Research

My research focuses on different interpretations of the uncertainty pricniple, mainly related to uniqueness problems of partial differential equations.

Publications

Preprints:

  1. A. Fernández-Bertolin, L. Roncal, A. Rüland, D. Stan, Discrete Carleman estimates and three balls inequalities.

  2. A. Fernández-Bertolin, A. Greecu, L. Ignat, Hardy uniqueness principle for the linear Schrödinger equation on quantum regular trees.

Published (or accepted for publication):

  1. A. Fernández-Bertolin, E. Malinnikova, Dynamical versions of Hardy's uncertainty principle: a survey. Bull. Amer. Math. Soc. 58 (2021), no. 3, 357--375.

  2. A. Fernández-Bertolin, Ph. Jaming, S. Pérez-Esteva, An uncertainty principle for solutions of the Schrödinger euqation on H-type groups. J. Aust. Math. Soc. 111 (2021), no. 1, 1--16.

  3. A. Fernández-Bertolin, Ph. Jaming, Uniqueness for solutions of the Schrödinger equation on trees. Ann. Mat. Pura Appl. (4) 199 (2020), no. 2, 681--708

  4. A. Fernández-Bertolin, Convexity properties of discrete Schrödinger evolutions. J. Evol. Equ. 20 (2020), no.1, 257--278.

  5. A. Fernández-Bertolin, J. Zhong, Hardy's uncertainty principle and unique continuation property for stochastic heat equations. ESAIM: Control Optim. Calc. Var. no. 26 (2020), Paper no. 9, 22pp.

  6. A. Fernández-Bertolin, A discrete Hardy's uncertainty principle and discrete evolutions. J. Anal. Math. 137 (2019), no. 2, 507--528.

  7. A. Fernández-Bertolin, K. Gröchenig, Ph. Jaming, From Heisenberg uniqueness pairs to properties of the Helmholtz and Laplace equations. J. Math. Anal. Appl. 469 (2019), no . 1, 202--219.

  8. A. Fernández-Bertolin, L. Vega, Uniqueness properties for discrete equations and Carleman estimates. J. Funct. Anal. 272 (2017), no. 11, 4853--4869.

  9. A. Fernández-Bertolin, Discrete uncertainty principles and Virial identities. Appl. and Comput. Harm. Anal. 40 (2016), 229--259.




Talks/Conferences

I have spoken at the following conferences:

  • 8th ECM (Portoroz, Slovenia, 2021, online)

  • 9th Workshop for Young Researchers in Mathematics (Bucharest, Romania, 2019)

  • XV Encuentro de la Red de Análisis Funcional y aplicaciones en memoria del profesor Bernardo Cascales (Bilbao, Spain, 2019)

  • III. Euskal Matematikarien topaketa (Eibar, Spain, 2018)

  • 9th Itinerant Workshop in PDEs (Bordeaux, France, 2018)

  • Journées du GDR AFHP (Bordeaux, France, 2017)

  • IV Congreso Jovenes Investigadores RSME (Valencia, Spain, 2017)

  • Journées du GDR AFHP (Toulouse, France, 2016)

  • Workshop in Harmonic Analysis & PDEs (Bilbao, Spain, 2015)

  • EARCO 2014 (Girona, Spain, 2014)


I have delivered research talks at the departments of mathematics of the following universities:

  • Université de Bordeaux, Bordeaux, France (2020, 2017, 2016)

  • Universidad del País Vasco - Euskal Herriko Unibertistatea, Leioa, Spain (2020, 2017, 2015)

  • Stanford University, Stanford, USA (2020)

  • Universidad de Cantabria, Santander, Spain (2019)

  • IMAR, Bucharest, Romania (2018)

  • Université de Lille, Lille, France (2018)

  • Universidad de Zaragoza, Zaragoza, Spain (2017)

  • Wien universität, Vienna, Austria (2016)

  • NTNU, Trondheim, Norway (2016)

  • MSRI, Berkeley, USA (2015)

  • University of Helsinki, Helsinki, Finland (2015)