Équations aux Dérivées Partielles Stochastiques, Systèmes Dynamiques Aléatoires, Physique Mathématique.
IECL – Site de Nancy
Faculté des sciences et Technologies
Campus, Boulevard des Aiguillettes
54506 Vandœuvre-lès-Nancy
FACULDADE DE CIÊNCIAS DA UNIVERSIDADE DE LISBOA
Integrated member CMAFcIO
Centro de Matemática, Aplicações Fundamentais
Departamento de Matemática
Universidade de Lisboa
Faculdade de Ciências
Gabinete C. 1. 10
Campo Grande, Edifício C. 6
P-1749-016 Lisboa
(PORTUGAL)
Telephone: +351 217 500 276 ext. 26169
pavuillermot@fc.ul.pt
Secretary: Mrs. Helena Afonso
Telephone: +351 217 500 340 ext. 26104
hidafonso@fc.ul.pt
Fields of Research: Stochastic Partial Differential Equations, Random Dynamical Systems, Mathematical Physics.
Notable Honors and Awards: von Humboldt Junior Fellowship Award (academic year 1978-1979, declined).
Fellow of the Max Planck Society, MPI, Bonn (academic years 1989-1991).
Research Professorship Award, MSRI (currently Simons Laufer Mathematical Sciences Institute or SLMath), Berkeley (academic year 1997-1998, stochastic analysis program).
Selected Publications: With B. Scarpellini: Smooth Manifolds for Semilinear Wave Equations on R2: on the Existence of Almost-Periodic Breathers, Journal of Differential Equations 77 (1989) 123-166.
Global Exponential Attractors for a Class of Almost-Periodic Parabolic Equations on RN, Proc. Amer. Math. Soc. 116 ( 1992) 775-782.
With B. Bergé and I. D. Chueshov: On the Behavior of Solutions to Certain Parabolic SPDEs driven by Wiener Processes, Stochastic Processes and Their Applications 92 (2001) 237-263.
With M. Sanz-Solé: Equivalence and Hölder-Sobolev Regularity of Solutions for a Class of Non-Autonomous Stochastic Partial Differential Equations, Ann. I. H. Poincaré-PR 39 (2003) 703-742.
With D. Nualart: Variational Solutions for Partial Differential Equations driven by a Fractional Noise, Journal of Functional Analysis 232 (2006) 390-454.
On the Time Evolution of Bernstein Processes associated with a Class of Parabolic Equations, Discrete and Continuous Dynamical Systems Series B 23 (2018) 1073-1090.
With J. C. Zambrini: On Bernstein Processes generated by Hierarchies of Linear Parabolic Systems in Rd, Stochastic Processes and Their Applications 130 (2020) 2974-3004.
With S. Bögli: On the Asymptotic Behavior of Solutions to a Class of Grand Canonical Master Equations, Portugaliae Mathematica 80 (2023) 269-289.
Selected Invited Lectures and Courses: Smooth Manifolds for Nonlinear Klein-Gordon Equations in the Presence of Small Divisors, International Conference on Nonlinear Hyperbolic Equations, Varenna (1990).
A Geometric Theory of Semilinear Almost-Periodic Parabolic Partial Differential Equations on RN, Summer School Course on the Qualitative Aspects and Applications of Nonlinear Evolution Equations, International Center of Theoretical Physics, Trieste (1990).
Some Recent Results on Fractional Partial Differential Equations, International Conference on Stochastic Partial Differential Equations, SNP, Pisa (2006).
New Developments in Stochastic Partial Differential Equations, Second US-Chile Workshop on New Developments in Partial Differential Equations, Santiago de Chile (2008).
Inhomogeneous Bernstein Diffusions and Parabolic Equations: Some Recent Results, Mini-Course, Semester Program on Stochastic Analysis and Applications, EPFL, Lausanne (2012).
Bernstein Processes of Maximal Entropy, 2nd Conference of the European Physical Society Statistical and Nonlinear Physics Division, Nordita, Stockholm (2019).
Most Recent Papers Online: to be announced.
Editorial Activities: Editorial Board Member for Stochastic Analysis and Applications.
Pierre-A. Vuillermot was born in Couvet (NE), Switzerland. He studied at the Swiss Institute of Technology in Zurich, where he obtained his Master’s degree in the Physical Sciences in 1971. He then worked as a Research Assistant at the Physics Department of the University of Neuchâtel, Switzerland, where he wrote a thesis titled « Some Rigorous Results in Statistical Mechanics with Applications to the Problem of Phase Transitions » published in French by Lang Druck AG in 1974, thereby obtaining his Ph.D. degree in Mathematical Physics. After one more year as a Research Fellow at that institution, he spent the following three years as a Research Scientist at Princeton University, USA, supported by grants from the Swiss National Science Foundation for Scientific Research and the Holderbank Stiftung zur Förderung der wissenschaftlichen Fortbildung. In 1978 he was awarded a von Humboldt Junior Fellowship which would have allowed him to pursue his career at the University of Göttingen, Germany; however, he eventually declined that fellowship and remained in the USA for sixteen years thereafter, first holding faculty positions at Emory University and the Georgia Institute of Technology in Atlanta, and then a Full Professorship in Mathematics at the University of Texas at Arlington. Since 1994 until 2014 he was a Full Professor of Mathematics at the University Henri Poincaré in Nancy, France, which became part of the newly created University of Lorraine on January 1, 2012. Since then he is Emeritus Professor of Mathematics at that institution.
His current research activities lie in the field of deterministic and random dynamical systems, with a special emphasis on nonlinear deterministic and stochastic partial differential equations, as well as in some areas of Mathematical Physics. For his accomplishments in those areas he was awarded a Max Planck Fellowship in 1989 and spent the following two academic years in residence at the MPI in Bonn, Germany. He was also honored with a Research Professorship Award from the MSRI (currently Simons Laufer Mathematical Sciences Institute or SLMath) in Berkeley in 1997, where he was in residence during one semester of that academic year.
He is a regular academic guest of several institutions, including the Mathematics Research Center of the Swiss Institute of Technology in Zurich, and is an integrated member of the Center of Mathematics and its Applications of the University of Lisbon.