Mathematical Physics, Spectral Theory, Partial Differential Equations

Students supervised
• Matías Moreno Bustamante, master thesis in Mathematical engineering at U. de Chile, graduated October 2022.
• Danko Aldunate Bascuñan, co-supervisor with E. Stockmeyer, PhD in Physics at Pontificia Universidad Católica de Chile, graduated June 2025.
• Benjamín Borquéz, master thesis in Mathematical engineering at U. de Chile, co-supervisor with Rayssa Caju,graduated June 2025.
• Joaquín Marquéz Delgado, master thesis in Mathematical engineering at U. de Chile, graduated March 2026.
• Xavier Carrera, Phd student at DIM - UChile, March 2025 – current.

Postdocs supervised
• Paola Rioseco, 2021-2025, funded by CMM and a Fondecyt postdoctoral project.
• Danko Aldunate Bascuñan, 2026– current, funded by CMM

OUTREACH
August 2025
School visit : Organization of visit to university for high school students taking the optional subject Limits, Derivatives and Integrals.

June 2025
Keynote Speaker : vestigando Conecciones en Física Matemática in the context of Seminario Liderando el Cambio: Mujeres que Otorgan Valor a la Ciencia,
to promote the participation of women in STEM for students and researchers of the universities of Valparaíso and Federico Santa María.

November 2023
November 2024
Public Lectures : Organization of public lectures Escuchando al Universo, últimos avances
con las ondas gravitacionales by Alicia Sintes (UIB) and Explorando el
Universo a través de Ondas Gravitacionales by Tomás Andrade (BSC).

November 2022
Column: Entrelazamiento enigmático (Entanglement Enigma) to explain the 2022
Nobel in physics, published in the online medium La Tercera.

TALKS
In Conferences
• Emerging Horizons in Geometric Spectral Theory: an ECRs workshop, Isaac Newton Institute Cambridge (UK), February 2-6 2026. Talk: The Yamabe problem for manifolds with boundary and its quantitative stability, and participation in Carreer panel.
• III simposio sobre Ecuaciones diferenciales parciales y teoría de números, Santiago (Chile), October 13–16 2025. Talk: Spectral flow methods for edge states at soft walls.
• Encuentro anual Somachi, Valdivia (Chile), December 10–12 2024. Plenary talk: Operadores de Birman Schwinger para problemas en mecánica cuántica.
• Congreso Latino-Americano y del Caribe de Matemáticas, João Pessoa (Brazil), August 26-30 2024. Semi-plenary talk: Bounds on the ground-state energy for Dirac Operators.
• Stability of Functional Inequalities” , ICMAT Madrid (Spain), October 23-26th, 2023.Talk: Keller-Lieb-Thirring estimates for Dirac operators.
• Congreso Mujeres Matemáticas WOMATHS, Santiago, May 10–12 2023. Minicourse: Matemáticas para Mecánica Cuántica
• The analysis of relativistic quantum systems, CIRM Marseille 9–13 January 2023, member of scientific committee and talk Results on the spectral stability of the one-dimensional nonlinear Dirac equation of Soler type.
• Jornadas Matemáticas de la Zona Sur, Concepción (Chile), April 19–21 2023, Talks in sessions on Mathematical Physics and Differential Equations.
• New trends in Mathematics of Dispersive, Integrable and Nonintegrable Modelsin Fluids, Waves and Quantum Physics, BIRS Banff, October 9–14, 2022 online participant in hybrid event. Talk: Spectral stability in the nonlinear Dirac equation with Soler type nonlinearity.
• Shape Optimisation and Geometric Spectral Theory , ICMS Edinburgh, September 20-23, 2022. Talk: Optimizers for a Poincaré-Sobolev inequality.
• Analytic and Geometric Aspects of Spectral Theory, BIRS Oaxaca, August 14–19 2022:Online participation in hybrid work-in-groups.
• Mathematical Congress of the Americas, Buenos Aires July 19–24, 2021(online). Talk in Mathematical Physics session: Spectral Stability in the nonlinear Dirac equation with Soler-type nonlinearity in dimension 1.
• FLACAM 2019, CMM Santiago, November 5–8, 2019. Talk in PDE session: Optimizers for a Poincaré-Sobolev inequality.
• The Analysis of Complex Quantum Systems: Large Coulomb Systems and Related Matters, CIRM Marseille, October 21–25, 2019. Talk: A critical Poincaré-Sobolev inequality.
• Many-body theory, effective equations & PDE’s, Mittag- Leffler Institute, Stockholm, March 18 –22, 2019. Talk: A critical Poincaré-Sobolev inequality.
• Eigenvalues and Inequalities, Mittag- Leffler Institute, Stockholm, May 14–18, 2018. Talk: Spectrum of Graphene Quantum dots.
• EEQUADD MathAmSud Workshop, Santiago, December 7, 2017. Talk: Non-existence of minimizers for the TFDW functional and related problems.
• Encuentro SOMACHI, Talca, November 3, 2017. Talk in PDEs sesion: Non-existence of minimizers for the TFDW functional and related problems.
• Mathematical Congress of the Americas, Montreal, July 26, 2017. Talk in Mathematical Physics sesion: Spectral gaps of Dirac operators describing graphene quantum dots.
• 50 years of hearing drums, Santiago, May 16–20, 2016: Spectral gaps of Dirac operators describing graphene quantum dots.
• Young Researchers Symposium, June 25, 2015, Santiago: Phase transitions in probabilistic cellular automata : an intermediate model, .
• International conference on Spectral Theory and Mathematical Physics, November 24–29, 2014, Santiago: Phase transitions in probabilistic cellular automata : an intermediate model.

Coloquia
• El flujo espectral como herramienta en física matemática, Coloquio de Matemática del DMCC-USACH, July 11, 2025.
• El flujo espectral como herramienta en física matemática, Coloquio de Matemáticas de las Palmeras, Universidad de Chile, April 23, 2025.
• Solitary waves in Nonlinear Dirac Equations, Coloquio de Matemáticas las Palmeras, Universidad de Chile, November 9, 2022
• Quantum Dots de Grafeno, Coloquio del Instituto de Física UC, Pontificia Universidad Católica de Chile, November 8, 2022
• Solitary waves in Nonlinear Dirac Equations, Colloquim Ceremade Paris Dauphine, October 4 2022.
• Dirac operators for the description of graphene, Coloquio de Matemáticas Pontificia Universidad Católica de Chile, November 2022, 2019.

Seminar talks
• The Yamabe problem for manifolds with boundary and its quantitative stability, CEREMADE analysis and probability seminar, Paris Dauphine PSL (France), February 17, 2026.
• Keller-Lieb-Thirring estimates for Dirac operators, London PDE Seminar, Imperial College London (UK), January 29 2026.
• Dirac operators with delta-interactions supported on curves with corners MCS-MP online seminar, December 16, 2025.
• Boundary conditions for Dirac operators: smooth boundaries vs. corners. FisMat seminar PUC, Santiago, November 12, 2025.
• Gagliardo-Nirenberg-Sobolev inequalities in domains, APDE seminar in UPV/EHU and BCAM, Bilbao, October 19 2023
• A Keller-Lieb-Thirring Inequality for Dirac operators, Seminario de Análisis y Geometría, PUC, Santiago, June 13 2023.
• A Keller-Lieb-Thirring inequality for Dirac Operators (online talk ) , Analysis Seminar - Fernuniverstität Hagen, December 7 2022
• A Keller-Lieb-Thirring inequality for Dirac Operators (online talk ) , Math Phys seminar GAT-ECH, Atlanta, November 10 2022.
• Gagliardo-Nirenberg-Sobolev inequalities in domains, Seminario CAPDE, DIM UChile, Santiago, April 19, 2018.
• Graphene quantum dots: boundary conditions and spectrum, Physics Center Universidad Adolfo Ibañez, Santiago, April 2, 2018.
• Spectral gaps of Dirac operators describing graphene quantum dots, Seminario CAPDE, DIM UChile, Santiago, October 2, 2017.
• Spectral gaps of Dirac operators describing graphene quantum dots, Seminario de Analísis y Geometría, PUC, Santiago, May 2, 2017.
• Spectral gaps of Dirac operators describing graphene quantum dots, Aarhus Universitet, June 29, 2016.
• A criterion for the existence of zero modes for the Pauli operator with fastly decaying fields, seminario universität Stuttgart, November 25, 2015, Stuttgart.
• Introducción matemática para minicurso Rigorous results in the Ginzburg-Landau model of superconductivity, PUC, Santiago, October 22, 2015.
• A criterion for the existence of zero modes for the Pauli operator with fastly decaying fields, seminario de Teoría Espectral PUC, March 19, 2015, Santiago.
• Phase transitions in probabilistic cellular automata, seminario Universidad Adolfo Ibáñez, May 9-13, 2014, Santiago.
• Phase transitions in PCA and associated mean field models, seminario de Teoría Espectral PUC, November 21, 2013, Santiago.