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Administrative data

Gonzalo Cao Labora

gonzalo.caolabora@epfl.ch

Nationality: EU (Spanish)

EPFL SB MATH AMCV
MA B2 455 (Bâtiment MA)
Station 8
1015 Lausanne

Expertise

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.

News

Selected results
Analysis and geometry
  • Schiffer's conjecture. With J. de Dios Pont, we showed that Schiffer's conjecture fails in the plane: there are smooth planar domains, other than disks, that carry a Neumann eigenfunction of the Laplacian which is constant on the boundary. This also disproves the Pompeiu conjecture in the plane. With A. J. Fernández, we also constructed a contractible Schiffer counterexample on the half-sphere.
  • Einstein metrics. With A. Rodríguez-Vázquez, we constructed the first inhomogeneous Einstein metrics on ℂPⁿ for 3 ≤ n ≤ 7, answering a 1965 question of Berger for ℂP⁴ and ℂP⁶.
Fluid dynamics
  • Implosion for compressible fluids. With T. Buckmaster and J. Gómez-Serrano, we constructed smooth imploding solutions of the 3D compressible Euler and Navier–Stokes equations for all adiabatic exponents, including the first smooth self-similar profiles for monatomic gases. With J. Gómez-Serrano, J. Shi and G. Staffilani, we obtained the first non-radial and periodic implosions, both for compressible fluids and for the supercritical defocusing nonlinear Schrödinger equation.
  • Instability of the Taylor–Green vortex. With M. Colombo, M. Dolce and P. Ventura, we proved that the two-dimensional Taylor–Green vortex (cellular flow) is linearly and nonlinearly unstable for the Euler equations, through a new eigenvalue criterion for Hamiltonian operators and a computer-assisted proof.
  • Unstable singularities. In a collaboration between mathematicians and Google DeepMind, we discovered new families of unstable self-similar blow-up solutions for the incompressible porous media equation and the 3D Euler equation with boundary, computed to near machine precision, as required for computer-assisted proofs.

Media and outreach

Background
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

Working languages: English, Spanish, Galician and Catalan.

Contact and online profiles

Education

PhD in Mathematics

| Thesis: “Self-similar singularity formation and wellposedness theory for compressible fluids and dispersive PDE”. MIT Presidential Fellow.

2020 – 2024 Massachusetts Institute of Technology (MIT)
Directed by Gigliola Staffilani

BSc in Mathematics

| First of the class. Final degree thesis at Princeton University (2019–2020), awarded the 2021 Emmy Noether Prize.

2016 – 2020 Universitat Politècnica de Catalunya (UPC), CFIS double degree
Directed by Javier Gómez-Serrano

BSc in Engineering Physics

| Double degree with Mathematics.

2016 – 2020 Universitat Politècnica de Catalunya (UPC), CFIS double degree

Professionals experiences

Courant Instructor

Postdoctoral position (Courant Instructor) at the Courant Institute of Mathematical Sciences. Taught Analysis I (Fall 2024, Spring 2025).

2024–2025

Courant Institute of Mathematical Sciences, New York University (USA)

Awards

Vicent Caselles Mathematical Research Prize

Royal Spanish Mathematical Society (RSME) – BBVA Foundation

2026

R. E. Moore Prize for Applications of Interval Analysis (with T. Buckmaster and J. Gómez-Serrano)

Editorial board of the journal Reliable Computing

2025

Emmy Noether Prize for the best mathematics bachelor's thesis in Catalonia

Catalan Mathematical Society (SCM) – Institut d'Estudis Catalans

2021

Presidential Fellowship (PhD studies)

Massachusetts Institute of Technology (MIT)

2020

Two gold medals and one silver medal (2017–2019)

International Mathematics Competition for University Students (IMC)

2019

Bronze medal (2014) and honourable mention (2015)

International Mathematical Olympiad (IMO)

2015

Selected publications

Counterexamples to Schiffer's conjecture

Gonzalo Cao-Labora, Jaume de Dios Pont
Published in arXiv preprint 2608.05114 in 2026

Inhomogeneous Einstein metrics on complex projective spaces

Gonzalo Cao-Labora, Alberto Rodríguez-Vázquez
Published in arXiv preprint 2608.16880 in 2026

Instability of two-dimensional Taylor–Green vortices

Gonzalo Cao-Labora, Maria Colombo, Michele Dolce, Paolo Ventura
Published in arXiv preprint 2601.23040 in 2026

Smooth imploding solutions for 3D compressible fluids

Tristan Buckmaster, Gonzalo Cao-Labora, Javier Gómez-Serrano
Published in Forum of Mathematics, Pi 13, e6 in 2025

Non-radial implosion for compressible Euler and Navier–Stokes in T³ and R³

Gonzalo Cao-Labora, Javier Gómez-Serrano, Jia Shi, Gigliola Staffilani
Published in Cambridge Journal of Mathematics 13 (4), 753–885 in 2026

Discovery of unstable singularities

Yongji Wang, Mehdi Bennani, James Martens, Sébastien Racanière, Sam Blackwell, Alex Matthews, Stanislav Nikolov, Gonzalo Cao-Labora, Daniel S. Park, Martin Arjovsky, Daniel Worrall, Chongli Qin, Ferran Alet, Borislav Kozlovskii, Nenad Tomašev, Alex Davies, Pushmeet Kohli, Tristan Buckmaster, Bogdan Georgiev, Javier Gómez-Serrano, Ray Jiang, Ching-Yao Lai
Published in arXiv preprint 2509.14185 in 2025

Teaching & PhD

Courses

Introduction to partial differential equations

MATH-305

This is an introductory course on Elliptic Partial Differential Equations. The course will cover the theory of both classical and generalized (weak) solutions of elliptic PDEs.