Hi! I am a third year PhD student in Princeton PACM, working under the supervision of my advisor Charles Fefferman. I am working in interpolation, data reconstruction and data analysis problems when we have analytical conditions and theoretical knowledge that the data should follow. I am interested in using these techniques (and more generally data analysis) on solving problems to make people’s lives better. Read more below!

# Maths

I am very interested in theoretical problems that explain the connections between a discrete world (the computer) and a continuous world (the reals, the space of functions, manifolds…). The interest for these problems comes from hearing about Hassler Whitney and his work done in 1934. You can read a great survey on the progress done so far in that problem here. I am especially interested in how can these theorems be translated into efficient, scalable and implementable algorithms. Here is an incomplete list of problems I am currently working on:

• How “big” are the sets of functions that can interpolate a given set of points with some restrictions (on, for example, $$\mathcal{C}^m$$ norm). Can we produce “best” functions inside those sets? (Turns out sometimes we can) Some restrictions may include differential equations!
• What does it mean to interpolate a manifold?
• Can we use the Topological information that we obtain from a point cloud to better understand its analytical properties?

Here is another incomplete list of questions that I find fascinating:

• How can we fight against round-off error in numerical computations? Can we trust numerical simulations to help in rigorous proofs?
• Does it make sense to have randomized algorithms in numerical analysis? How about quantum algorithms?
• On a slightly tangential note, I like everything about protocols and applied security, from authentication to privacy.

Feel free to contact me if you want to discuss a neat idea/problem!

# Impact

In the end, I want to use these results and software in real-world problems. In particular I have found a passion in projects that can make a positive impact in society and can help foster equal opportunities and rights for everyone. I am currently working on understanding the impact of educational programs in the US (WIP) and starting to learn about infectious diseases and what mathematical tools are needed to gain insight on how they work. I am not afraid of using new techniques in my projects: The end goal is to solve the problem.

I am interested in any project that can have a meaningful impact in people’s lives. If you have an idea for a project that you feel can help you/others in the search for justice and equality, at any level, contact me.

# Life

I’ve been two full years already in the US. What a journey it has been! I have been lucky to be supported in my first two years by a Fulbright-Telefonica scholarship given out by the Fulbright Comission in Spain.

I was born and raised in a small town near Barcelona, Spain, and made a small incursion in Germany in my last year of undergraduate studies. I attended Universitat Politècnica de Catalunya and studied a double degree in applied mathematics and telecommunication engineering thanks to the CFIS (Center for Interdisciplinary Superior Formation). I did my master’s thesis on energy efficient data centers in the field of the European project All4Green and afterwards I worked for a year on computational genomics in the MMB group leaded by Modesto Orozco. I have also worked on data privacy, quantum information theory, and like to mentor and teach students. I entered Princeton’s PACM in 2014.

I trained Taekwondo since I was 4 until I was 22 and have been trying other Martial Arts since then. This year you may find my wife and me in a Krav Maga lesson! I have also been playing the clarinet since I was 6, and am eager to learn new instruments: Spanish guitar and Irish whistle. I am always trying to learn new things… Right now, I am trying to learn JS to improve this website (which by the way, is in permanent construction). If you want to give me any advice, please contact me!