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 2013

MATH 140,141: Calculus I, II

Spring 2013

MATH 670: Introduction to ODEs - II

Fall 2012

MATH 670: Introduction to ODEs - I

Fall 2011

MATH 462: PDEs for Scientists and Engineers, [PDF]

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

Spring 2010

Differentiable Manifolds (at Penn State Univ.)

Fall 2010

Real Analysis (at Penn State Univ.)


Research Interests:

o    Smooth and Hamiltonian dynamics, Arnold diffusion, celestial mechanics

o    Growth of Sobolev norms for Hamiltonian PDEs

o    Billiards and spectral rigidity


Recent Research (past few years):

Arnold diffusion in three degrees of freedom

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

o     `` Announcement: A strong form of Arnold diffusion for two and a half degrees of freedom’’, with K. Zhang, preprint, 2013, 25pp, [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), 535588, [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, to appear in Journal of the European Mathematical Society, [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] 2011, 58pp, [PDF]

 

o    `` Normally normally hyperbolic invariant manifolds near strong double resonance’’, with K. Zhang, arXiv:1202.1032 [math.DS], 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, 315, 2012, 643--697, 2012 [PDF]

 

o    ``Generic fast diffusion for a class of non-convex Hamiltonians with two degrees of freedom’’, with A. Bounemoura, arxiv.1304.3050 [math.DS], 24pp, 2013, to appear in Moscow Mathematical Journal, [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, 2012, 28pp, to apppear in Communications in Pure and Applied Mathematics, [PDF]

Oscillatory motions and Cantor sets of large Hausdorff dimension

o    ``Conservative homoclinic bifurcations and some applications’’, with A. Gorodetski, Steklov Institute 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, 2013, 75pp, [PDF]

Instabilities for the three-body problem

o    ``Kikrwood gaps and diffusion along mean motion resonance for the restricted planar three body problem’’, with J. Fejoz, M. Guardia, P. Roldan, arXiv:1109.2892 [math.DS] 2013, to appear in Journal of the European Mathematical Society, [PDF]

 

o    ``Destruction of invariant curves in the restricted planar circular three body problem using action comparison’’, with J. Galante, Duke Math J, vol. 159, no. 2 (2011), 275327, [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]

 

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

 

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