- Zdzislaw Brzezniak, University of York
Istvan Gyongy, University of Edinburgh
Tadahiro Oh, University of Edinburgh
- Oana Pocovnicu, Heriot-Watt University
This five-day workshop is devoted to the areas of harmonic analysis,
stochastic analysis and partial differential equations (PDEs).
Harmonic analysis, stochastic analysis and PDEs are intimately
related fields of great importance in mathematics. The relationship
between harmonic analysis and PDE theory has a long and extremely
successful history; harmonic analysis played a fundamental role in
settling some of the central problems in the field of linear and
nonlinear PDEs, including elliptic, parabolic, dispersive and hyperbolic
equations and systems. On the other hand, recent advances in our
theoretical understanding of PDEs has stimulated further development of
analytical ideas and tools in harmonic analysis.
harmonic analysis, stochastic analysis and PDEs
- By the help of a generalisation of the Hardy-Littlewood
inequality and by the Fefferman-Stein inequality, Krylov has recently
built an theory of PDEs and SPDEs of parabolic type.
Weis presented an
alternative approach to the same question, based on
infinite-dimensional harmonic analysis.
Harmonic analysis is important in the foundations of stochastic
approach turbulence phenomena in fluids, understanding the very weak
solutions and the phenomena of regularisation by noise,
in particular in
the context of 3-d Navier-Stokes equations.
analysis has also played a fundamental
role in the recent theories of Hairer's regularity structures and
Gubinelli's paracontrolled distributions.
The interaction of harmonic analysis, PDE techniques
and stochastic analysis was essential
in the recent
spectacular progress in the theory of nonlinear dispersive
equations with random initial data and/or stochastic forcing.
This include probabilistic construction of
solutions, invariant measures and transport properties of Gaussian
measures under deterministic PDEs, where the latter extends a classical
problem in probability theory to the PDE setting.
The main goal of this workshop
is to bring together researchers in different fields (analysis, probability and PDEs) to generate cross-disciplinary research interactions and an exchange of ideas and methods from PDEs, probability and harmonic analysis.
It is our desire to make the workshop accessible to researchers who are not specialists in certain areas of the this workshop.
This will be made possible through a variety of the lecture series
by world-leading experts,
a wide range of contributed talks
and plenty of time for free discussion.
will be four lecture series, each consisting of 3 one-hour lectures:
Franco Flandoli (Scuola Normale Superiore, Pisa):
Regularization by noise for linear and nonlinear PDEs
Massimiliano Gubinelli (Hausdorff Center for Mathematics, Bonn):
Nicolai Krylov (University of Minnesota, USA):
Ito stochastic processes, Ito stochastic equations, and Markov diffusion processes with drift in Ld
Lutz Weis (Karlsruhe Institute for Technology, Germany):
There will be 40 minute and 25 minute talks
by a mixture of leading experts and young researchers:
Bjoern Bringmann (UCLA, USA): short talk
Sandra Cerrai (University of Maryland, USA)
Andreia Chapouto (The University of Edinburgh, UK): short talk
Konstantinos Dareiotis (University of Leeds, UK): short talk
Justin Forlano (Heriot-Watt University, UK): short talk
Máté Gerencsér (IST, Austria): short talk
Masato Hoshino (Kyushu University, Japan)
Utpal Manna (Indian Institute of Science Education and Research, India): short talk
Mario Maurelli (Università degli Studi di Milano, Italy): short talk
Szymon Peszat (Jagiellonian University, Poland)
Enrico Priola (University of Pavia, Italy)
Tristan Robert (Universität Bielefeld, Germany)
Michael Röckner (Universität Bielefeld, Germany)
Chenmin Sun (Université de Cergy-Pontoise, France): short talk
Mark Veraar (Delft University of Technology, Netherland)
Jim Wright (The University of Edinburgh, UK)
On Tuesday night, we will hold a public lecture accessible
to the general audience:
Geordie Richards (Department of Mechanical and Aerospace Engineering, Utah State University, USA)
There will be a poster session by young participants
on Monday evening.
Details regarding participation will appear at
the ICMS website in due course