Here you can download my CV.

Positions

1. Ramón y Cajal Researcher, Universidad de Sevilla, Dec. 2022 –
2. Marie Skłodowska-Curie Individual Fellow, Universitat de Barcelona, Sept. 2021 – Nov. 2022
3. ERC Post-doctoral Researcher, Universitat de Barcelona, July 2020 – Aug. 2021
4. Hans Rademacher Instructor of Mathematics, University of Pennsylvania, Aug. 2018 – June 2020
5. FPU Predoctoral Fellow, Universidad de Sevilla, Sept. 2015 – June 2018

Education

1. PhD student in Mathematics. Universidad de Sevilla (FPU Fellowship, 2018).
   • Research stay at University of Pennsylvania (June-July 2017)
   • Research stay at Princeton University (April-May 2018)
2. (4-year) Degree in Mathematics. Universidad de Sevilla (2014)
3. (5-year) Degree in Industrial Engineering. Universidad de Sevilla (2014)

My research interests lie within analysis, partial differential equations and fluid mechanics. More specifically, I am interested in the evolution of moving interfaces in incompressible flows coming from physical models.

Publications:

1. Well-Posedness of the 3D Peskin Problem, with P.-C. Kuo, Y. Mori, R. Strain. Submitted, arXiv:2301.12153, (2023).
2. Global Regularity of 2D Navier-Stokes Free Boundary with Small Viscosity Contrast, with F. Gancedo. Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire, (2021). (Link to ArXiv)
3. Quantitative Hölder Estimates for Even Singular Integral Operators on Patches, with F. Gancedo. Journal of Functional Analysis, 283 (9), (2022). (Link to ArXiv)
4. Self-similar solutions for the Muskat equation, with J. Gómez-Serrano, H. Q. Nguyen, B. Pausader. Advances in Mathematics, 399, (2022). (Link to ArXiv).
5. The Peskin Problem with Viscosity Contrast, with Y. Mori, R. Strain. To appear in Analysis & PDE, arXiv:2009.03360, (2020). (Link to ArXiv)
6. Global Regularity for Gravity Unstable Muskat Bubbles, with F. Gancedo, N. Patel and R. Strain. To appear in Memoirs of the American Mathematical Society, arXiv:1902.02318, (2019). (Link to ArXiv)
7. Regularity results for viscous 3D Boussinesq temperature fronts, with F. Gancedo.  Communications in Mathematical Physics, 376, 1705-1736 (2020). (Link to ArXiv)
8. On the Muskat problem with viscosity jump: Global in time results,
   with F. Gancedo, N. Patel and R. Strain. Advances in Mathematics, 345,  552-597, (2019). (Link to ArXiv)
9. Global regularity of 2D density patches for inhomogeneous Navier-Stokes,
   with F. Gancedo. Archive for Rational Mechanics and Analysis, 229 (1), 339-360, (2018). (Link to ArXiv)
10. Global regularity for 2D Boussinesq temperature patches with no diffusion,
    with F. Gancedo. Annals of PDE 3, 14, (2017). (Link to ArXiv)

Research profiles: ArXiv, ORCID, Google Scholar,  ResearchGate, Scopus, Web of Science,  MathSciNet. Information about talks, workshops and grants can be found in my Curriculum Vitae.

Office Hours Spring 2023

Email: egarcia12@us.es

Teaching

2021/2022 (Universitat de Barcelona)

• Introduction to Fluid Mechanics (BGSMath Graduate Course) (Spring)

2020/2021 (Universitat de Barcelona)

• Equacions Diferencials (Spring)

2019/2020 (University of Pennsylvania)

• Math 425: Partial Differential Equations (Spring)
• Math 241: Calculus IV, PDE (Spring)
• Math 115: Multivariate Calculus, with Probability and Matrices (Fall)

2018/19 (University of Pennsylvania)

• Math 425: Partial Differential Equations (Spring)
• Math 312: Linear Algebra (Spring, group 002)
• Math 312: Linear Algebra (Fall, group 001)

2017/18 (Universidad de Sevilla)

• Mathematical Analysis (Physics degree)
• Mathematics (Chemistry degree)
• Infinitesimal Calculus

2016/17 (Universidad de Sevilla)

• Mathematical Analysis (Physics degree)
• Mathematics (Chemistry degree)
• Differentiation of functions in Rn
• Integration of functions in Rn

I completed my studies in Industrial Engineering and Mathematics at Universidad de Sevilla in 2014. Later I did a PhD in mathematics under the supervision of Francisco Gancedo (Universidad de Sevilla and IMUS). I currently work as a Ramón y Cajal researcher at Universidad de Sevilla. Previously, I worked as a postdoc at Universitat de Barcelona (BGSMath), first as a member of the ERC Starting Grant CAPA leaded by Javier Gómez-Serrano and then as a MSCA Individual Fellow. Before that, I was a Hans Rademacher Instructor of Mathematics at University of Pennsylvania. My postdoctoral mentor at UPenn was Robert M. Strain.

Contact Information:

E-mail: egarcia12@us.es
Office: Modulo 15 (1st floor), N7
Phone:

Mailing address:

Departamento de Análisis Matemático
Facultad de Matemáticas, Universidad de Sevilla
C/ Tarfia s/n (Campus Reina Mercedes)
41012, Sevilla, Spain