BCAM Course | Self-similar singularity formation in nonlinear PDE
Date: Mon, Nov 16 - Fri, Nov 20 2026
Hour: 11:00 - 13:00
Location: Maryam Mirzakhani Seminar Room
Speakers: Gonzalo Cao-Labora (EPFL)
Register: Registration Link
Abstract
Self-similar singularities are classical candidates for blowup of nonlinear PDE, and their study has gained tremendous traction in the last decades. In combination with convex-integration techniques, they were used to construct singularities for the forced incompressible Navier-Stokes equations. We will discuss the most recent developments of the self-similar techniques in the last years, starting with the breakthrough work of Merle, Raphael, Rodnianski and Szeftel for compressible fluids and defocusing supercritical NLS. Then, we will treat incompressible fluids and focusing NLS.
Registration deadline: November 12th, 2026
Organizers:
BCAM
Confirmed speakers:
Short bio:
I am a mathematical analyst working on nonlinear partial differential equations, mainly in mathematical fluid dynamics and in problems at the interface of analysis and geometry. My work often combines analytical techniques with rigorous computer-assisted proofs.
I received my PhD from MIT in 2024 under the supervision of Gigliola Staffilani, after undergraduate degrees in Mathematics and Engineering Physics at UPC (Barcelona). Before joining EPFL, I was a Courant Instructor at the Courant Institute, New York University
2026 — Vicent Caselles Prize (Royal Spanish Mathematical Society – BBVA Foundation).
2026 — New preprints: counterexamples to Schiffer's conjecture (with J. de Dios Pont), inhomogeneous Einstein metrics on complex projective spaces (with A. Rodríguez-Vázquez) and instability of two-dimensional Taylor–Green vortices (with M. Colombo, M. Dolce and P. Ventura).
2025 — R. E. Moore Prize for Applications of Interval Analysis, with T. Buckmaster and J. Gómez-Serrano, for our paper on smooth implosion for compressible fluids (Forum of Mathematics, Pi).
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