Frank Trujillo

Centre de Recerca Matemàtica

ftrujillo at crm.cat

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I am currently a Marie Sklodowska-Curie postdoctoral fellow at the Centre de Recerca Matemàtica (CRM), in Spain, through the grant REXHALODYN funded by the European Union under its Horizon Europe - MSCA program.

For a few months in 2024 I was a Maria de Maeztu postdoctoral fellow at the CRM under the supervision of Marcel Guardia, Professor at University of Barcelona. Before this I was a postdoctoral researcher at the University of Zurich under the supervision of Corinna Ulcigrai, Professor at the University of Zurich.

I completed a PhD in Mathematics at the IMJ-PRG, Université Paris Cité, under the joint supervision of Hakan Eliasson, Professor at the Université de Paris, and Bassam Fayad, CNRS Senior Research Scientist at the IMJ-PRG and Professor at the University of Maryland.

Background

  • 2024-: MSCA Postdoctoral fellow at Centre de Recerca Matemàtica, Spain.
  • 2024: Posdoctoral researcher at Centre de Recerca Matemàtica, Spain.
  • 2020-2023: Postdoctoral researcher at University of Zurich, Switzerland.
  • 2018-2020: Temporary teacher and researcher (ATER in French) at Université de Paris, France.
  • 2016-2020: Ph.D. in Mathematics at IMJ-PRG, Université de Paris, France.
  • 2013-2015: M.Sc. in Mathematics at IMPA (Instituto de Matemática Pura e Aplicada), Brazil.
  • 2009-2012: B.Sc. in Mathematics at Universidad Nacional de Colombia.
You can find a detailed version of my CV here.

Research


My research focuses on Dynamical Systems, particularly in Hamiltonian Dynamics, KAM Theory, Circle Maps and Interval Exchange Transformations.

Publications


Published

1.
Trujillo F. Hausdorff Dimension of Invariant Measures of Multicritical Circle Maps.
Annales Henri Poincaré.
2020;21(9):2861-2875.
DOI: 10.1007/s00023-020-00940-2
2.
Trujillo F. Uniqueness properties of the KAM curve.
Discrete and Continuous Dynamical Systems.
2021;41(11):5165.
DOI: 10.3934/dcds.2021072
3.
Trujillo F. Smooth, mixing transformations with loosely Bernoulli Cartesian square.
Ergodic Theory and Dynamical Systems.
2022;42(3):1252-1283.
DOI: 10.1017/etds.2021.39
4.
Trujillo F. Lyapunov instability in KAM stable Hamiltonians with two degrees of freedom.
Journal of Modern Dynamics.
2023;19(0):363-383.
DOI: 10.3934/jmd.2023010
5.
Trujillo F. On the Hausdorff dimension of invariant measures of piecewise smooth circle homeomorphisms.
Ergodic Theory and Dynamical Systems.
2024;44(12):3599-3629
DOI: 10.1017/etds.2024.25
6.
Berk P, Trujillo F. Rigidity for piecewise smooth circle homeomorphisms and certain GIETs.
Advances in Mathematics.
2024;441:109560.
DOI: 10.1016/j.aim.2024.109560
7.
Trujillo F. Surviving lower-dimensional tori of an invariant resonant torus with any number of resonances.
Transactions of the American Mathematical Society.
2025;378(10):6975-7008.
DOI: 10.1090/tran/9380
8.
Berk P, Trujillo F, Wu H. Ergodic properties of infinite extension of symmetric interval exchange transformations.
Journal de l’École polytechnique — Mathématiques.
2025;12:853-880.
DOI: 10.5802/jep.302

Accepted

9.
Trujillo, F. & Ulcigrai, C. Affine interval exchange maps with a singular conjugacy to an IET.
To appear in Annali Scuola Normale Superiore - Classe di Scienze.
Published online in 2024
DOI: 10.2422/2036-2145.202305_001
10.
Berk, P. & Trujillo, F. On the ergodicity of infinite antisymmetric extensions of symmetric IETs.
To appear in Journal of the European Mathematical Society.
Published online in 2025
DOI: 10.4171/JEMS/1635.
11.
Berk P, Trujillo F, Ulcigrai C. Ergodicity of explicit logarithmic cocycles over IETs.
To appear in Mathematische Annalen.
Published online in 2025
DOI: 10.1007/s00208-025-03246-y

Submitted

12.
Trujillo, F. On the uniqueness of affine IETs semi-conjugated to IETs.
DOI: 10.48550/arXiv.2411.06419 (2024).
13.
Argentieri, F., Berk, P. & Trujillo, F. Ergodicity of skew-products over typical IETs.
DOI: 10.48550/arXiv.2405.07645 (2024).
14.
Berk, P., Frączek, K. & Trujillo, F. On the ergodicity of anti-symmetric skew products with singularities and its applications.
DOI: 10.48550/arXiv.2412.21067 (2024).

Papers in Conferences

15.
Trujillo, F. Surviving lower dimensional tori from an invariant resonant torus.
In Oberwolfach Reports (eds. Arnaud, M.-C., Hofer, H., Hutchings, M. & Kaloshin, V.) vol. 18 1786–1788 (EMS Press, 2021).
DOI: 10.4171/owr/2021/33

Recent talks


Conference Talks

Seminar Talks

Minicourses and Lecture series

Teaching


Contact


Centre de Recerca Matemàtica (CRM)
Campus de Bellaterra, Edifici C
08193 Bellaterra, Barcelona
fatrujilloa at gmail dot com

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