Publications

My research focuses on partial differential equations (PDEs), which describe physical and natural phenomena through relationships between a function and its derivatives. I am particularly interested in the wave equation and the Schrödinger equation, which models the evolution of quantum systems. My work primarily examines time-independent solutions associated with high-energy values, an area known as semiclassical analysis, and their connections to various geometric aspects within the field of spectral geometry.

Below, you will find a list of my publications:

Conferences and Seminars 

In recent years, I have had the opportunity to present my research at various international conferences and seminars. Below, you will find a non-exhaustive list of these talks, with access to the slides used in some of them. 

Mini-courses:

• • Invited lecture at the 14th International Summer School on Geometry, Mechanics and Control (July 2022, Burgos, Spain). 5-hour mini-course  co-presented with Alberto Enciso titled Nodal sets of high-energy eigenfunctions of Schrödinger operators.

Long talks:

• Seminar at the Seminario de Doctorado Rubio de Francia IUMA at the University Institute of Mathematics and Applications (IUMA) of the University of Zaragoza  (May 2025, Zaragoza, Spain).  1-hour talk titled Zonas de silencio: explorando los ceros de las autofunciones.

• Seminar at the Spectral Geometry in the Clouds Seminar (May 2025, On-line). 1-hour talk titled High-Energy Laplace Eigenfunctions on Integrable Billiards. 

• Invited talk at the Workshop: Women in Geometry of the Institute of Mathematics at the University of Granada - IMAG (April 2025).  1-hour talk titled High-Energy Laplace Eigenfunctions on Integrable Billiards.

• Invited talk at the Jornada (y media) de Análisis Geométrico of the Universitat de València (Dec. 2024, Valencia, Spain). 1-hour talk titled Local behaviour of high-energy eigenfunctions of integrable billiards.

• Seminar at the Probability & Statistics Group of the Université du Luxembourg (Dec. 2024, Belval Esch-sur-Alzette, Luxembourg). 1-hour talk titled Berry’s Random Wave Model: heuristic, different formulations and consequences.

• Seminar at the PDE and spectral theory working group of the lab. Institut de Mathématiques de Bordeaux (Nov. 2024, Bordeaux, France).  1-hour talk titled Local behaviour of high-energy eigenfunctions of integrable billiards

• Colloque des doctorants 2024 – Université Côte d’Azur (Mayo 2024, Nice, France).  2-hour talk titled Eigen… what? Some Open Problems for the Laplacian.

• Invited talk at the Workshop Geometry and statistics of eigenfunctions at the Instituto de Matemáticas de la Universidad de Sevilla (Nov. 2023, Spain).  1-hour talk titled High-energy eigenfunctions and inverse localization.

• Invited talk at the Fifth meeting of the ANR ADYCT - Aléatoire, Dynamique et Spectre (Sept. 2023, Nice, France).  1-hour talk titled High-energy eigenfunctions and inverse localization.

• Invited talk at the XVI Workshop de jóvenes investigadores Madrid (Sept. 2023, Madrid, Spain).  1-hour talk titled High energy eigenfunctions and inverse localization.

• Seminar at the Partial Differential Equations and Numerical Analysis of the Laboratoire J.A. Dieudonné (March 2023, Nice, France).  1-hour talk titled High energy eigenfunctions on flat tori. 

• Seminar at the Red de Doctorandos en Matemáticas de la UCM (March 2023, Madrid, Spain).  1-hour talk titled Autofunciones de alta energía en toros planos.

• Seminar at the Ecuaciones en Derivadas Parciales del Departamento de Matemáticas de la UAM (June 2022, Madrid, Spain).  1-hour talk titled Eigenfunctions and inverse localization.

•  Invited talk at the AGAPI Days VII of the Universidad Politécnica de Madrid (March 2022, Madrid, Spain).  1-hour talk titled High-energy eigenfunctions and inverse localization.

• Joint Mathematics Junior Colloquium ICMAT-UAM-UC3M-UCM (Feb. 2022, Madrid, Spain). 1-hour talk titled Autofunciones de alta anergía y localización inversa.

Short talks:

• Contributed talk at the parallel session Partial Differential Equations III: Mathematical Analysis and Applications of the VII Congress of Young Researchers of the Royal Spanish Mathematical Society (RSME) (Ene. 2025, Bilbao, Spain). 30-min talk titled Prescribed local extrema of Laplace eigenfunctions of polygonal domains.

• Contributed talk at the parallel session Partial Differential Equations I: Elliptic and Parabolic Equations of the VII Congress of Young Researchers of the Royal Spanish Mathematical Society (RSME) (Ene. 2025, Bilbao, Spain). 30-min talk titled Local behaviour of high energy Laplace eigenfunctions of polygonal domains.

• Contributed talk at the conference Math SOMMa Junior Meeting organized by the Centre de Recerca Matemàtica (Oct. 2024, Barcelona, Spain). 30-min talk titled Local behaviour of high energy eigenfunctions of polygonal domains.

• Contributed talk at the conference Young researchers in PDEs (Sept.-Oct. 2023, Madrid, Spain). 30-min talk titled High energy eigenfunctions on flat tori. 

• Contributed talk at the parallel session Geometría Diferencial del VI Congreso de Jóvenes Investigadores de la Real Sociedad Matemática Española (Feb. 2023, León, Spain). 30-min talk titled High energy eigenfunctions on flat tori.

• Contributed talk at the conference fourth BYMAT organized by Universitat de València and Universitat Politècnica de València (Nov. 2022, On-line). 30-min talk titled Eigenfunctions and inverse localization.

Some of the slides used in the talks: 

Organizing Committees:

I have also been part of the organizing committee for several conferences and seminars during this time: 

• Fifth BYMAT Conference (Bringing Young Mathematicians Together), held at the Instituto de Ciencias Matemáticas (Madrid, Spain) from November 13-16, 2023. 

• Junior Joint Mathematical Colloquium (ICMAT-UAM-UCM-UC3M), organized during the academic years 2022/2023 and 2023/2024. 

• Parallel Session on Geometric Analysis, as part of the VII Congress of Young Researchers of the Royal Spanish Mathematical Society (RSME) (Bilbao, Spain) in January 13-17, 2025.