Vadim Kaloshin

The Michael Brin Chair in Mathematics 
Department of Mathematics, 

University of Maryland at College Park,  3111 Math. Building, College Park,    MD 20740

ph:   (301) 405-5132
fax:  (301) 314-0827

E-mail: vadim.kaloshin@gmail.com


CV


Education:

Ph.D. Mathematics 2001

Princeton University

M.Sc. Mathematics 1998

Princeton University

B.Sc. Mathematics 1994

Department of Mechanics and Mathematics,  Moscow State University, Russia


Recent Teaching:

 

Fall 2010

Real Analysis

Spring 2011

Differentiable manifolds

Fall 2011

Math 462: Partial Differential Equations for Scientists & Engineers,  undergraduate, [PDF];

Math 648K:  Selected Topics in Analysis: The Principle of Least Action in Geometry & Dynamics, [PDF]


Research Interests:

o    Hamiltonian systems and Hamiltonian PDEs

o    Celestial mechanics

o    Smooth dynamical systems

Recent Research (the past few years):

 

                                    Arnold diffusion in dimension 3

o     `` A strong form of Arnold diffusion for two and a half degrees of freedom’’, with K. Zhang, preprint, 2012, 207pp, [PDF];

 

 

                       Central Configurations and Smale’s 6th problem

o      `` Finiteness of central configurations of five bodies in the plane’’, with A. Albouy, Annals of Mathematics 176 (2012), 535—588, [PDF];

 

                  Growth of Sobolev norms for Hamiltonian PDEs

o      `` Growth of Sobolev norms in the cubic defocusing nonlinear Schodinger equation’’, with M. Guardia,
arXiv:1205.5188 [math.AP], 2012, submitted, [PDF];

 

       Marked length spectrum and rigidity for convex billiards  

o      `` On conjugacy of convex billiards’’, with A. Sorrentino, arXiv:1203.1274 [math.DS]  24pp, 2012, [PDF];

 

                                  Arnold diffusion and its examples

 

o     `` Arnold diffusion in arbitrary degrees of freedom and 3-dimensional normally hyperbolic invariant cylinders, with P. Bernard and K. Zhang, arXiv:1112.2773 [math.DS] 17 Dec 2011, 58pp, [PDF];

 

o    `` Normally normally hyperbolic invariant manifolds near strong double resonance’’, with K. Zhang, arXiv:1202.1032 [math.DS], 6 Feb 2012, 44pp, [PDF];

 

o    ``An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension, with M. Saprykina, Communications in Mathematical Physics, 2012, 55pp, [PDF];

 

o    ``Almost dense orbit on energy surface’’, with Ke Zhang and Yong Zheng, Proceedings of XVITH International Congress on Mathematical Physics.  Held 3-8 August 2009 in Prague, Czech Republic. Edited by Pavel Exner (Doppler Institute, Prague, Czech Republic). Published by World Scientific Publishing Co, 314—322, [PDF];

 

                                      Arnold diffusion in a lattice 

 

o    ``Arnold diffusion in a pendulum lattice’’, with M. Levi and M. Saprykina, preprint, 2010, 22pp, submitted, [PDF];

 

 

                  Oscillatory motions and Cantor sets of large Hausdorff dimension

 

o    ``Conservative homoclinic bifurcations and some applications’’, with Anton Gorodetski, Steklov Institue Proceedings, Vol. 267 (2009), dedicated to the 70th anniversary of Vladimir Arnold, [PDF];

 

o    ``Hausdorff dimension of oscillatory motions for restricted three body problems’’, with A. Gorodetski, preprint, (2011), 70pp, [PDF];

 

                           Instabilities for the three body problem

 

o    ``Diffusion along mean motion resonance for the restricted planar three body problem’’, with J. Fejoz, M. Guardia, P. Roldan, arXiv:1109.2892 [math.DS] 13 Sep 2011, submitted, [PDF];

 

o    ``Destruction of invariant curves in the restricted planar circular three body problem using action comparison’’, Duke Math J, vol. 159, no. 2 (2011), 275—327, [PDF];

 

o    `` The method of spreading cumulative twist and application to the restricted planar circular three body problem’’, with J. Galante, preprint, 2010, 48pp, [PDF];

 

o    ``Destruction of invariant curves in the restricted planar circular three body problem using ordering condition, with J. Galante, preprint, 2010, 28pp, [PDF];

 

                                                     Prevalence

 

o    ``Prevalence’’, with B. Hunt , chapter 2, Handbook in dynamical systems, edited by H. Broer, F. Takens, B. Hasselblatt, Vol. 3, 2010, pg. 43—87, [PDF]; see also http://www.sciencedirect.com/science/article/pii/S1874575X10003103

 

    List of my papers and preprints ordered by topics  [PDF];

 

   List of my papers and preprints in chronological order  [PDF];