27-31 March 2017

Organisers: Istvan Gyongy (Edinburgh), Martin Hairer (Warwick), Andrew Stuart (Warwick)

Scientific summary: The interaction between the theory of PDEs and probability is a very fruitful area for research in mathematics, both because of the intrinsic mathematical challenges presented, and because of the range of applications. Examples of recent advances in the field include the emerging theories of regularity structures and paracontrolled distributions for the definition of singular stochastic PDEs, the theory of dispersive wave equations with random data, the study of PDE models from continuum mechanics with random input data, and the use of large deviations to study a range of problems in physics. Despite working on very similar mathematical objects, the stochastic PDE community is somewhat fragmented. The purpose of the workshop is to bring together three diverse communities which share interests across this research interface to explore:-

(1) Evolution equations with stochastic forcing: This is a research area that has seen major advances in the last few years, driven significantly by the theory of regularity structures, for which Hairer was awarded the Fields Medal in 2014. Applications to date include a variety of important equations arising in mathematical physics, but the potential for development of this theory in other applications domains, such as nonlinear filtering and mathematical biology, is enormous. The workshop will bring together researchers interested in both theoretical advancement of the subject area and its application.

(2) Dispersive/conservative equations with random initial data: There have been significant recent advances in this research area, including, for example, the work of Chatterjee on the soliton resolution conjecture, and numerical work of Debussche and coworkers. Furthermore the fall 2015 program at MSRI will have a focus on research at this intersection, and the proposed workshop at Warwick will be timed well to capitalize on this activity. The workshop will bring together theoreticians and numerical analysts in this area.

(3) Numerical analysis of partial differential equations in the presence of stochastic forcing and/or random input data: The numerical analysis community working in stochastic PDEs has been largely divided into two separate groups, working on Ito stochatiscally forced PDEs on the one hand, and PDEs with (smoother) random coefficients. This workshop will bring together these two communities and cement them through common research methodologies, such as polynomial chaos approximation.

Confirmed Speakers:

H. Bessaih (Wyoming)
E. Buckwar (Linz)
A. Debussche (ENS, Cachan; TBC)
F. Flandoli (Pisa)
M. Gerencser (IST Austria)
E. Hausenblas (Leoben)
T. Hou (Caltech)
M. Jara (IMPA)
A. Jentzen (ETHZ)
K. Khanin (Toronto)
D. Khoshnevisan (Utah)
C. Labbe (Paris Dauphine)
G. Lord (Heriot-Watt)
K. Matetski (Toronto)
L. Mytnik (Technion)
T. Oh (Edinburgh)
F. Otto (MPI Leipzig)
C. Powell (Manchester)
B. Rozowsky (Brown)
L. Ryzhik (Stanford)
M. Sanz-Sole (Barcelona)
T. Shardlow (Manchester)
H. Shen (Columbia)
G. Staffilani (MIT)
R. Tempone (KAUST)
E. Vanden Eijnden (NYU)
D. Vvedensky (Imperial)
H. Weber (Warwick)
L. Zambotti (Paris Jussieu).

Draft Schedule available here

See also:
Mathematics Research Centre
Mathematical Interdisciplinary Research at Warwick (MIR@W)
Past Events 
Past Symposia