Associate Professor at UPC from 1990-1995. Associate Professor at UAB from 1995 until now. As a researcher I have proposed to solve problems that range from approximation questions for solutions of elliptic equations in different norms, problems on geometric measure theory related to the semiaditivity of analytic capacity, singular integrals, quasi-conformal mappings and in recent years I am mainly interested in problems related to the applications of harmonic analysis in fluid mechanics and in material sciences. In all these fileds I have obtained quite interesting results.

• Harmonic Analysis
• Geometric Measure Theory
• Euler Equation
• Aggregation Equation

-2017-SGR-0395. Grup d'Anàlisi Harmònica i Complexa i Equacions en Derivades Parcials. AGAUR, Generalitat de Catalunya. Tolsa Domènech Xavier. Universitat Autònoma de Barcelona (UAB). 01/01/2017-31/12/2020. 65896 euros. Investigador.
- MTM2016-77635-P. Análisis y ecuaciones en derivadas parciales. MINECO/FEDER 2016. Mateu Bennassar, Juan Eugenio. Universitat Autònoma Barcelona (UAB). 30/12/2016 – 29/12/2020. 67639 euros. Investigador Principal.

1. On dislocation theory
Carrillo, J. A.; Mateu, J.; Mora, M. G.; Rondi, L.; Scardia, L.; Verdera, J. 2020. The ellipse law: Kirchhoff meets dislocations. Comm. Math. Phys. 373. p. 507–524.
2. On linear transport equations.
Clop, Albert; Jiang, Renjin; Mateu, Joan; Orobitg, Joan 2016. Linear transport equations for vector fields with subexponentially integrable divergence. Calc. Var. Partial Differential Equations . 55.
3. On rotating vortex patches. This paper has had a big influence and has a lot of citations.
Hmidi, Taoufik; Mateu, Joan; Verdera, Joan 2013. Boundary regularity of rotating vortex patches. Arch. Ration. Mech. Anal.. 209. p. 171 – 208.
4. On relations between harmonic anlaysis and geometric measure theory.
Chousionis, V.; Mateu, J.; Prat, L.; Tolsa, X. 2012. Calderón-Zygmund kernels and rectifiability in the plane. . Adv. Math. 231 (2012), no. 1, 535-568. 231. p. 535 – 568.
5. On classical harmonic analysis
Mateu, J.; Orobitg, J.; Verdera, J. 2011. Estimates for the maximal singular integral in terms of the singular integral: the case of even kernels. Annals of Mathematics. 174. p. 1429 – 1483.
6. On quasiconformal mappings. Later this techniques were applied in fluid mechanics
Mateu, J.; Orobitg, J.; Verdera, J.2009. Extra cancellation of even Calderón-Zigmund operators and quasiconformal mappings. J. Math. Pures Appl. . 91. p. 402 – 431.
7. On quasiconformal mappings.
Astala, K.; Clop, A.; Mateu, J.; Orobitg, J.; Uriarte-Tuero, I. 2008. Distortion of Hausdorff measures and improved regularity for quasiregular mappings. Duke Math. J.. 141. p. 539 – 571.