Martí Prats Soler

Lecturer Professor

Scopus Author ID: 56573732400

Researcher ID: AAJ-2202-2021

Knowledge area: Anàlisi Matemàtica

Grup de recerca en Equacions en Derivades Parcials

Contact Information
Department of Mathematics and Computer Science
Despatx P1 38 Facultat de Matemàtiques i Informàtica Gran Via, 585
934035747
martiprats(a)ub.edu

Journal Publications

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 . Institutional Repository . ISSN: 0010-3640

Prats, M. (2020). Triebel-Lizorkin regularity and bi-Lipschitz maps: composition operator and inverse function regularity. arXiv.org . Preprint (https://arxiv.org/abs/2007.10070) . ISSN: 2331-8422

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

Prats, M. (2019). Measuring Triebel-Lizorkin fractional smoothness on domains in terms of first‐order differences. Journal of the London Mathematical Society-Second Series, 100(2), pp. 692 - 716 . https://doi.org/10.1112/jlms.12225 . ISSN: 0024-6107

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

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

Prats, M. (2018). Beltrami equations in the plane and Sobolev regularity. Communications on Pure and Applied Analysis , 17(2), pp. 319 - 332 . https://doi.org/10.3934/cpaa.2018018 . ISSN: 1534-0392

Oliva, M.; Prats, M. (2017). Sharp bounds for composition with quasiconformal mappings in Sobolev spaces. Journal of Mathematical Analysis and Applications, 451(2), pp. 1026 - 1044 . https://doi.org/10.1016/j.jmaa.2017.02.016 . ISSN: 0022-247X

Prats, M.; Saksman, E. (2017). A T(1) theorem for fractional Sobolev spaces on domains. Journal of Geometric Analysis, 27, pp. 2490 - 2538 . https://doi.org/10.1007/s12220-017-9770-y . ISSN: 1050-6926

Prats, M. (2017). Sobolev regularity of the Beurling transform on planar domains. Publicacions Matemàtiques, 61(2), pp. 291 - 336 . https://doi.org/10.5565/PUBLMAT6121701 . ISSN: 0214-1493

Prats, M.; Tolsa, X. (2015). A T(P) theorem for Sobolev spaces on domains. Journal of Functional Analysis, 268(10), pp. 2946 - 2989 . https://doi.org/10.1016/j.jfa.2015.01.007 . ISSN: 0022-1236

Participations in Conferences

Prats, M. (2019). Measuring Triebel-Lizorkin fractional smoothness on domains in terms of first-order differences. (Speech) . Barcelona Analysis Conference . https://mat.uab.cat/~mprats/Presentacions/BAC19%20-%20Prats.pdf . Barcelona . SPAIN

Prats, M. (2017). Regularity of quasiconformal self-maps. (Speech) . Congreso de jóvenes investigadores . http://mat.uab.cat/~mprats/Presentacions/CJI%20-%20Prats-Presentacio.pdf . València . SPAIN

Prats, M. (2017). Stability of Calderón's inverse problem in 2D. (Invited conference) . Applied Inverse Problems conference . http://mat.uab.cat/~mprats/Presentacions/AIP2017.pdf . Hangzhou . CHINA

Prats, M. (2017). Characterization for stability in planar conductivities. (Invited conference) . III Encuentros de problemas inversos . https://mat.uab.cat/~mprats/Presentacions/UAM-seminar.pdf . Madrid . SPAIN

Prats, M. (2016). Regularity of planar quasiconformal mappings. (Speech) . Barcelona Analysis Conference . http://mat.uab.cat/~mprats/Presentacions/BAC-Presentacio.pdf . Barcelona . SPAIN

Prats, M. (2014). Boundedness of Calderón-Zygmund operators in Sobolev spaces of a Lipschitz domain. (Speech) . School on Nonlinear Analysis, Function Spaces and Applications . http://mat.uab.cat/~mprats/Presentacions/NAFSA-Prats.pdf . Trest . CZECH REPUBLIC

Prats, M. (2014). Bounding Calderón-Zygmund operators in Sobolev spaces on Lipschitz domains. (Speech) . Encuentros de Análisis Real y Complejo . http://mat.uab.cat/~mprats/Presentacions/EARCO-Prats.pdf . Girona . SPAIN

Prats, M. (2013). A T(1) theorem for Sobolev spaces on domains. (Speech) . II Congreso de Jóvenes Investigadores . http://mat.uab.cat/~mprats/Presentacions/CJI-Prats.pdf . Sevilla . SPAIN

Prats, M. (2013). Rectifiable sets and the Traveling Salesman Problem. (Speech) . T(1) and T(b) theorems and applications . http://mat.uab.cat/~mprats/Presentacions/T1TBTA-Prats.pdf . Kopp . GERMANY

Prats, M. (2013). Smoothness of the Beurling transform in Lipschitz domains. (Speech) . International Workshop on Complex and Harmonic Analysis . http://mat.uab.cat/~mprats/Presentacions/CARA-Prats.pdf . Málaga . SPAIN

Prats, M. (2022). The two-phase problem for harmonic measure in VMO via jump formulas for the Riesz transform. (Speech) . Workshop on harmonic analysis, singular integrals and PDEs . Bonn . GERMANY

Lectures

The two-phase problem for harmonic measure in VMO via jump formulas for the Riesz transform . (Seminario de análisis y aplicaciones UAM-ICMAT). 12/03/2021. Madrid. SPAIN

The two-phase problem for harmonic measure in VMO via jump formulas for the Riesz transform . (Harmonic analysis seminar, Helsingin Yliopisto). 06/03/2020. Helsinki. FINLAND

Thin one-phase free-boundary problem (part 2) . (Analysis and PDE seminar, Aalto Yliopisto). 13/02/2020. Espoo. FINLAND

Thin one-phase free-boundary problem . (Analysis and PDE seminar, Aalto Yliopisto). 29/01/2020. Espoo. FINLAND

Measuring Triebel-Lizorkin fractional smoothness on domains in terms of first-order differences . (Analysis and PDE seminar, Aalto Yliopisto). 09/10/2019. Espoo. FINLAND

Measuring Triebel-Lizorkin fractional smoothness on domains in terms of first-order differences . (Geometric and Functional Analysis Seminar, Helsingin Yliopisto). 03/10/2019. Helsinki. FINLAND

El problema del venedor ambulant . (Seminari de doctorands, Departament de matemàtiques, Universitat Autònoma de Barcelona). 22/06/2018. Cerdanyola del Vallès. SPAIN

Rectifiable sets and the Traveling Salesman Problem . (Seminario Júnior UAM-ICMAT). 27/09/2017. Madrid. SPAIN

Stability of Calderón's inverse problem in 2D . (Seminari d'anàlisi de Barcelona, UB-UAB). 26/06/2017. Cerdanyola del Vallès. SPAIN

Characterization for stability in planar conductivities . (Funktionaalianalyysin seminaari, Helsingin Yliopisto). 16/03/2017. Helsinki. FINLAND

Characterization for stability in planar conductivities . (Inverse problems seminar, Jyväskylän Yliopisto). 13/03/2017. Jyväskylä. FINLAND

Singular integral operators on Sobolev spaces on domains and quasiconformal mappings . (Seminario de Análisis y Aplicaciones UAM-ICMAT). 13/11/2015. Madrid. SPAIN

The Beurling transform in Sobolev spaces of a Lipschitz domain . (Jyväskylä Analysis Seminar, Jyväskylän Yliopisto). 26/11/2014. Jyväskylä. FINLAND

The Beurling transform in Sobolev spaces of a Lipschitz domain . (Geometrisen analyysin seminaari, Helsingin Yliopisto). 23/09/2014. Helsinki. FINLAND

A T(1) theorem for Sobolev spaces on domains . (Seminari d'Anàlisi de Barcelona (UB-UAB)). 07/10/2013. Barcelona. FINLAND

Riemann mapping and regularity in the Sobolev and Triebel-Lizorkin scale . (Complex analysis and operator theory seminar (IMUS)). 01/06/2021. Sevilla. SPAIN

The two-phase problem for harmonic measure in VMO via jump formulas for the Riesz transform . (Oberseminar Discrete harmonic and harmonic analysis, Würzburg). 08/07/2021. Würzburg. GERMANY

Measuring Triebel-Lizorkin fractional smoothness on domains in terms of first-order differences . (Barcelona Analysis Conference). 27/06/2019. Barcelona. SPAIN

The two-phase problem for harmonic measure in VMO via jump formulas for the Riesz transform . (Workshop on Analysis, singular integrals and PDEs, Hausdorff Research Institute for Mathematics). 01/02/2022. Bonn. GERMANY

Teaching imparted

Taller preparatori de matemàtiques a l'escola d'enginyeria (Bachelor's degree) - Gestión Aeronáutica - Universidad Autónoma de Barcelona.

Càlcul (Bachelor's degree) - Ingeniería Informática(1) - Universidad Autónoma de Barcelona.

Laboratori integrat 3 (Llicenciatura degree) - Biotecnología - Universidad Autónoma de Barcelona.

Funcions de variable real (Bachelor's degree) - Matemáticas - Universidad Autónoma de Barcelona.

Càlcul en diverses variables i optimització (Bachelor's degree) - Matemáticas - Universidad Autónoma de Barcelona.

Estadística (Bachelor's degree) - Ciencia y Tecnología de los Alimentos(1) - Universidad Autónoma de Barcelona.

Introducció al Càlcul Integral (Bachelor's degree) - Matemáticas - Universidad de Barcelona.

Càlcul Integral en Diverses Variables (Bachelor's degree) - Matemáticas - Universidad de Barcelona.

Càlcul en diverses variables (Bachelor's degree) - Computational mathematics and data analytics - Universidad Autónoma de Barcelona.

Càlcul en una variable (Bachelor's degree) - Computational mathematics and data analytics - Universidad Autónoma de Barcelona.

Càlcul (Bachelor's degree) - Aeronautical management - Universidad Autónoma de Barcelona.

Anàlisi Harmònica i Teoria del Senyal (Bachelor's degree) - Matemáticas - Universidad de Barcelona.

Introducció al Càlcul Diferencial (Bachelor's degree) - Matemáticas - Universidad de Barcelona.

Càlcul Diferencial en Diverses Variables (Bachelor's degree) - Matemáticas - Universidad de Barcelona.

Anàlisi Matemàtica (Bachelor's degree) - Matemáticas - Universidad de Barcelona.

Anàlisi Complexa (Bachelor's degree) - Matemáticas - Universidad de Barcelona.

Teaching Activities

Using Teams to support teaching (10h) (A1. Attendance to courses to improve university teaching) . 21/09/2020 - 07/10/2020

Codirection of Ignasi Guillén's Ph.D. thesis (A7. Training of junior researchers: direction or co-direction of thesis in progress) . 01/09/2020 - 01/04/2024

Deliver the workshop 'Complex dynamics put simple' in the program 'Matikkaakatemia' (academy of mathematics) for high school students (2h) (Other teaching merits) . 02/10/2019 - 02/10/2019

Continuous evaluation in large groups (8h) (A1. Attendance to courses to improve university teaching) . 21/01/2019 - 23/01/2019

Regular collaboration elaborating the section Bits of mathematics on mathematical software in the semiannual magazine Notícies of the Catalan Society of Mathematics (Other teaching merits) . 01/09/2018 - 2022

Preparatory workshop for mathematics in the engineering school (6h) (C10. Development of tasks related to the secondary school - university transition) . 01/09/2018 - 21/09/2018

Park City Mathematics Institute Research Program on Harmonic Analysis (48h) (A1. Attendance to courses to improve university teaching) . 01/07/2018 - 21/07/2018

School on Real Harmonic Analysis and its Applications to Partial Differential Equations and Geometric Measure Theory (12h) (A1. Attendance to courses to improve university teaching) . 21/05/2018 - 01/06/2018

Mathematics between high school and college. The history of mathematics, 2018 (5h) (A1. Attendance to courses to improve university teaching) . 05/04/2018 - 05/04/2018

Supervision of the doctoral thesis. How to prevent and deal with problems and incidents (8h) (A1. Attendance to courses to improve university teaching) . 24/01/2018 - 25/01/2018

Tutorial course on Applied Inverse Problems (18h) (A1. Attendance to courses to improve university teaching) . 26/05/2017 - 28/05/2017

Deliver twice the workshop 'Mathematics' (1:15) for high school students in the Science Week program (Other teaching merits) . 07/11/2016 - 07/11/2016

Publication of dissemination articles in the online literary magazine PLACER, numbers 1, 4, 6 and 9, see lamordidaliteraria.com/placer (Other teaching merits) . 01/01/2016 - 31/12/2018

Jury at the Spanish mathematical olympiad (Other teaching merits) . 19/03/2015 - 22/03/2015

Quasiconformal mappings and complex dynamics (Núria Fagella, Xavier Tolsa, Albert Clop, 60h) (A1. Attendance to courses to improve university teaching) . 15/02/2015 - 30/06/2015

Partial Differential Equations (Xavier Cabré, María de Mar González, 60h) (A1. Attendance to courses to improve university teaching) . 15/02/2015 - 30/06/2015

School on Nonlinear Analysis, Function Spaces and Applications (27h) (A1. Attendance to courses to improve university teaching) . 09/06/2014 - 15/06/2014

Deliver the workshop 'Conical Sections' in the program Crazy for Mathematics (4h / year) (Other teaching merits) . 01/01/2014 - 31/12/2017

T(1) and T(b) theorems and applications (25h) (A1. Attendance to courses to improve university teaching) . 13/07/2013 - 26/07/2013

Doc-course Complex Analysis and Related Areas (58h) (A1. Attendance to courses to improve university teaching) . 01/02/2013 - 15/02/2013

3r curs anual de l'aFFaC: la segregació escolar (A1. Attendance to courses to improve university teaching) . 09/03/2021 - 25/03/2021

Jornades Docents Facultat de Matemàtiques i Informàtica Juny 2022, 6 hores (A1. Attendance to courses to improve university teaching) . 29/06/2022 - 29/06/2022

Academic training

Llicenciatura en Matemàtiques . Universitat de Barcelona . 13/09/2005 . (Diploma / Degree / Activities)

Doctorat en Matemàtiques . Universitat Autònoma de Barcelona . 21/10/2015 . (Ph.D.)

Màster en Matemàtica Avançada . Universitat Autònoma de Barcelona . 24/11/2011 . (Official Master)

Diploma Universitari de Postgrau en Matemàtiques per a Secundària . Universitat Pompeu Fabra . 06/07/2010 . (Specialized Training)

Certificat d'Aptitud Pedagògica . Universitat de Barcelona . 18/05/2005 . (Specialized Training)

Stays abroad in Research Centers

ICMAT. Madrid. SPAIN. 2018 (12 Days) . Research term on real harmonic analysis and its applications to PDE and GMT . Postdoctoral

Park City Mathematics Institute - Institute of Advanced Studies. Park City. UNITED STATES. 2018 (21 Days) . PCMI research program on harmonic analysis . Postdoctoral

University of Helsinki. Helsinki. FINLAND. 2017 (12 Days) . Research stay . Postdoctoral

University of Helsinki. Helsinki. FINLAND. 2016 (7 Days) . Research stay . Postdoctoral

University of Helsinki. Helsinki. FINLAND. 2014 (3 Months) . Predoctoral stay . Ph.D. Student

Instituto de matemáticas Universidad de Sevilla, Universidad de Málaga. Sevilla. SPAIN. 2013 (1 Months 15 Days) . Doc-course Complex analysis and related areas . Ph.D. Student

Hausdorff Research Institute for mathematics. Kopp. GERMANY. 2013 (6 Days) . Summer school 'T(1) and T(b) theorems and applications' . Pre-Doctoral

Projects

Juan de la Cierva (incorporación): Singular integrals, harmonic measure and free boundary problems (Sense especificar) . 2020 - 2023 . Ref.IJC2018-035373-I . Ministerio de Economia y Competitividad . PI: Xavier Tolsa Domenech; Martí Prats Soler . (2 Researchers)

Quasiconformal Methods in Analysis and Applications (HORIZON 2020. PILLAR 1-EXCELLENT SCIENCE. ERC. European Research Council.) . 2019 - 2024 . Ref.834728 . Unió Europea . PI: Kari Astala . (2 Researchers) . Postdoc position obtained by public contest

Geometric analysis in the euclidean space (IDEAS. 7è Programa Marc. ERC IDEAS Programme (Programa IDEES del Consell Europeu de Recerca).) . 2013 - 2018 . Ref.320501 . Unió Europea . PI: Xavier Tolsa Domenech . (3 Researchers)

Analisis armónico, teoría geométrica de la medida y aplicaciones (Matemáticas (MTM)) . 2016 - 2020 . Ref.MTM2016-77635-P . Ministerio de Economia y Competitividad . PI: Xavier Tolsa Domenech

Anàlisi real i complexa, i equacions en derivades parcials (Ajuts de Suport als Grups de Recerca de Catalunya (SGR)) . 2017 - 2021 . Ref.2017SGR395 . Agència de Gestió d'Ajuts Universitaris i de Recerca (AGAUR) . PI: Xavier Tolsa Domenech

Geometric function theory, inverse problems and fluid dynamics (IDEAS. 7è Programa Marc. ERC IDEAS Programme (Programa IDEES del Consell Europeu de Recerca).) . 2012 - 2018 . Ref.307179 . Unió Europea . PI: Daniel Faraco . (2 Researchers) . Postdoc obtained by public contest

Programa d'ajuts per a la contractació de personal investigador novell (FI-DGR) () . 2012 - 2015 . Ref.2012FI_B 00842 . Agència de Gestió d'Ajuts Universitaris i de Recerca (AGAUR) . PI: Xavier Tolsa Domènech . (1 Researchers) . Beca predoctoral

Integrales singulares, teoría geométrica de la medida y espacios de Sobolev (Matemáticas (MTM)) . 2014 - 2016 . Ref.MTM2013-44304-P . Ministerio de Economia y Competitividad . PI: Xavier Tolsa Domenech

Grup d'Anàlisi Harmònica i Complexa (Ajuts de Suport als Grups de Recerca de Catalunya (SGR)) . 2014 - 2017 . Ref.2014SGR00075 . Agència de Gestió d'Ajuts Universitaris i de Recerca (AGAUR) . PI: Joan Orobitg Huguet . (15 Researchers)

Análisis geométrico en el espacio euclídeo (Matemáticas (MTM)) . 2011 - 2013 . Ref.MTM2010-16232 . Ministerio de Ciencia e Innovación (MICINN) . PI: Xavier Tolsa Domenech

Unidades de excelencia «María de Maeztu». Centre de Recerca Matemàtica (CRM) (Sense especificar) . 2022 - 2025 . Ref.CEX2020-001084-M . Ministerio de Ciencia, Innovación y Universidades . PI: Marcel Guardia Munarriz

INTEGRALES SINGULARES, TEORIA GEOMETRICA DE LA MEDIDA Y EDP'S (Sense especificar) . 2021 - 2025 . Ref.PID2020-114167GB-I00 . Ministerio de Ciencia, Innovación y Universidades . PI: Xavier Tolsa Domenech . (9 Researchers)

Varias variables complejas y distribución óptima de puntos () . 2022 - 2025 . Ref.PID2021-123405NB-I00 . Ministerio de Ciencia e Innovación (MICINN) . PI: Joaquim Ortega Cerdà

EDPs i macánica de fluidos () . 2022 - 2025 . Ref.PID2021-125021NA-I00 . Ministerio de Ciencia e Innovación (MICINN) . PI: Xavier Ros Oton, Javier Gómez Serrano

Currricul@'s texts

Born in Barcelona in 1983, I studied in this university from 2001 to 2005. After some years working in secondary education I did my way back to mathematics in 2010, in the master in Advanced Mathematics from UAB.

Since then I did my Ph.D with Xavier Tolsa (2015), a postdoc in UAM with Daniel Faraco's ERC grant (15-17), a postdoc in UAB with Tolsa's ERC grant (17-19), and a postdoc in Aalto Yliopisto (Espoo, Finland) with Kari Astala's ERC grant (19-20).

I gained a position in UAB via the program Juan de la Cierva-Incorporación in 2020, but soon after that I obtained my actual position in UB as Professor Lector (associate professor).

My research interests are all related to harmonic analysis in the broad sense, with intersections with geometric measure theory, complex analysis, analysis of PDE's, and functional analysis. My Ph.D, for instace, started with the study of Calderón-Zygmund operators in Sobolev spaces in domains (HA and GMT), but ended up with applications to quasiconformal mappings (PDE's and CA). After that, both in Madrid and Espoo I worked on the inverse Calderón-Zygmund problem (with techniques from quasiconformal mappings) and also studying the relation of quasiconformal mappings with Sobolev and Triebel-Lizorkin spaces (PDE, CA and HA). In my positions in UAB and in UB I have been focusing on free boundary problems and in the study of harmonic measure (PDE's, GMT and HA), which is now my main line of research.