+44 1865 615104
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Welcome to my tiny piece of the internet! I am a third-year DPhil student at the EPSRC Centre for Doctoral Training in Partial Differential Equations: Analysis and Applications at the University of Oxford.
My general mathematical interest is in the study of singularity formation in nonlinear elliptic and parabolic PDEs. In particular, my DPhil project is focused on touchdown formation and positivity results in degenerate Cahn-Hilliard equations using insight from thin-film and lubrication theory. The main tools I use are perturbation methods, functional analysis and numerical simulations. I am also interested in phase-field models and free boundary problems.
At University of Oxford:
Tutor for B4.1 Functional Analysis I and B5.2 Applied PDEs (Michaelmas Term 2020).
Teaching assistant for C4.6 Fixed Point Methods for Nonlinear PDEs and B4.3 Distribution Theory and Analysis of PDEs (Michaelmas Term 2019, Hilary Term 2020).
At University of Chile:
Tutor for Mathematics II: Limits and function continuity (Summer School 2013-2014), Calculus in Several Variables (Autumn semesters 2015 and 2018), Nonlinear Analysis of PDEs (Spring semester 2017), Evolution Models (Autumn semester 2017).
Teaching Assitant for Calculus in Several Variables (Spring 2013, Autumn 2014 and Autumn 2016).
Los Dos Relojes Workshop for engineering students (Spring 2017).
Prizes, awards, and scholarships:
DPhil. scholarship BECAS CHILE from the Chilean Education Ministry.
M.Sc. academic excellence scholarship from the Mathematical Modeling Centre of the University of Chile.
Major / recent publications:
J. Dávila, M. Del Pino, C. Pesce, J. Wei. Blow-up for the 3-dimensional axially symmetric harmonic map flow into $ S^2 $. AIMS Discrete & Continuous Dynamical Systems. (2019) vol 39, 6913-6943.