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:

Spring 2015

MATH 643: Dynamical systems II,

Fall 2014

MATH 642: Dynamical systems I, [PDF]

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.)

 

Summer School on Dynamical Systems, University of Maryland, College Park:

Summer School on Dynamical Systems, University of Maryland, College Park, August 17-25, 2014


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 several degrees of freedom

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, cond. accepted to Acta Mathematica, [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    `` A strong form of Arnold diffusion for two and a half degrees of freedom, with K. Zhang, arXiv:1212.1150, 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]

 

o    ``A strong form of Arnold diffusion for three and a half degrees of freedom'', with K. Zhang, preprint, 2014, 36pp, [PDF]

 

o    `` Dynamics of the dominant Hamiltonian, with applications to Arnold diffusion'', with K. Zhang, arXiv:1410.1844, preprint, 2014, 84pp, [PDF]

 

o    ``Orbits of nearly integrable tori accumulating to KAM tori'', with M. Guardia, arXiv:1412.7088, preprint, 2014, 115pp, [PDF]

 

o    ``A note on micro-instability for Hamiltonian systems close to integrable'', with A. Bounemoura, arXiv:1412.7455, preprint, 2014, 8pp, [PDF]

Stochastic behavior of Arnold's example

o    `` Random Iteration of Maps on a Cylinder and diffusive behavior, with O. Castejon, arXiv:115917, 2015, 60pp, [PDF]

Spectral rigidity and Birkhoff conjecture

o    `` An integrable deformation of an ellipse of small eccentricity is an ellipse, with A. Avila, J. De Simoi, arXiv:1412.2853, preprint, 22pp, [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, to appear in Journal of the European Mathematical Society, [PDF]

Examples of Arnold diffusion

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    ``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]

 

o    ``Global instability in the elliptic restricted three body problem'', with A. Delshams, A. de la Rosa, T. Seara, arXiv:1501.01214, preprint, 2014, 41pp, [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]