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CRM > English > Activities > Curs 2015-2016 > 3rd BCN Summer School on Stochastic Analysis: A 2016 EMS Summer School
3rd BCN Summer School on Stochastic Analysis: A 2016 EMS Summer School
General information
Dates: June 27 to July 1, 2016

Timetable (to be posted) 
Final practical information for participants (to be posted)

The Barcelona Summer School on Stochastic Analysis is a one-week scientific activity consisting mainly of courses addressed to PhD students and young researchers on current research topics in Stochastic Analysis. Selected participants are also given the opportunity to deliver short talks or to display posters.

 The courses in 2016 will be the following (a detailed description is given below)

  • On Approximations of Stochastic PDEs, by István Gyöngy (University of Edinburgh, UK)
  • Regularity Structures, by Martin Hairer (University of Warwick, UK)

The Summer School will consist on the following two courses:

On Approximations of Stochastic PDEs

István Gyöngy, University of Edinburgh, UK

Approximation methods are often used to establish solvability of equations. They are also important to solve numerically stochastic PDEs, for example equations of nonlinear filtering problems.  

In the course mostly parabolic stochastic PDEs are considered. Temporal and spatial approximation schemes with emphasis on their rate of convergence will be studied. In particular, Wong-Zakai approximations, Euler approximations, splitting-up, methods, Galerkin approximations, finite element and finite difference schemes will be thoroughly investigated. 

Effective numerical methods with high accuracy are important in practice. For this reason accelerated numerical schemes will also be presented and analysed. 


Regularity Structures

Martin Hairer, University of Warwick, UK

One of the main challenges of modern mathematical physics is to understand the behaviour of systems at or near criticality. In a number of cases, one can argue heuristically that this behaviour should be described by a nonlinear stochastic partial differential equation. Some examples of systems of interest are models of phase coexistence near the critical temperature, one-dimensional interface growth models, and models of absorption of a diffusing particle by random impurities. Unfortunately, the equations arising in all of these contexts are mathematically ill-posed to the extent that they defeat classical stochastic PDE techniques.

Recently, the theory of regularity structures has allowed us to give a rigorous mathematical interpretation to such equations and to build the mathematical objects conjectured to describe the abovementioned systems near criticality. It also comes with a robust solution theory allowing to prove various approximation results by solutions to classical PDEs, possibly with diverging coefficients. The aim of these lectures is to give an overview of the main results and concepts of the theory. Whenever practical, we will give at least sketches of proofs that are as self-contained as possible.


Scientifc Committee
Dave Applebaum, University of Sheffield
Robert Dalang, École Polytechnique Fédérale de Lausanne
Marta Sanz-Solé, Universitat de Barcelona
Frederic Utzet, Universitat Autònoma de Barcelona
Organising Committee
Lluís Quer-Sardanyons, Universitat Autònoma de Barcelona
Marta Sanz-Solé, Universitat de Barcelona
Frederic Utzet, Universitat Autònoma de Barcelona
Josep Vives, Universitat de Barcelona  

Contributed talks and Poster presentation
Deadline for application: May 1, 2016
If the participant would like to give a talk or present a poster, a short abstract (pdf and tex files) and CV will have to be submited (fill in the application form below).

Registration and Lodging grants 

Deadline for application: March 31, 2016 (closed)

Resolutions will be sent by email during the last week of April.

Participants can apply for registration and/or lodging grants. These grants are addressed exclusively to PhD students and early Post-doctoral students.
Lodging grants will cover the accommodation from June 26 to July 2, 2016, in Vila Universitària​ (in shared apartments). 
Applicants should submit the application form below along with a curriculum vitae and a reference letter (for PhD students, preferably from their thesis advisor). 
​Registration fee: 180€
Deadline for registration: May 31, 2016
Registration includes: attendance to the courses, documentation package, one copy of the lecture notes of each course, lunch tickets, a guided tour in Barcelona, the social dinner, and the coffee breaks.​
Lodging information

For lodging in the area please click here​
For off-campus and family accommodation click here​​​​


This Summer School has been partially supported by the AGAUR (SGR 2014 422), by the EMS, and by the Ministerio de Economía y Competitividad. Secretaría de Estado de Investigación, Desarrollo e Innovación (reference number: MTM 2012-31192, MTM 2012 33937).

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Contact information
If you have any questions please contact:

Núria Hernandez  (​​​)​​