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About me

I completed my studies in Industrial Engineering and Mathematics at the University of Seville in 2014. Later I held an FPU Fellowship granted by the Government of Spain to do my PhD thesis under the supervision of Francisco Gancedo (University of Seville and IMUS). I am currently a Hans Rademacher Instructor of Mathematics at the University of Pennsylvania. My postdoctoral mentor is Robert M. Strain.

Contact Information:Foto visado (2)

Office: 3N4C, DRL

Mailing address:

Department of Mathematics
David Rittenhouse Lab.
209 South 33rd Street
Philadelphia, PA 19104-6395, USA


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Download my CV for a complete description of my education, awards, talks, etc. You can also visit my LinkedIn profile. In this site, the main points will be highlighted.


  1. PhD student in mathematics. University of Seville (FPU Fellowship, 2014-2018).
  2. (4-year) Degree in Mathematics. University of Seville (2010-2014)
  3. (5-year) Degree in Industrial Engineering. University of Seville (2007-2014)


  1. Francisco Gancedo,
  2. Robert M. Strain,
  3. Diego Córdoba,
  4. Antonio Rojas, (teaching)


  1. BCAM, Bilbao, Spain. May 2015.
  2. PHD Seminar, IMUS, Seville, Spain. September 2015.
  3. PDEs and fluid mechanics Seminar, ICMAT, Madrid, Spain. May 2017.
  4. Conversaciones fluidas Seminar, IMUS, Seville, Spain. May 2017.
  5. IV Young Researchers Conference, RSME, Valencia, Spain. September 2017.
  6. Ecuaciones Diferenciales Seminar, IEMath-GR, Granada, Spain. November 2017.
  7. Analysis Seminar, University of Pennsylvania, Philadelphia, USA. October 2018.

Conferences Attended

  1. Workshop on Mathematics and its Applications, BCAM. May 2015, Bilbao, Spain.
  2. Summer Graduate School Incompressible Fluid Flows at High Reynolds Number, MSRI. 27 July-7 August 2015, Berkeley, California, USA.
  3. Mini-school and workshop Analysis of PDEs of Fluid Mechanics and Related Models, Rice University. October 2015. Houston, Texas, USA.
  4. International Summer School on Evolution Equations, Charles University and Institute of Mathematics of the Czech Academy of Sciences. July 2016, Prague.
  5. Spanish-French Workshop on Analysis of PDEs from fluid Mechanics, ICMAT. September 2016, Madrid.
  6. Workshop Recent advances in PDEs: Analysis, Numerics and Control, IMUS. January 2017, Sevilla.
  7. Summer School and Workshop: Mathematical Analysis of Water Waves and Related Models, Bodega Marine Laboratory, University of California, Davis. June 2017, Bodega Bay, CA, USA.
  8. IV Young Researchers Meeting, Real Sociedad Matemática Española. June 2017, Valencia.
  9. Workshop Mathematical Analysis in Incompressible Fluids, IMUS. June 2018, Sevilla.
  10. Summer School and Workshop: Geometric Function Theory in Fluid Mechanics, BGSMath. July, 2018, Barcelona.
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My research interests lie within analysis, partial differential equations and fluid mechanics. More specifically, I am interested in the evolution of moving incompressible fluid interfaces coming from physical models.
During my graduate career, I have studied the global well-posedness and interface regularity for patch problems in nonlinear parabolic equations such as Navier-Stokes and Boussinesq. I have also worked on the Muskat problem, addressing additional questions like large-time decay of solutions or ill-posedness.

A brief summary of my current research can be found in this short version of my ResearchStatement. I am always avalaible through email for more information (


  1. Global regularity for 2D Boussinesq temperature patches with no diffusion,
    with F. Gancedo. Ann. PDE (2017), 3: 14.
  2. Global regularity of 2D density patches for inhomogeneous Navier-Stokes,
    with F. Gancedo. Arch. Ration. Mech. Anal. (2018), 229:339.
  3. On the Muskat problem with viscosity jump: Global in time results,
    with F. Gancedo, N. Patel and R. Strain. To appear in Adv. Math., arXiv:1710.11604, (2017).
  4. Regularity results for viscous 3D Boussinesq temperature fronts, with F. Gancedo. Submitted, arXiv:1809.00701, (2018).

Preprints of my papers can be found in ArXiv, ResearchGate. Information about talks, workshops and grants can be found in my Curriculum Vitae.

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Office Hours Fall 2018

On Mondays 12:30-2:30 pm (or appointment by email)
Location: Office 3N4C, DRL.





  • Mathematical Analysis (Physics degree)  (2.25 ECTS)
  • Mathematics (Chemistry degree) (2.40 ECTS)
  • Differentiation of functions in Rn (0.40 ECTS)
  • Integration of functions in Rn (0.40 ECTS)