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
(301) 314-0827




Ph.D. Mathematics 2001

Princeton University


Spring 2019

Probability theory,

Spring 2019

Complex Analysis for Scientists and Engineers,

Spring 2018

Hamiltonian systems,

Fall 2017

Topics in Hamiltonian dynamics: Arnold diffusion,

Spring 2016

Complex Analysis for Scientists and Engineers,



Schools on Dynamical Systems

Summer school on stochastic motions in Hamiltonian Systems and Symplectic Geometry, July 23 - August 03, 2018, Berkeley, USA. Mathematical Sciences Research Institute

Winter school in conservative dynamics, February 5-11, 2017, Engelberg, Switzerland. Sponsored by the ETH Institute for Theoretical Studies

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



Research Interests:

o    Stochastic Arnold diffusion, stochastic behavior in Kirkwood gaps , random iteration of conservative maps


o    Integrable billiards, Birkhoff Conjecture, and "Can you hear the shape of a drum?"


o    Arnold diffusion, instabilities in celestial mechanics and Hamiltonian PDEs



Recent Research (past few years):

Integrable billiards, Birkhoff Conjecture, and "Can you hear the shape of a drum?"


o    " An integrable deformation of an ellipse of small eccentricity is an ellipse", with A. Avila, J. De Simoi, Annals of Mathematics, Vol. 184 (2016), 527--558, [PDF]


o    " On the local Birkhoff Conjecture for convex billiards", with A. Sorrentino, Annals of Mathematics, Vol. 188 (2018), 315--380, [PDF]


o    " Nearly circular domains which are integrable close to the boundary are ellipses", with G. Huang, A. Sorrentino, Geometric and Functional Analysis, Vol. 28, 2 (2018), 334--392, [PDF]


o    " On Marked Length Spectrums of Generic Strictly Convex Billiard Tables", with G. Huang, A. Sorrentino, Duke Math. J, Vol. 167, 1 (2018), 175--209, [PDF]


o    " Deformational spectral rigidity among Z_2-symmetric domains close to the circle", with J. De Simoi, Q. Wei, (Appendix B coauthored with H. Hezari), Annals of Mathematics, Vol. 186 (2017), 277-314 , [PDF]



Stochastic Arnold diffusion


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


o    " A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems", with M. Guardia, J. Zhang , Communications in Mathematical Physics November 2016, Volume 348, Issue 1, 321361 , [PDF]


o    " Normally Hyperbolic Invariant Laminations and diffusive behaviour for the generalized Arnold example away from resonances", with J. Zhang, K. Zhang , preprint, 85pp, 2015, [PDF]


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, Acta Mathematica, Vol. 217, 1 (2016), 1--79, [PDF]


o    "Generic fast diffusion for a class of non-convex Hamiltonians with two degrees of freedom", with A. Bounemoura, Moscow Mathematical Journal, vol. 14, 2, 181--203, 2014, [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, Nonlinearity, 28, no. 8, 2699--2720, [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  , to appear in Bull French Mathematical Society, [PDF]


o    "A note on micro-instability for Hamiltonian systems close to integrable", with A. Bounemoura, arXiv:1412.7455  , Proc. Amer. Math. Soc. 144 (2016), 1553-1560, [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, 535--588, 2012, [PDF]


Growth of Sobolev norms for Hamiltonian PDEs

o    "Growth of Sobolev norms in the cubic defocusing nonlinear Schodinger equation", with M. Guardia,
Journal of the European Mathematical Society, vol. 17, 1, 71--149, 2015, [PDF]



Examples of Arnold diffusion

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, Volume 67, Issue 5, pages 748--775, May 2014, 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  , Journal of the Eur. Math. Soc. 18, 23132401, [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), 275--327, [PDF]


o    "Global instability in the elliptic restricted three body problem", with A. Delshams, A. de la Rosa, T. Seara, arXiv:1501.01214  to appear in Communications in Mathematical Physics, [PDF]



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


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