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July, 11th
July, 12th
July, 13th
July, 14th
Courses
Regularisation by noise for ODEs and PDEs
Speaker: Franco Flandoli
Abstract: Standing the fact that many fluid mechanic equations do not have uniqueness of weak solutions, or regular solutions are not known to be global, in the last two decades there has been an intense activity to understand whether random perturbations may regularize the equations.
In finite dimensions, or for linear PDEs with a Lagrangian side, several results of restoration of uniqueness by noise have been proved; they will be illustrated in the first part of the lectures. However, for nonlinear PDEs they do not work well and several counterexamples have been proved.
On the contrary, it seems that noise may help to prevent blow-up for certain equations, possibly including the vorticity field of 3D Navier-Stokes equations. These delays of blow-up results will be described in the second part of the lectures.
The research is supported by the European Commission Project NoisyFluid, n. 101053472
Self-similarity, singularity, and non-uniqueness in partial differential equations of fluids dynamics.
Speaker: Dallas Albritton
Abstract: Self-similarity is a key ingredient in recent work on singularity formation in the Euler equations (Elgindi; Hou and Chen) and non-uniqueness in the Euler equations (Bressan, Murray, and Shen; Vishik) and Navier-Stokes equations (Jia, Sverak, and Guillod; A., Brué, and Colombo), with contributions by many more.
The goal of this course is to familiarize the audience with the kind of self-similarity analysis which appears in the above works and will continue to play an important role in the development of the field.
Speakers:
- Hyunju Kwon (ETH, Zürich)
- Samuel Punshon-Smith (Tulane University, New Orleans, USA)
- William Cooperman (University of Chicago, IL, USA)
- Umberto Pappalettera (Scuola Normale Superiore, Pisa, IT)
- Francesco Grotto (Scuola Normale Superiore, Pisa, IT)
- Paolo Bonicatto (University of Warwick, Coventry, UK)
- Laurel A. Ohm (Princeton, NJ, USA)
- Anuj Kumar (UC Santa Cruz, CA, USA)
- Stefano Bianchini (SISSA, Trieste, IT)
- Nicola De Nitti (FAU, Erlangen, DE)
- Gianluca Crippa (Universität Basel, CH)
Organizing Committee:
- Luigi Ambrosio (Scuola Normale Superiore, Pisa)
- Elia Brué (Scuola Normale Superiore, Pisa)
- Maria Colombo (EPFL, Losanna)
Schedule
Monday, July, 10th
9:00
Registration
9:00
9:30
Albritton
Albittron
11:00
Coffee break
11:00
11:30
Crippa
Crippa
12:30
Lunch
12:30
16:30
Lezione Leonardesca
Matching probability measures: a problem at the interface between combinatorics, probability and analysis
Leonardo da Vinci Lecture by the Riemann Prize Laureate at sala adunanze, Istituto Lombardo Accademia di Scienze e Lettere, Milan
Tuesday 11th
9:00
Flandoli
Flandoli
9:00
10:30
Coffee break
11:00
Albritton
Albritton
11:00
12:30
Lunch
14:00
Bonicatto
14:00
15:00
Punshon-Smith
Punshon-Smith
16:00
Coffee break
16:00
16:30
Flandoli
Flandoli
Wednesday 12th
9:00
Flandoli
Flandoli
9:00
10:30
Coffee break
11:00
Albritton
Albittron
11:00
12:30
Lunch
14:00
Kwon
Kwon
14:00
15:00
Kumar - Cooperman
16:00
Coffee break
16:00
16:30
Albritton
Thursday 13th
9:00
Flandoli
Flandoli
9:00
10:30
Coffee break
11:00
De Nitti
De Nitti
11:00
11:30
Bianchini
Bianchini
12:30
Lunch
12:30
14:00
Ohm
15:00
Grotto
Grotto
15:00
18:30
Social trip to Sacro Monte
We will visit also the Cript and Casa Museo Pogliaghi
20:00
Social dinner
at Location Camponovo
20:00
Friday 14th
11:00
Riemann Prize Ceremony
at Palazzo Estense, Varese
Hosted by Andrea Parlangeli
11:00
Opening at the presence of authorities
Interview to the awardee by Umberto Bottazzini
Award ceremony
Award ceremony and delivery of the Riemann Prize sculpture by Marcello Morandini and the Riemann Medal
25x2 years of memories about the University of Insubria
by Gianni Spartà
Riemann Lecture by Luigi Ambrosio
Il trasporto ottimale e le sue tante applicazioni
Music tribute
by Corrado Greco (piano) and Francesca Lombardi Mazzulli (soprano)
Supported by
