Recent Breakthroughs
in Singular Stochastic PDEs

Overview

The aim of this school is to present some recent breakthroughs in the theory of non-linear stochastic PDEs, that allow to give a rigorous meaning to some important singular equations for which classical methods fail, due to the irregularity of the noise. Examples include the Kardar-Parisi-Zhang (KPZ) equation in 1d, the equation of stochastic quantization in 3d, the parabolic Anderson model in 2d.

The school is mainly targeted at PhD students and young researchers. There will be two mini-courses by Massimiliano Gubinelli (Université Paris Dauphine) and Lorenzo Zambotti (Université Pierre et Marie Curie), presenting different approaches but discussing analogous examples.

Courses

Massimiliano Gubinelli (Université Paris Dauphine)

Paracontrolled distributions and SPDEs

I will explain how ideas from the theory of non-linear waves, namely the paradifferential calculus of Bony, can be used to tackle problems in SPDEs and, more generally, problems involving non-linear operations on distributions. The aim of the mini-course is to develop the ideas and framework necessary to understand and give a meaning to singular (random) PDEs. We will also lay out links with the recent theory of regularity structures by Martin Hairer.

Lorenzo Zambotti (Université Pierre et Marie Curie)

Introduction to the theory of Regularity Structures

In this course we want to present the main ideas of this recent theory due to Martin Hairer. The motivation is given by a class of singular stochastic PDEs and their renormalization, but the scope of the theory is larger: I plan to emphasize how this formalism can be used to construct a pathwise stochastic integration with respect to multi-parameter (Gaussian) noises, thus generalizing the classical Ito versus Stratonovic integration to a filtration-free setting.

Some Photos

Massimiliano Gubinelli

Lorenzo Zambotti

The Audience

The Social Dinner

Registration

Participation to the school is free, but registration is mandatory. Please email us, no later than Thursday 29 January 2015, specifying the arrival/departure dates.

Program (updated)

The school starts on Monday 2 February 2015 (afternoon) and finishes on Friday 6 February 2015 (morning). Each course consists in 4 lectures of 2 hours each, held in room 3014 (info below), with the following schedule:

On the first day (Monday 2 February)

• A registration desk will be open in room 3014, in the time slots 11:30-12:00 and 13:30-14:00.
• Participants willing to join for lunch, before the school starts, are are welcome to do so: just be present at 12:00 in front of room 3014.
• A "welcome" social dinner will take place on Monday 2 February at 19:00, in the restaurant Refettorio Simplicitas, located in the very center of Milan (map). The dinner will feature a full Italian meal (vegetarian options available) and will have a cost of 30 euros/person (including water and wine). Participants willing to participate are kindly requested to let us know before Thursday 29 January 2015.

Downloadable Material

• Lecture notes for Massimiliano Gubinelli's course (section 2 can be skipped, as it will not be treated).
• Beamer slides for Massimiliano Gubinelli's course.
• Beamer slides for Lorenzo Zambotti's course.

Practical Info

Venue

The school is hosted by the Department of Mathematics and Applications of the University of Milano-Bicocca.
The lectures will be given in room 3014 (3rd floor) of the U5 building (via Roberto Cozzi 55, map).

Once you enter the building, take the corridor on the right and you will find the elevators (and stairs) on the right. Go up to the third floor, take the corridor on the left and in a few steps you will reach room 3014.

Wireless Internet Access

If you have access to eduroam at your home institution, you should be able to connect to the Bicocca eduroam network in the conference building using the same credentials.

Otherwise, we can give you access to the guest wifi network (possibly more reliable than eduroam) through a personal account, but for this we need to have your name, surname, nationality, date and place of birth, ID/passport number. Please send us this information no later than Monday 26 January 2015.

How to get here

See the dedicated page.

Accommodation

There is limited availability of accommodation on campus at Residenza delle Fontane (map), which is good value for money (60-70 euros/night, depending on the room). Reservations must be made contacting us.

For accommodation outside campus, participants are invited to make reservations on their own. Feel free to contact us for advice.

Financial support

Financial support for accommodation has been provided to young participants.

Lunch meals will be provided to participants at discounted price (5.50 euros/meal).

Registered Participants

Contacts

Organizing Committee: Francesco Caravenna, Federica Masiero, Gianmario Tessitore

Sponsors

We gratefully acknowledge the financial support of:

• Department of Mathematics and Applications
• Doctoral School in Mathematics and Applications of the University of Milano-Bicocca
• PRIN 2010-2011 'Problemi differenziali di evoluzione: approcci deterministici e stocastici e loro interazioni'