France). ^ 1999, 2000, 2001, 2002, 2004, 2005, 2006.
The ab ove sp elling of my name is according to the AMS system; it is an accurate transliteration of my Russian name, . Other sp ellings appearing in various official do cuments are Andrei Sobolevski (or Sobolevski i) and Andrey Sobolevskiy.
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The Isaac Newton Institute for Mathematical Sciences. (Cambridge, UK). January and February 2002. The Abdus Salam International Center for Theoretical Physics. (Trieste, Italy). December 1998. Center for Paral lel Computing, KTH. (Stockholm, Sweden). November 1996. Teaching Probability theory. Lectures and problem solving classes for theoretical physics students of the 3rd year, spring term, since 2006. Thermodynamics and Statistical Physics. Lectures and problem solving classes for physics students of the 4th year, fall and spring terms, since 1999. For these two courses, see notes in Russian at http://ansobol.googlepages.com/courseseng (English table of contents). Optimization Methods in Mathematical Physics. A course for theoretical physics students of the 4th year, fall and spring terms, 20022005. Theoretical Models of Turbulence. A course for theoretical physics students of the 4th year, fall 2001. Introduction to Idempotent Analysis and its Applications. A course for physics and mathematics/mechanics students, spring 2000, with V. P. Maslov, G. L. Litvinov, and G. B. Shpiz. Other Activities Refereeing. Physica D, The Mathematical Physics Electronic Journal, Linear Algebra and Applications, AMS Contemporary Mathematics conference proceedings series, Moscow Mathematical Journal. Bo ok Translation and Publishing. Turbulence: The Legacy of A. N. Kolmogorov. By U. Frisch. Cambridge, Cambridge Univ. Press, 1995. Russian edition: Moscow, Phasis, 1998. Translation, TEX typesetting. Numerical Toolbox for Verified Computing I: Basic Numerical Problems. By R. Hammer, M. Hocks, U. Kulisch, D. Ratz. Berlin etc, Springer, 1993. Russian edition: Izhevsk, RCD, 2005. Editing (with A. G. Yakovlev and V. Kreinovich), translation and TEX typesetting (with S. Korop) Organization of Conferences. Euler Equations: 250 Years On. (Aussois, France, June 2007) Member of the organization group. The Nonlinear Cosmology Workshop. (Observatoire de la C^ d'Azur, Nice, France, ote January 2006) Co-organizer, with U. Frisch, J. Peebles, S. Shandarin, and R. Triay.
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The Large-Scale Reconstruction workshop. (Observatoire de la C^te d'Azur, Nice, o France, AugustSeptember 2004). Co-organizer, with U. Frisch, R. Mohayaee and R. Brent Tully. L. V. Kantorovich Memorial Conference. (POMI, St. Petersburg, Russia, January 2004). Assistance to the program committee (A. M. Vershik). The Nonlinear Cosmology Programme. (Observatoire de la C^ d'Azur, Nice, France, ote JuneAugust 2003). Co-organizer, with U. Frisch and R. Mohayaee. Other. Endorser for the mathematics, mathematical physics and nonlinear science sections of arXiv (http://arXiv.org/) since the introduction of the endorsement system in January 2004. Personal weblog (in Russian): http://ansobol.blogsome.com/ Research Interests Quasilinear systems of conservation laws. In my M.Sc. and Ph.D. theses, the method of vanishing viscosity is applied to construct Ya. G. Sinai's "generalized variational principle" for the zero-pressure one-dimensional flow of "sticky particles" [1]. After a several years' hiatus, I resumed the study of zero-pressure gas dynamics in several spatial dimensions using a combination of methods from the optimal transportation theory [P1], vanishing viscosity, and a novel reformulation of the equations [P5]. The HamiltonJacobi equation and the weak KAM theory. The main result of the study of periodic solutions of a periodically forced HamiltonJacobi equation [2, 3, 4] is a uniqueness criterion in terms of the rotation number of the invariant measure of the corresponding Lagrangian dynamical system. This result, also obtained independently by Weinan E, pertains to the "weak KAM" or AubryMather theory. Another result is an example of a new blow-up phenomenon in solutions to the HamiltonJacobi equation in an unbounded domain discovered together with K. Khanin and D. Khmelev in [13, 14]. Optimal mass transportation and its applications. In [9] and [10], a new method of reconstruction of the large-scale past dynamical history of the Universe is proposed. The method is based on a variational technique introduced by Y. Brenier for solving the MongeAmp` equation and reduces the problem to an instance of ere linear program (an optimal Euclidean matching problem). A thorough exposition of the new method and its possible extensions is given in [11]. A refined method of reconstruction, based on quadratic rather than linear optimization, is proposed in [P2, P3]. In [P4], "quenched disorder" in a random discrete model of incompressible fluid is studied. The model, originally proposed by Y. Brenier in a deterministic form, is based on a Euclidean matching problem similar to the one used in the reconstruction work. Idempotent interval analysis. In a series of publications [5, 6, 7, 8], a variant of interval analysis suitable for solving a wide class of (combinatorial) optimization problems is proposed and developed.
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Refereed Publications
[1] A. N. Sobolevski The small viscosity method for a one-dimensional system of equations of i. gas dynamic typ e without pressure. Dokl. Akad. Nauk, 356(3):310312, 1997 (in Russian). [2] A. N. Sob olevski. Periodic solutions of the Hamilton-Jacobi equation with a perio dic force. i Uspekhi Mat. Nauk, 53(6(324)):265266, 1998 (in Russian). [3] A. N. Sobolevski Perio dic solutions of the Hamilton-Jacobi equation with a perio dic i. nonhomogeneity, and the Aubry-Mather theory. Mat. Sb., 190(10):87104, 1999 (in Russian). [4] A. N. Sob olevski Aubry-Mather theory and idemp otent eigenfunctions of Bellman op erator. i. Commun. Contemp. Math., 1(4):517533, 1999. [5] A. N. Sobolevski Interval arithmetic and linear algebra over idemp otent semirings. Dokl. i. Akad. Nauk, 369(6):747749, 1999. [6] G. L. Litvinov, V. P. Maslov, and A. N. Sob olevski Idempotent mathematics and interval i. analysis. Vychisl. Tekhnol., 6(6):4770, 2001. [7] G. L. Litvinov and A. N. Sob olevski Exact interval solutions of the discrete Bellman i. equation, and the polynomial complexity of problems in interval idemp otent linear algebra. Dokl. Akad. Nauk, 374(3):304306, 2000. [8] G. L. Litvinov and A. N. Sobolevski Idemp otent interval analysis and optimization problems. i. Reliab. Comput., 7(5):353377, 2001. [9] U. Frisch, S. Matarrese, R. Mohayaee, and A. Sob olevski. A reconstruction of the initial conditions of the Universe by optimal mass transportation. Nature, 417:260262, May 2002. [10] R. Mohayaee, U. Frisch, S. Matarrese, and A. Sob olevski Back to the primordial Universe i. by a MongeAmp` ereKantorovich optimisation scheme. Astron. & Astrophys., 406:393401, 2003. [11] Y. Brenier, U. Frisch, M. Hґ enon, G. Lo ep er, S. Matarrese, R. Mohayaee, and A. Sob olevski. i Reconstruction of the early Universe as a convex optimization problem. Mon. Not. R. Astron. Soc., 346:501524, 2003. [12] A. Sobolevski U. Frisch. An application of the optimal transp ort theory to reconstruction of i, the early Universe. In A.M. Vershik, editor, Representation Theory and Dynamical Systems, vol. XI. POMI, St Petersburg, 2004, 303-309 (in Russian). [13] K. Khanin, D Khmelev, and A. Sobolevskii. A blow-up phenomenon in the Hamilton Jacobi equation in an unbounded domain. In G. Litvinov and V. Maslov, editors, Idempotent mathematics and mathematical physics. AMS, Providence, RI, 2004, 161180. [14] K. Khanin, D. Khmelev, and A. Sob olevskii. On velo cities of Lagrangian minimizers. Moscow Math. J., 5:157169, 2005. [15] V. I. Keilis-Borok, A. A. Soloviev, C. B. All`gre, A. N. Sob olevskii, and M. D. Intriligator. e Patterns of macro economic indicators preceding the unemployment rise in Western Europ e and the USA. Pattern Recognition, 38:423435, 2005 [16] U. Frisch, A. Sobolevski Application of optimal transport theory to reconstruction of the i. early Universe. Journal of Mathematical Sciences, 133:1539-1542, 2006.

Current Preprints and Work in Progress
[P1] A. Andrievski S. Gurbatov, A. Sobolevski Ballistic aggregation in symmetric and noni, i. symmetric flows. Available at arXiv.org:nlin.PS/0601006; to b e submitted to J. Experimental Theor. Phys, 2006. [P2] A. Kurnosov, A. Sob olevski A variational approach to reconstruction of galactic p eculiar i. velo cities. Submitted to Moscow U. Physics Bul letin, 2006. [P3] A. Kurnosov, S. Sergeev, A. Sob olevski A fast algorithm for a quadratic optimization i. problem arising in reconstruction of galactic peculiar velo cities. In preparation, 2006. [P4] T. Kala idzhyan, A. Sobolevski Combinatorial optimization, "quenched disorder," and i. invariant measures in a discrete model of incompressible fluid. In preparation, 2006. [P5] A. Andrievski P. Cho quard (EPFL, Switzerland), A. Kurnosov, A. Sob olevski On weak i, i. solutions of zero-pressure gas dynamics in several spatial dimensions. In preparation, 2006.

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Talks Seminars. ґ Sґminaire de Gґ ґtrie, Ecole Polytecnique Federale de Lausanne, Lausanne, e eome Switzerland, 2006. P. N. Lebedev Physics Institute of the Russian Academy of Sciences, Moscow, Russia, 2005 (with V. P. Maslov). V. M. Polterovich and V. I. Danilov seminar on mathematical economics, Central Institute of Mathematics and Economics, Moscow, Russia, 2005 (with V. P. Maslov). Department of Mathematics and Computer Science, Emory University, Atlanta, GA, USA, 2004. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, USA, 2004. ґ Section de mathґ ematiques, Ecole Polytecnique Federale de Lausanne, Lausanne, Switzerland, 2004. Department of Mathematical Sciences, Loughborough University, Loughborough, UK, 2002. V. V. Kozlov's seminar, Mechanics and Mathematics Department, M. V. Lomonossov Moscow State University, Moscow, Russia, 2000. ґ Session 74, Ecole de physique des Houches, les Houches, France, 2000 (with J. Bec). I. A. ShishmarЁv's seminar, Computational Mathematics and Kybernetics Department, e M. V. Lomonossov Moscow State University, Moscow, Russia, 1999, 2000, 2002. Physics Department, M. V. Lomonossov Moscow State University, Moscow, Russia, 1999.

Conferences. Nonlinear Cosmology Workshop 2006, Observatoire de la C^ d'Azur, Nice, ote France, 2006. Recent Advances in Calculus of Variations and PDEs, University of Pisa and Scuola Normale Superiore, Pisa, Italy, 2005 (with K. Khanin and D. KhmelЁ ev) The Large Scale Reconstruction Workshop, Observatoire de la C^ d'Azur, Nice, ote France, 2004 (with M. Hґnon). e L. V. Kantorovich Memorial Conference, POMI, St. Petersburg, Russia, 2004. Workshop on Optimal Mass Transport and Dynamical Systems, Pacific Institute for Mathematical Sciences, Vancouver, Canada, 2003. A. N. Kolmogorov Centennial Conference, M. V. Lomonossov Moscow State University, Miscow, Russia, 2003. Workshop on Idempotent Mathematics and Mathematical Physics, the Erwin SchrЁ odinger Institute for Mathematical Physics, Vienna, Austria, 2003. 6th Workshop on Burgers Turbulence and Beyond, the Erwin SchrЁdinger Institute o for Mathematical Physics, Vienna, Austria, 2002. 6th Workshop on Nonlinear Dynamics and Earthquake Prediction, the Abdus Salam ICTP, Trieste, Italy, 2001. Control Applications of Optimization, 11th IFAC International Workshop, St. Petersburg, Russia, 2000 (with G. L. Litvinov). Voronezh Winter Mathematical School, Voronezh University, Voronezh, Russia, 2000.
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4th Workshop on Burgers Turbulence and Beyond, Observatoire de la C^ e ot d'Azur, Nice, France, 1999. L. D. Kudryavtsev's 75th Anniversary Conference, Patrice Lumumba University, Moscow, Russia, 1998. Grants and Awards Centre National de la Recherche Scientifique, Henri Poincarґ Fellowship, 2003. e INTAS Young Scientist Fellowship YSF011172, 2001. Russian Foundation for Basic Research, Young Scientist Fellwoship 010106248, 2001. 3rd Prize, Young Scientists Contest, Physics Department, M. V. Lomonossov Moscow State University, 1999.

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