Currently associate professor (professor lector) at Universitat de Barcelona. I my Ph.D. in UAB under Xavier Tolsa's tuition, on Calderón-Zygmund operators and Sobolev spaces on domains, with applications to quasiconformal mappings. After that I have been postdoc in UAM with Daniel Faraco and in Aalto Yliopisto with Kari Astala, working on the Calderón inverse problem with techiques of quasiconformal mappings. We could develop a characterization for the sets of conductivities where the inverse mapping is continuous. I also obtained a postdoc position and a JdC-I position in UAB with Xavier Tolsa to work on free boundary problems, reaching remarkable results on the thin one-phase free boundary problem and in the VMO two-phase problem for harmonic measure. Actually I am working in harmonic measure problems with Xavier Tolsa and our Ph.D. student Ignasi Guillén.
Personal webpage: https://mat.uab.cat/~mprats/
- Calderón-Zygmund operators.
- Harmonic measures.
- Free boundary problems.
- Calderón inverse problem.
- Quasiconformal mappings.
Ph.D. (FI-DGR) in UAB with Xavier Tolsa 2012-2015.
Postdoc (ERC project GFTIPFD) in UAM with Daniel Faraco 2015-2017.
Postoc (ERC project GAES) in UAB with Xavier Tolsa 2017-2019.
Postdoc (ERC project QUAMAP) in Aalto Y. with Kari Astala 2019-2020.
Investigador JdC-I in UAB 2020-21.
Professor lector in UB since 2021.
Prats, M.; Tolsa, X. (2020). The two-phase problem for harmonic measure in VMO. Calculus of Variations and Partial Differential Equations, 59(102) . https://doi.org/10.1007/s00526-020-01760-2 . ISSN: 0944-2669.
Prats, M. (2019). Sobolev regularity of quasiconformal mappings on domains. Journal d'Analyse Mathematique, 138, pp. 513 - 562 . https://doi.org/10.1007/s11854-019-0031-9. ISSN: 0021-7670.
Astala, K.; Prats, M.; Saksman, E. (2019). Global smoothness of quasiconformal mappings in the Triebel-Lizorkin scale. arXiv.org . Preprint (https://arxiv.org/abs/1901.07844) . ISSN: 2331-8422.
Engelstein, M.; Kauranen, A.; Prats, M.; Sakelaris, G.; Sire, Y. (2021). Minimizers for the thin one-phase free boundary problem. Communications on Pure and Applied Mathematics, 74(9), pp. 1971 - 2022. Publicació online (https://onlinelibrary.wiley.com/doi/10.1002/cpa.22011) ISSN: 0010-3640.
Faraco, D.; Prats, M. (2018). Characterization for stability in planar conductivities. Journal of Differential Equations, 264(9), pp. 5659 - 5712 . https://doi.org/10.1016/j.jmaa.2017.02.016 . ISSN: 0022-0396