Research
My research focuses on different interpretations of the uncertainty pricniple, mainly related to uniqueness problems of partial differential equations.
Publications
Preprints:
A. Fernández-Bertolin, L. Roncal, A. Rüland, D. Stan, Discrete Carleman estimates and three balls inequalities.
A. Fernández-Bertolin, A. Greecu, L. Ignat, Hardy uniqueness principle for the linear Schrödinger equation on quantum regular trees.
Published (or accepted for publication):
A. Fernández-Bertolin, E. Malinnikova, Dynamical versions of Hardy's uncertainty principle: a survey. Bull. Amer. Math. Soc. 58 (2021), no. 3, 357--375.
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.
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
A. Fernández-Bertolin, Convexity properties of discrete Schrödinger evolutions. J. Evol. Equ. 20 (2020), no.1, 257--278.
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.
A. Fernández-Bertolin, A discrete Hardy's uncertainty principle and discrete evolutions. J. Anal. Math. 137 (2019), no. 2, 507--528.
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.
A. Fernández-Bertolin, L. Vega, Uniqueness properties for discrete equations and Carleman estimates. J. Funct. Anal. 272 (2017), no. 11, 4853--4869.
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)