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 2020

Probability theory

Spring 2019

Probability theory

Spring 2019

Transform Methods for Scientists and Engineers

Fall 2018

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]