Jeremy Quastel

Jeremy Quastel, 2012

Jeremy Quastel (born December 20, 1963 ) is a Canadian mathematician.

Quastel studied at McGill University and received his PhD in 1990 with SRS Varadhan at the Courant Institute of New York University (Diffusion of Color in the Simple Exclusion Process). He was a post-doctoral student at MSRI and the University of California, Davis . From 1998 he was at the University of Toronto , where he is a professor.

He deals with models of statistical mechanics , interacting particle systems and stochastic partial differential equations . Quastel found the first exact solution (one-point distribution) of the KPZ equation (Kardar-Parisi-Zhang equation, a stochastic differential equation for describing random interfaces and their growth) made further advances in the theory of the KPZ and the universality class (for long times, large scales), which it represents (proof of a 25-year-old conjecture about the scaling exponent of the KPZ universality class, construction of the transition probabilities in KPZ fixed point Markov processes, which represent the long-term limit values for the KPZ universality class). Thus he demonstrated the universality of the KPZ equation by showing that it is the scaling limit of a large class of nonlinear stochastic partial differential equations of the Hamilton-Jacobi type. He found a general solution for the TASEP model and thus the fixed point of its universality class.

He also derived the incompressible Navier-Stokes equation for a class of interacting particle systems, derived equations for internal DLA and proved a conjecture for the velocity of the propagation front in the stochastic Fisher-Kolmogorov-Petrovsky-Piskunov equation for branched diffusion processes.

In 2016 he became a Fellow of the Royal Society of Canada . He was a Sloan Research Fellow from 1996 to 1998 and received a Killam Research Fellowship in 2013. In 2010 he was invited speaker at the International Congress of Mathematicians in Hyderabad ( Weakly Asymmetric Exclusion and KPZ ). In 2012 he gave the St. Flour Lectures and was plenary speaker at the International Congress on Mathematical Physics in Aalborg . For 2018 he received the CRM Fields PIMS Prize , in 2019 the Jeffery Williams Prize .

Fonts (selection)

Diffusion of color in the simple exclusion process, Communications on Pure and Applied Mathematics, Volume 45, 1992, pp. 623-679
with EM LaBolle, GE Fogg: Diffusion theory for transport in porous media: Transition-probability densities of diffusion processes corresponding to advection-dispersion-equations, Water Resources Research, Volume 34, 1998, pp. 1685-1693
with F. Rezakhanlou, SRS Varadhan: Large deviations for the symmetric simple exclusion process in dimensions d≥ 3, Probability theory and related fields, Volume 113, 1999, pp. 1-84
with EM LaBolle, GE Fogg, J. Gravner: Diffusion processes in composite porous media and their numerical integration by random walks: Generalized stochastic differential equations with discontinuous coefficients, Water Resources Research, Volume 36, 2000, pp. 651-662
with M. Balazs, T. Seppäläinen: Fluctuation exponent of the KPZ / stochastic Burgers equation, Journal of the American Mathematical Society, Volume 24, 2011, pp. 683-708
Introduction to KPZ, Current developments in mathematics, Volume 2011, Somerville: International Press 2012, pp. 125–194
with G. Amir, I. Corwin: Probability distribution of the free energy of the continuum directed random polymer in 1+ 1 dimensions, Communications on pure and applied mathematics, Volume 64, 2011, pp. 466-537
with G. Flores, D. Remenik: Endpoint distribution of directed polymers in 1 + 1 dimensions, Arxiv 2011
with Tom Alberts, Konstantin Khanin: The intermediate disorder regime for directed polymers in dimension 1 + 1, Annals of Probability, Volume 42, 2014, pp. 1212–1256, Arxiv
with Herbert Spohn : The one-dimensional KPZ equation and its universality class, Arxiv 2015
with Martin Hairer : A class of growth models rescaling to KPZ, Arxiv 2015
with Janosch Ortmann, Daniel Remenik: Exact formulas for random growth with half-flat initial data, Annals of Probability, Volume 26, 2016, pp. 507-548, Arxiv
with Konstantin Matetski: From the totally asymmetric simple exclusion process to the KPZ fixed point, Arxiv 2017
with Konstantin Matetski, Daniel Remenik: The KPZ fixed point, Arxiv 2017

Web links

Individual evidence

personal data
SURNAME	Quastel, Jeremy
BRIEF DESCRIPTION	Canadian mathematician
DATE OF BIRTH	December 20, 1963

[1] Jeremy Quastel in the Mathematics Genealogy Project (English)

[2] CRM Fields PIMS price for Quastel