Hello, I am

Joaquín Domínguez de Tena

Math Researcher | Analysis and PDEs

Who am I ?

I am a researcher in mathematics. Currently, I am working in the Institute of the Mathematical Sciences of Spain (ICMAT) in collaboration with Aníbal Rodríguez Bernal and José María Arrieta, while doing my PhD. I also teach some courses in the Faculty of Mathematics of Universidad Complutense de Madrid. I am part of the CADEDIF research group.

ICMAT
UCM
CADEDIF

Research Interests

My research is mainly on Analysis and PDEs. Some of the topics I study are:

  • Regularity of PDEs: Elliptic and Parabolic regularity, a priori estimates...
  • Spectral Theory : Mainly its application to semigroups...
  • Evolution equations : Asymptotic behaviour, blow-ups...
  • Homogenization : Thin domains, quasi-periodic structures...

Where to find me?

UCM Office

You can find me in the Faculty of Mathematics, Office 302B on the third floor.

ICMAT Office

At ICMAT, you can find me in Office 119 on the first floor.

Publications

    Global existence and asymptotic behavior for diffusive Hamilton-Jacobi equations with Neumann boundary conditions J. Domínguez-de-Tena, P. Souplet.
    Asymptotic behaviour of the heat equation in an exterior domain with general boundary conditions I. The case of integrable data. J. Domínguez-de-Tena, A. Rodríguez Bernal.
    On the loss of mass for the heat equation in an exterior domain with general boundary conditions. J. Domínguez-de-Tena, A. Rodríguez Bernal.
Works in progress:
    Asymptotic behaviour of the heat equation in an exterior domain with general boundary conditions II. The case of bounded an Lp data. J. Domínguez-de-Tena, A. Rodríguez-Bernal.
    Thin domains with doubly oscillatory boundary: the weak-resonant case. J. Arrieta, J. Domínguez-de-Tena, M. Villanueva-Pesqueira.

Talks

    Asymptotic behaviour of the heat equation in an exterior domain (Young researchers in PDEs (ICMAT), 2023)
    Homogenization Theory in Mathematics. (PhDay Contest 2023, Accesit)
    Thin domains with doubly oscillatory boundary: the weak-resonant case. (ICMC 2023)
    Semigroup theory and Evolution equations (Young Colloquium, UCM, 2021)
    Asymptotic behaviour of the heat equation in an exterior domain (CADEDIF Seminar, UCM, 2021)

Teaching

Current

Past

   Numerical Methods for PDEs 2022-2023
   Differential Equations II 2022-2023
   Numerical Methods for PDEs 2021-2022

Supervised Projects

    Numerical Methods for the Kolmogorov Equation (Final Degree project of María Camarillo Martínez, codirected with Alberto Pérez Cervera) 2022-2023

My Resume

Education

2021 - Present

PhD in Mathematics

I am currently studying a PhD in Mathematics while working at ICMAT. I am studying parabolic problems with large initial data in exterior domains.

2020 - 2021

Master in Advanced Mathematics

I studied a Master in advanced mathematics at Universidad Complutense de Madrid. I expertised in Analysis and PDEs. My master degree thesis was about elliptic regularity.

2020 - 2021

Master in Advanced Mathematics

I studied a Master in advanced mathematics at Universidad Complutense de Madrid. I expertised in Analysis and PDEs. My master degree thesis was about elliptic regularity.

2019 - 2020

1 year stay in KTH University

I did some of my studies in the Royal Institute of Technology in Stockholm (KTH) with an Erasmus scholarship.

2015 - 2020

Double Degree in Mathematics and Physics

I studied Mathematics and Physics at Universidad Complutense de Madrid. I expertised in Theoretical Physics and Pure and Applied Mathematics.

Occupations

2021 - Present

Researcher at ICMAT (CSIC)

I work at Spanish National Research Council (CSIC) with a Severo Ochoa contract funded by the ministry of science to research in Partial Differential Equations.

2021 - Present

Teaching assistant at UCM

I teach some courses of the Mathematics Degree of UCM. In 2021 I taught Numerical Analysis for PDEs (4th year course). This year I will teach Differential Equations (3rd year course) and Numerical Analysis for PDEs again.

2022 - Present

PIM teacher

I work as a teacher of PIM project at ICMAT. This project of the Institute of Mathematical Sciences in collaboration with the Department of Mathematics of the Autonomous University of Madrid and the Spanish Royal Mathematical Society has the main objective of fostering interest in mathematics and encouraging students to enter the fascinating world of mathematics. The project is aimed at people between 14 and 18 years old.

Awards and Contests

During my university and pre-university studies I have participated in several contest and olympiads.

Some of the pre-university ones are: Mathematics Olympiad of Spain (Silver Medal), Physics Olympiad of Spain (Gold Medal), Iberoamerican Physics Olympiad (Gold medal, 2nd), Chemistry National Olympiad (Bronze Medal), Informatics National Olympiad...

Some of the university ones are: International Mathematics Competition for University Students (2 Gold and 1 Silver medals), Iberoamerican Math Olympiad for University Students (1 Silver, 1 Bronze, 2 Honourable mentions), Plancks Competition (Ranked 4th), II Contest of Mathematical Modeling of Spain (1st place)...

I have also received some grants from the Spanish and Madrid goverments as the "Collaboration Grant at Severo Ochoa Excellence Centers CSIC 2020", "ICMAT Introduction to Research 2019" or "Excellence Scholarships 2015-2019" to support my studies as well as to promote my research career.

Languages

Spanish
English
French
Swedish

Get in touch

Phone :
+ (34) 913944462
Address :
Faculty of Mathematics UCM: Office 302B
ICMAT: Office 119
Email :

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