Frank Trujillo

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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

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

Trujillo F. Hausdorff Dimension of Invariant Measures of Multicritical Circle Maps.
Ann Henri Poincaré. 2020;21(9):2861-2875.
DOI: 10.1007/s00023-020-00940-2

Trujillo F. Uniqueness properties of the KAM curve.
Discrete and Continuous Dynamical Systems. 2021;41(11):5165.
DOI: 10.3934/dcds.2021072

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

Trujillo F. Lyapunov instability in KAM stable Hamiltonians with two degrees of freedom.
JMD. 2023;19(0):363-383.
DOI: 10.3934/jmd.2023010

Trujillo F. On the Hausdorff dimension of invariant measures of piecewise smooth circle homeomorphisms.
Ergodic Theory and Dynamical Systems. Published online April 11, 2024:1-31.
DOI: 10.1017/etds.2024.25

Accepted

Berk, P. & Trujillo, F. On the ergodicity of infinite antisymmetric extensions of symmetric IETs.
To appear in Journal of the European Mathematical Society.
DOI: 10.48550/arXiv.2304.01868.

Trujillo, F. Surviving Lower Dimensional Invariant Tori of a Resonant Torus with any Number of Resonances.
To appear in Transactions of the American Mathematical Society.
DOI: 10.1090/tran/9380.

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.
DOI: 10.2422/2036-2145.202305_001

Submitted

10.

Berk, P., Trujillo, F. & Ulcigrai, C. Ergodicity of explicit logarithmic cocycles over IETs.
DOI: 10.48550/arXiv.2210.16343 (2023).

11.

Berk, P., Trujillo, F. & Wu, H. Ergodic properties of infinite extension of symmetric interval exchange transformations.
DOI: 10.48550/arXiv.2409.12168 (2024).

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

Workshop on Spectral Rigidity for Billiards, Budapest, Hungary, Nov 2024.
School and Workshop on Dynamical Systems at ICTP, Trieste, Italy, Aug 2024.
IMJ-PRG Summer School 2024 - Stability and rigidity in dynamical systems, beyond classical KAM theory, Paris, France Jun 2024.
BMS-BGSMath Junior Meeting, Berlin, Germany, Jun 2024.
Barcelona Mathematical Days, Institut d'Estudis Catalans, Spain, Nov 2023.
Workshop on two-dimensional maps, Institute Mittag-Leffler, Sweden, Apr 2023.
Combinatorial and geometric approaches on dynamics, Universidad de Chile, Chile, Dec 2022.
2nd Jangada dinâmica workshop on dynamical systems, ergodic theory and related areas, Universidade Federal do Ceará, Brazil, Oct 2022.
Paraguayan colloquium on mathematics and related sciences, Universidad Nacional de Asunción, Paraguay, Nov 2021.
8th SwissMAP general meeting, SwissMAP research station, Switzerland, Sep 2021.
Oberwolfach workshop on dynamical systems, Mathematisches Forschungsinstitut Oberwolfach (MFO), Oberwolfach, Germany, Jul 2021.
Penn State workshop in dynamical systems and related topics, Pennsylvania State University, USA, Nov 2020.

Seminar Talks

Toruń ergodic theory and dynamical systems seminar, Uniwersytet Mikołaja Kopernika, Poland, Oct 2024.
Seminar in dynamical systems at IST (DynamIST), IST, Austria, Fev 2024.
Dynamics and Group Geometry Early Researchers Seminar (DAGGER), University of Warwick, Warwick, United Kingdom, Jun 2023.
Quasiworld (online) seminar, May 2023.
UB-UPC (Universitat de Barcelona - Universitat Politècnica de Catalunya) Dynamical Systems Seminar, Spain, Mar 2023.
Ergodic theory and dynamical systems seminar, University of Zurich, Switzerland, Apr 2023.
Geometry and dynamical systems seminar, Université de Neuchâtel, Switzerland, Nov 2022.
Seminar in dynamical systems at IST (DynamIST), IST, Austria, Jun 2022.
Inter-institutional seminar on dynamical systems, ergodic theory and related areas (dinâmica arretada), Universidades do Nordeste, Brazil, Mar 2022.
Toruń ergodic theory and dynamical systems seminar, Uniwersytet Mikołaja Kopernika, Poland, Apr 2021.
Geometry, analysis and dynamical systems seminar, Université Nice Sophia Antipolis, France, Fev 2021.
Dynamics and probability seminar, Université de Picardie Jules Verne, France, Jul 2020.
Ergodic theory and dynamical systems seminar, University of Zurich, Switzerland, Oct 2020.
Dynamical systems seminar, Institut de Mathématiques de Jussieu, France, May 2020.
Ergodic theory and dynamical systems seminar, Université Paris Sud, France, Dec 2019.

Minicourses and Lecture series

An Introduction to KAM Theory, Workshop on Ergodic theory and parabolic dynamics, IMPAN, Poland, May-Jun 2023. Link to recordings

Teaching

Instructor, Qualitative Theory of Differential Equations, University of Zurich, 2023.
Instructor, Student seminar on Dynamical Systems, University of Zurich, 2023.
Instructor, Student seminar on Hamiltonian Dynamics, University of Zurich, 2022.
Instructor, Foundations of Mathematics, University of Zurich, 2021.
Teaching assistant, Complex Analysis, University of Zurich, 2021.
Instructor, Student seminar on Circle Dynamics, University of Zurich, 2020.
Teaching assistant, Calculus I, Université Paris Descartes, 2020.
Teaching assistant, Measure Theory, Université Paris Descartes, 2019.
Teaching assistant, Probability, Université Paris Descartes, 2019.
Teaching assistant, Advanced Analysis and Algebra, Université Paris Diderot, 2018.
Teaching assistant, Elementary Analysis and Algebra, Université Paris Diderot, 2017.
Teaching assistant, Advanced Analysis and Algebra, Université Paris Diderot, 2016.