I am a Hans Rademacher Instructor of Mathematics at the University of Pennsylvania. My postdoctoral mentor is Robert M. Strain. I did my PhD at the University of Seville under the supervision of Francisco Gancedo. My research focuses on the analysis of incompressible fluid interfaces.
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.
Office: 3N4C, DRL
Department of Mathematics
David Rittenhouse Lab.
209 South 33rd Street
Philadelphia, PA 19104-6395, USA
- PhD student in mathematics. University of Seville (FPU Fellowship, 2018).
- (4-year) Degree in Mathematics. University of Seville (2014)
- (5-year) Degree in Industrial Engineering. University of Seville (2014)
- Francisco Gancedo, email@example.com
- Robert M. Strain, firstname.lastname@example.org
- Diego Córdoba, email@example.com
- Antonio Rojas, firstname.lastname@example.org (teaching)
- BCAM, Bilbao, Spain. May 2015.
- PHD Seminar, IMUS, Seville, Spain. September 2015.
- PDEs and fluid mechanics Seminar, ICMAT, Madrid, Spain. May 2017.
- Conversaciones fluidas Seminar, IMUS, Seville, Spain. May 2017.
- IV Young Researchers Conference, RSME, Valencia, Spain. September 2017.
- Ecuaciones Diferenciales Seminar, IEMath-GR, Granada, Spain. November 2017.
- Analysis Seminar, University of Pennsylvania, Philadelphia, USA. October 2018.
- Conversaciones fluidas Seminar, IMUS, Seville, Spain. January 2019.
- Joint Mathematics Meetings AMS Special Session on Mathematical Analysis in Fluid Dynamics, Baltimore, USA. January 2019.
- Analysis of Fluids and Related Topics Seminar, Princeton University, Princeton, USA. February 2019.
- Differential Equations Seminar, University of Michigan, Ann Arbor, USA. March 2019.
- Partial Differential Equations Seminar, Brown University, Providence, USA. May, 2019.
- Workshop on Mathematics and its Applications, BCAM. May 2015, Bilbao, Spain.
- Summer Graduate School Incompressible Fluid Flows at High Reynolds Number, MSRI. 27 July-7 August 2015, Berkeley, California, USA.
- Mini-school and workshop Analysis of PDEs of Fluid Mechanics and Related Models, Rice University. October 2015. Houston, Texas, USA.
- International Summer School on Evolution Equations, Charles University and Institute of Mathematics of the Czech Academy of Sciences. July 2016, Prague.
- Spanish-French Workshop on Analysis of PDEs from fluid Mechanics, ICMAT. September 2016, Madrid.
- Workshop Recent advances in PDEs: Analysis, Numerics and Control, IMUS. January 2017, Sevilla.
- 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.
- IV Young Researchers Meeting, Real Sociedad Matemática Española. June 2017, Valencia.
- Workshop Mathematical Analysis in Incompressible Fluids, IMUS. June 2018, Sevilla.
- Summer School and Workshop: Geometric Function Theory in Fluid Mechanics, BGSMath. July, 2018, Barcelona.
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 (email@example.com).
- Global regularity for 2D Boussinesq temperature patches with no diffusion,
with F. Gancedo. Ann. PDE (2017), 3: 14.
- Global regularity of 2D density patches for inhomogeneous Navier-Stokes,
with F. Gancedo. Arch. Ration. Mech. Anal. (2018), 229:339.
- On the Muskat problem with viscosity jump: Global in time results,
with F. Gancedo, N. Patel and R. Strain. Adv. Math., Vol. 345, P. 552-597, (2019).
- Regularity results for viscous 3D Boussinesq temperature fronts, with F. Gancedo. Submitted, arXiv:1809.00701, (2018).
- Global Regularity for Gravity Unstable Muskat Bubbles, with F. Gancedo, N. Patel and R. Strain. Submitted, arXiv:1902.02318, (2019).
Office Hours Spring 2019
Math 312: On Mondays 12:30-2:30 pm (or appointment by email)
Math 425: On Wednesdays 12:30-2:30 pm (or appointment by email)
Location: Office 3N4C, DRL.
- Math 425: Partial Differential Equations (Spring)
- Math 312: Linear Algebra (Spring, group 002)
- Math 312: Linear Algebra (Fall, group 001)
- Lecture Notes 1 – Chapter 2
- Lecture Notes 2 – Chapter 3
- Lecture Notes 3 – Chapter 4, Part I
- Lecture Notes 4 – Chapter 4, Part II, and Chapter 8
- Lecture Notes 5 – Chapter 5
- Lecture Notes 6 – Chapter 6, Part I
- Lecture Notes 7 – Chapter 6, Part II
- Lecture Notes 8 – Chapter 6, Part III
- Lecture Notes 9 – Review for Midterm II
- Lecture Notes 10 – SVD, Pseudoinverse
- Lecture Notes 11 – PCA
- Lecture Notes 12 – (Discrete) Markov chains
- Lecture Notes 13 – Perron-Frobenius Theorem
- Lecture Notes 14 – Graphs, PageRank
- Lecture Notes 15 – Linear Programming
- Homework 1
- Homework 2
- Homework 3
- Homework 4
- Homework 5
- Homework 6
- Homework 7
- Homework 8
- Homework 9
- Homework 10
- Homework 10 – Solutions
- Homework 11
- Homework 11 – Solutions
- Extra problems (Chap. 2, 3)
- Exam-like extra problems Midterm 1
- Exam-like extra problems Midterm 1 – solutions
- Midterm 1 – Practice Exam
- Midterm 1 – Practice Exam – solutions
- Midterm 1 – Exam of a previous year
- Midterm 1 – Exam of a previous year – solutions
- Midterm 1
- Midterm 1 – Solutions
- Exam-like problems Midterm 2 with solutions
- Midterm 2 – Practice Exam
- Midterm 2 – Practice exam solutions
- Midterm 2 – Exam Version A
- Midterm 2 – Exam Version A solutions
- Guide: What to know for the final
- Final exam – Practice exam
- True/False questions (all course)
- Mathematical Analysis (Physics degree) (2.25 ECTS)
- Mathematics (Chemistry degree) (1.60 ECTS)
- Soluciones problemas seminarios (integral definida y aplicaciones)
- Infinitesimal Calculus (1.00 ECTS)
- 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)