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Juan Cavero de Carondelet Fiscowich

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Phone: +34 912999

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Biographical Review

I was born in 1988 in Mahón, Spain. I earned my Bachelor's degree in Mathematical Sciences from the Universidad Complutense de Madrid. I have already finished my Master thesis at the Universidad Autónoma de Madrid under the direction of José María Martell. I had my first contact with research during the last year of my degree, where I studied Lacey and Thiele's proof of Carleson's Theorem under the supervision of Prof. Daniel Azagra. I became familiar with some topics like time-frequency analysis, weak inequalities or transference of multipliers. In the same year I attended a UAM Master course given by José María Martell and focused on Calderón-Zygmund operators, BMO functions, weight theory and extrapolation.

My fields of interest are Harmonic Analysis and Partial Differential Equations. During my Master I studied the technique of bootstrapping of Carleson measures applied to the proof of a perturbation result of elliptic operators. Furthermore, during 2012-2013 I attended several courses of the ICMAT special year "New Trends in Harmonic Analysis" as well as the workshop "Harmonic Analysis, PDEs and Geometry: A joint Workshop of the ANR-Harmonic Analysis at its boundaries and the ICMAT-Severo Ochoa" or the "9th International Conference on Harmonic Analysis and Partial Differential Equations" in El Escorial, Madrid.

I am currently working towards my Ph.D. under the supervision of José María Martell at the ICMAT. I have been awarded a four year fellowship from ''la Caixa-Severo Ochoa international Ph.D. program'' to work at the ICMAT. My thesis project is related to my Master thesis, with the addition of some Geometric Measure Theory aspects in order to enrich the problem. The combination of techniques from Harmonic Analysis, Partial Differential Equations and Geometric Measure Theory has been fundamental in the recent developments by Steve Hofmann and José María Martell, on which I am currently focused.

 

Research Interests

  • Harmonic Analysis: harmonic measure, scale invariant estimates, bootstrapping of Carleson measures
  • Partial Differential Equations: elliptic/parabolic problems, solvability, square function
  • Geometric Measure Theory: 1 sided NTA domains, sawtooth domains, dyadic grids