Recent Breakthroughs
in Singular Stochastic PDEs

Bicocca Winter School (Milan, 2-6 February 2015)

Some Photos

Massimiliano Gubinelli

Massimiliano Gubinelli   Massimiliano Gubinelli   Massimiliano Gubinelli

Lorenzo Zambotti

Lorenzo Zambotti   Lorenzo Zambotti   Lorenzo Zambotti

The Audience

The Audience   The Audience   The Audience

The Social Dinner

The Social Dinner


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.

Massimiliano Gubinelli

Massimiliano Gubinelli

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

Lorenzo Zambotti

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.


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:

Mon 2 Tue 3 Wed 4 Thu 5 Fri 6
10:00-12:00 - Zambotti Gubinelli Gubinelli Zambotti
14:00-16:00  Zambotti Gubinelli Gubinelli Zambotti -

On the first day (Monday 2 February)

Downloadable Material

Practical Info


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.


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

Name Affiliation
Davide Addona Università di Milano Bicocca
Federico Bassetti Università di Pavia
Carlo Bellingeri Università di Pavia
Alessandro Calvia Università di Milano Bicocca
Fulvia Confortola Politecnico di Milano
Jacopo Corbetta Università di Milano Bicocca
Francisco Javier Delgado Università di Pisa
Gaurav Dhariwal University of York
Francesco De Vecchi Università di Milano
Benedetta Ferrario Università di Pavia
Nahuel Foresta Politecnico di Milano
Marco Fuhrman Politecnico di Milano
Marco Furlan University of Paris-Dauphine
Xi Geng University of Oxford
Giulio Giusteri Università Cattolica Brescia
Giuseppina Guatteri Politecnico di Milano
Roberto Guenzani Università di Milano
Anselm Hudde University of Freiburg
Chaman Kumar University of Edinburgh
James-Michael Leahy University of Edinburgh
Tobias Lehmann University of Leipzig
Marta Leocata Unversità di Milano Bicocca
Sungbin Lim Korea University
Nick Lindemulder Delft University
Thibaut Mastrolia University of Paris-Dauphine
Peter Nelson University of Mainz
Alexander Nerlich University of Ulm
Nikolas Nuesken Imperial College London
André Oliveira Gomes Humboldt University Berlin
Carlo Orrieri Università di Pavia
Giovanni Paolinelli Università di Milano Bicocca
Fei Pu EPFL Lausanne
Mauro Rosestolato Luiss Roma
Elisa Tacconi Università Bocconi Milano
Niccolò Torri Université Claude Bernard-Lyon 1, Università di Milano Bicocca
Petr Veverka Politecnico di Milano
Martin Weidner Imperial College London
Margherita Zanella Università di Pavia


Organizing Committee: Francesco Caravenna, Federica Masiero, Gianmario Tessitore


We gratefully acknowledge the financial support of

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Last modified: 3 Feb 2015.