Conference on Nonlinear PDE’s
Sign into July 07, 2026
Venue: Institut d'Estudis Catalans (IEC)
REGISTRATION
Attendance at this conference is by invitation only.
SCHEDULE
Introduction
The modern study of the abstract properties of solutions to Nonlinear Partial Differential Equations brings together a rich variety of mathematical tools originating from diverse fields such as the Calculus of Variations, Functional Analysis, Harmonic Analysis, and Differential Geometry. This interplay of techniques makes the area very attractive, and also particularly significant for the mathematical community in Barcelona.
The 60th anniversary of our colleague Xavier Cabré offers an excellent occasion to celebrate his contributions with an international conference devoted to this area of research. As an outstanding researcher, Xavier Cabré has made profound contributions to the field of Nonlinear PDEs, and has played a central role in fostering and inspiring a strong local community of researchers. Our community owes him deep gratitude and recognition for his dedication, generosity, and scientific leadership.
Given the level of the invited speakers, we anticipate significant interest in the conference. However, due to capacity constraints and in order to preserve the focused and collaborative character of the event, attendance will be by invitation of the organizing committee. Should someone not initially invited wish to participate and their presence be considered valuable, the committee may extend additional invitations.
invited speakers
Scott Armstrong
New York University
Henri Berestycki
École des Hautes Études en Sciences Sociales
Guido De Philippis
Università degli Studi di Padova – New York University
Alessio Figalli
ETH Zürich
David Jerison
Massachusetts Institute of Technology
Elliptization of the Gradient Flow / Weighted Energy Dynamics and Applications
Fanghua Lin
New York University
Abstract
Sylvia Serfaty
New York University
Luis Silvestre
University of Chicago
ORGANISING and scientific committee
Xavier Ros-Oton | ICREA – Universitat de Barcelona – Centre de Recerca Matemàtica
Tomás Sanz-Perela | Universitat de Barcelona – Centre de Recerca Matemàtica
Joaquim Serra | ETH Zürich
Joan Solà-Morales | Universitat Politècnica de Catalunya
SCHEDULE
MondayJuly 6th |
TuesdayJuly 7th |
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09:15 – 09:50 |
Registration |
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09:50 – 10:00 |
Opening |
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10:00 – 11:00 |
Alessio FigalliETH Zürich |
David JerisonMassachusetts Institute of Technology |
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11:00 – 11:45 |
Coffee break + photo |
Coffee break |
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11:45 – 12:45 |
Luis SilvestreUniversity of Chicago |
Scott ArmstrongNew York University |
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12:45 – 15:00 |
Free time (lunch) |
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15:00 – 16:00 |
Sylvia SerfatyNew York University |
Fanghua LinNew York University |
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16:00 – 16:30 |
Coffee break |
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16:30 – 17:30 |
Guido de PhilippisUniversità degli Studi di Padova – New York University |
Henri BerestyckiÉcole des Hautes Études en Sciences Sociales |
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19:30 |
Social dinner |
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LIST OF PARTICIPANTS
| Name | Institution |
|---|---|
| Giovanni Catino | Politecnico di Milano |
| Iñigo Urtiaga Erneta | Rutgers University |
| Jean-Michel Roquejoffre | Toulouse III-Paul Sabatier University |
| Sylvia Serfaty | Sorbonne Université |
| Tomás Sanz Perela | Universitat de Barcelona |
| Joaquim Ortega Cerdà | Universitat de Barcelona |
| Maria Carmen Cascante Canut | Universitat de Barcelona |
| Gissell Estrada-Rodriguez | Universitat Politècnica de Catalunya |
| Neus Cónsul | Universitat Politècnica de Catalunya |
| Sebastian Xambó Descamps | Universitat Politècnica de Catalunya |
| Joan Solà-Morales | Universitat Politècnica de Catalunya |
| Salvador Villegas | Universidad de Granada |
| Fernando Quirós | Universidad Autónoma de Madrid |
| Maria del Mar González Nogueras | Universidad Autónoma de Madrid |
| Juan Luis Vazquez | Universidad Autónoma de Madrid |
| Enrico Valdinoci | University of Western Australia |
| Serena Dipierro | University of Western Australia |
| Fabiana Leoni | Sapienza University of Rome |
| Italo Capuzzo Dolcetta | Sapienza University of Rome |
| Luciano Mari | University of Milan |
| Eleonora Cinti | University of Bologna |
| Bruno Franchi | University of Bologna |
| Castorina Daniele | University of Naples Federico II |
| Carlo Mantegazza | University of Naples Federico II |
| Enric Florit | Swiss Federal Institute of Technology in Zurich |
| Fanghua Lin | New York University |
| Marcello Lucia | The City University of New York (CUNY) |
LODGING INFORMATION
ON-CAMPUS AND BELLATERRA
BARCELONA AND OFF-CAMPUS
acknowledgement
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For inquiries about this event please contact the Scientific Events Coordinator Ms. Núria Hernández at nhernandez@crm.cat
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Here I shall discuss a few applications related to the heat flow of harmonic map heat flow. In particular its global existence, uniqueness and regularity into singular spaces; the behavior of maps near the first time self-similar blow ups and the uniqueness of tangent flows; and properties of Rank 0 and Rank 1 sets of maps. The key tool is the monotonicity formulas of Struwe as well as that of Almgren-Poon type.