American Institute of Mathematical Sciences

Journals

Fields Medalists Research by AIMS

AIMS has published research from 12 Fields Medalists. Many of these Fields Medalists, some of which have held management positions on our editorial boards, have received other prestigious IMU awards.

In celebration of their accomplishments, you can enjoy complimentary access to their work below.

Artur Avila

The Kontsevich–Zorich cocycle over Veech–McMullen family of symmetric translation surfaces
Artur Avila, Carlos Matheus and Jean-Christophe Yoccoz
Journal of Modern Dynamics, 2019, Volume 14

Density of positive Lyapunov exponents for quasiperiodic SL(2, R)-cocycles in arbitrary dimension
Artur Avila
Journal of Modern Dynamics, October 2009, Volume 3, Issue 4

Density of positive Lyapunov exponents for quasiperiodic SL(2, R)-cocycles in arbitrary dimension
Artur Avila
Journal of Modern Dynamics, October 2009, Volume 3, Issue 4

Smoothness of solenoidal attractors
Artur Avila, Sébastien Gouëzel and Masato Tsujii
Discrete & Continuous Dynamical Systems, February 2006, Volume 15, Issue 1

Jean Bourgain

On quasi-periodic lattice Schrödinger operators
Jean Bourgain
Discrete & Continuous Dynamical Systems, February 2004, Volume 10, Issue 1&2

On random Schrödinger operators on $\mathbb Z^2$
Jean Bourgain
Discrete & Continuous Dynamical Systems, January 2002, Volume 8, Issue 1

Charles Fefferman

Structural stability for the splash singularities of the water waves problem
Angel Castro, Diego Córdoba, Charles Fefferman, Francisco Gancedo and Javier Gómez-Serrano
Discrete & Continuous Dynamical Systems, December 2014, Volume 34, Issue 12

Interpolation by linear programming I
Charles Fefferman
Discrete & Continuous Dynamical Systems, May 2011, Volume 30, Issue 2

Alessio Figalli

Regularity of monotone transport maps between unbounded domains
Dario Cordero-Erausquin and Alessio Figalli
Discrete & Continuous Dynamical Systems, December 2019, Volume 39, Issue 12

Characterization of isoperimetric sets inside almost-convex cones
Eric Baer and Alessio Figalli
Discrete & Continuous Dynamical Systems, January 2017, Volume 37, Issue 1

An excess-decay result for a class of degenerate elliptic equations
Maria Colombo and Alessio Figalli
Discrete & Continuous Dynamical Systems – S, August 2014, Volume 7, Issue 4

A global existence result for the semigeostrophic equations in three dimensional convex domains
Luigi Ambrosio Maria Colombo Guido De Philippis and Alessio Figalli
Discrete & Continuous Dynamical Systems, April 2014, Volume 34, Issue 4

Preface: Special Issue on Optimal Transport and Applications
Alessio Figalli and Filippo Santambrogio
Discrete & Continuous Dynamical Systems, April 2014, Volume 34, Issue 4

Asymptotics of the s-perimeter as s $\searrow 0$
Serena Dipierro, Alessio Figalli, Giampiero Palatucci and Enrico Valdinoci
Discrete & Continuous Dynamical Systems, July 2013, Volume 33, Issue 7

Fine properties of minimizers of mechanical Lagrangians with Sobolev potentials
Alessio Figalli and Vito Mandorino
Discrete & Continuous Dynamical Systems, December 2011, Volume 31, Issue 4

Partial regularity of Brenier solutions of the Monge-Ampère equation
Alessio Figalli and Young-Heon Kim
Discrete & Continuous Dynamical Systems, June 2010, Volume 28, Issue 2

Elon Lindenstrauss

Symmetry of entropy in higher rank diagonalizable actions and measure classification
Manfred Einsiedler and Elon Lindenstrauss
Journal of Modern Dynamics, 2018, Volume 13

On measures invariant under diagonalizable actions: the Rank-One case and the general Low-Entropy method
Manfred Einsiedler and Elon Lindenstrauss
Journal of Modern Dynamics, January 2008, Volume 2, Issue 1

Pointwise theorems for amenable groups
Elon Lindenstrauss
Electronic Research Announcements, 1999, Volume 5

P.-L. Lions

Continuity of admissible trajectories for state constraints control problems
M. Arisawa and P.-L. Lions
Discrete & Continuous Dynamical Systems, July 1996, Volume 2, Issue 3

Gregory A. Margulis

Values of random polynomials at integer points
Jayadev S. Athreya and Gregory A. Margulis
Journal of Modern Dynamics, 2018, Volume 12

Logarithm laws for unipotent flows, Ⅱ
Jayadev S. Athreya and Gregory A. Margulis
Journal of Modern Dynamics, 2017, Volume 11

Logarithm laws for unipotent flows, I
Jayadev S. Athreya and Gregory A. Margulis
Journal of Modern Dynamics, July 2009, Volume 3, Issue 3

Maryam Mirzkhani

Counting closed geodesics in moduli space
Maryam Mirzkhani
Journal of Modern Dynamics, January 2011, Volume 5, Issue 1

Terence Tao

On the universality of the incompressible Euler equation on compact manifolds
Terence Tao
Discrete & Continuous Dynamical Systems, March 2018, Volume 38, Issue 3

Global well-posedness of the Maxwell-Klein-Gordon equation below the energy norm
M. Keel, Tristan Roy and Terence Tao
Discrete & Continuous Dynamical Systems, August 2011, Volume 30, Issue 3

An inverse theorem for the Gowers $U^{s+1}\ [N]$-norm
Ben Green, Terence Tao and Tamar Ziegler
Electronic Research Announcements, 2011, Volume 18

Linear approximate groups
Emmanuel Breuillard, Ben Green and Terence Tao
Electronic Research Announcements, 2010, Volume 17

Resonant decompositions and the $I$-method for the cubic nonlinear Schrödinger equation on $\mathbb{R}^2$
J. Colliander, M. Keel, Gigliola Staffilani, H. Takaoka and T. Tao
Discrete & Continuous Dynamical Systems, August 2008, Volume 21, Issue 3

Two remarks on the generalised Korteweg de-Vries equation
Terence Tao
Discrete & Continuous Dynamical Systems, January 2007, Volume 18, Issue 1

Polynomial upper bounds for the instability of the nonlinear Schrödinger equation below the energy norm
J. Colliander, M. Keel, G. Staffilani, H. Takaoka and T. Tao
Communications on Pure & Applied Analysis, March 2003, Volume 2, Issue 1

Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm
J. Colliander, M. Keel, G. Staffilani, H. Takaoka and T. Tao
Discrete & Continuous Dynamical Systems, January 2003, Volume 9, Issue 1

Cédric Villani

Regularity of optimal transport and cut locus: From nonsmooth analysis to geometry to smooth analysis
Cédric Villani
Discrete & Continuous Dynamical Systems, May 2011, Volume 30, Issue 2

Celebrating Cercignani's conjecture for the Boltzmann equation
Laurent Desvillettes, Clément Mouhot and Cédric Villani
Kinetic & Related Models, March 2011, Volume 4, Issue 1

Entropy and chaos in the Kac model
Eric A. Carlen, Maria C. Carvalho, Jonathan Le Roux, Michael Loss and Cédric Villani
Kinetic & Related Models, March 2010, Volume 3, Issue 1

Shing-Tung Yau

Nodal geometry of graphs on surfaces
Yong Lin,  Gábor Lippner, Dan Mangoubi and Shing-Tung Yau
Discrete & Continuous Dynamical Systems, July 2010, Volume 28, Issue 3

Jean-Christophe Yoccoz

The Kontsevich–Zorich cocycle over Veech–McMullen family of symmetric translation surfaces
Artur Avila, Carlos Matheus and Jean-Christophe Yoccoz
Journal of Modern Dynamics, 2019, Volume 14

The action of the affine diffeomorphisms on the relative homology group of certain exceptionally symmetric origamis
Carlos Matheus and Jean-Christophe Yoccoz
Journal of Modern Dynamics, July 2010, Volume 4, Issue 3