Curriculum vitae · September 2026

Bernat Espigulé

Self-similar sets, topology, and scientific computation.
PhD candidate at the Universitat de Girona.

Thesis deposited 9 September 2026 · defence pending

Download CV · PDF ↓

bernat.espigule@gmail.com · complextrees.com
ORCID 0000-0002-8036-7851 · github.com/espigule

Education

2022–present: PhD candidate in mathematicsUniversitat de GironaThesis deposited 9 September 2026; defence pending. Doctoral programme in Technology. Thesis: Collinear Fractals and Connectedness Loci: Topology, Finite Capture, and Restricted Polynomial Roots. Supervisors: David Juher, Joan Saldaña.
2021: MSc in Advanced MathematicsUniversitat de BarcelonaThesis: Complex trees and their families of connected self-similar sets. Thesis completed in 2018; degree awarded in 2021. Supervisors: Núria Fagella, Xavier Jarque. Read the thesis ↗
2012: BSc in PhysicsUniversitat Autònoma de BarcelonaInternational study at UC Santa Barbara (2010–2011) and Heidelberg University (2011–2012).

Research & professional experience

2022–2025: Predoctoral researcherUniversitat de GironaResearch and scientific software development for the doctoral thesis, supported by IFUdG funding.
2013–2017; 2020–2021: ConsultantWolfram ResearchMathematical content, symbolic and numerical prototypes, interactive demonstrations, and technical communication in an international environment. Author of eight Wolfram Blog articles.
2019–2020: Content consultantCosmoCaixa BarcelonaMathematical and scientific content and participatory activities for museum visitors.

Research member, HOLODYN, Universitat de Barcelona (2017–2022). Long-term participant, Illustrating Mathematics, ICERM, Brown University (2019).

Research

I study the topology of self-similar sets and their parameter spaces, including connectedness, holes, contacts, and polynomial-root approximation. My work brings together symbolic dynamics, exact computation, and interactive visualization.

Collinear fractals and connectedness loci — doctoral research on topology, finite capture, and restricted polynomial roots.
Collinear Fractals Explorer — linked parameter and dynamical views for finite computational exploration.
4D Connectedness Atlas — planar binary similarity families, contact geometry, and finite numerical signatures.

Selected publications & preprints

2024

Collinear Fractals and Bandt's Conjecture

Journal article

Bernat Espigule, David Juher, Joan SaldañaFractal and Fractional 8(12), 725

DOI ↗arXiv ↗PDF ↗

Cite

@article{espigulejuhersaldana2024bandt,
  author = {Espigule, Bernat and Juher, David and Salda{\~n}a, Joan},
  title = {Collinear Fractals and {Bandt}'s Conjecture},
  year = {2024},
  journal = {Fractal and Fractional},
  volume = {8},
  number = {12},
  pages = {725},
  doi = {10.3390/fractalfract8120725},
  url = {https://doi.org/10.3390/fractalfract8120725}
}

2026

Finite capture and the closure of roots of restricted polynomials

Preprint

Bernat Espigule, David JuherarXiv:2603.07397

arXiv ↗PDF ↗Explorer ↗

Cite

@misc{espigulejuher2026capture,
  author = {Espigule, Bernat and Juher, David},
  title = {Finite capture and the closure of roots of restricted polynomials},
  year = {2026},
  eprint = {2603.07397},
  archivePrefix = {arXiv},
  primaryClass = {math.DS},
  note = {Preprint},
  doi = {10.48550/arXiv.2603.07397},
  url = {https://arxiv.org/abs/2603.07397}
}

2026

Infinitely many holes in connectedness loci for collinear affine iterated function systems

Preprint

Bernat EspigulearXiv:2606.01467

arXiv ↗PDF ↗

Cite

@misc{espigule2026holes,
  author = {Espigule, Bernat},
  title = {Infinitely many holes in connectedness loci for collinear affine iterated function systems},
  year = {2026},
  eprint = {2606.01467},
  archivePrefix = {arXiv},
  primaryClass = {math.DS},
  note = {Preprint},
  doi = {10.48550/arXiv.2606.01467},
  url = {https://arxiv.org/abs/2606.01467}
}

2026

Explicit interpolations among the Sierpiński, Rauzy, and Apollonian gaskets

Preprint

Bernat EspigulearXiv:2606.23278

arXiv ↗PDF ↗Explorer ↗

Cite

@misc{espigule2026gaskets,
  author = {Espigule, Bernat},
  title = {Explicit interpolations among the {Sierpi\'nski}, {Rauzy}, and {Apollonian} gaskets},
  year = {2026},
  eprint = {2606.23278},
  archivePrefix = {arXiv},
  primaryClass = {math.DS},
  note = {Preprint},
  doi = {10.48550/arXiv.2606.23278},
  url = {https://arxiv.org/abs/2606.23278}
}

2019

A Family of Fern-like Ternary Complex Trees

Proceedings article

Bernat EspiguléBridges 2019, pp. 147–154

Publication ↗PDF ↗

Cite

@inproceedings{espigule2019ferns,
  author = {Espigul{\'e}, Bernat},
  title = {A Family of Fern-like Ternary Complex Trees},
  year = {2019},
  booktitle = {Proceedings of Bridges 2019: Mathematics, Art, Music, Architecture, Education, Culture},
  pages = {147--154},
  publisher = {Tessellations Publishing},
  address = {Phoenix, Arizona},
  editor = {Goldstine, Susan and McKenna, Douglas and Fenyvesi, Krist{\'o}f},
  url = {https://archive.bridgesmathart.org/2019/bridges2019-147.html}
}

Full publication list, sources & citations ↗

Teaching & workshops

2025 and 2026: Bojos per les MatemàtiquesUniversitat de BarcelonaDesigned and taught four-hour workshops for advanced secondary-school students on fractals, polynomial roots, computational exploration, conjectures, and proofs.
2014–2017: Wolfram Educational Summer ProgramsMassachusettsTeaching and project mentoring across four editions, covering computational mathematics, Wolfram Language, visualization, and the development of research questions.
10 January 2022: Arbres complexos i fractalsFANJACOnline workshop.
2019: Invited session on fractal geometry and designUIC Barcelona
2018: Barcelona Tech Math Summer CampUniversitat Politècnica de CatalunyaComputational mathematics outreach.

Communication & mathematical art

History of Mathematics Project — eight interactive learning journeys with Wolfram Research and the National Museum of Mathematics.
Eight Wolfram Blog articles, 2014–2021.
Complex Trees art portfolio — mathematical images, animation, and sculpture; exhibitions include the Joint Mathematics Meetings, Bridges, and ICERM.

Selected research presentations

Institut Henri Poincaré, Paris — March 2026. Recorded talk ↗
One World Numeration Seminar — June 2026.
ICERM Illustrating Mathematics Reunion/Expansion — online, 2025.

Tools & languages

Wolfram Language / Mathematica
Python
JavaScript / TypeScript
GLSL / WebGL
Git / GitHub
LaTeX
Exact algebraic computation
Interval arithmetic

Catalan: native. Spanish and English: fluent in academic and professional contexts.