Embedded Files
About me.
About me.
I obtained my Master's degree in Brussels in 2016. I obtained my PhD title under the supervision of Prof. Dr. Eva Miranda at the Labeoratory of Geometry and Dynamical Systems, unofficially named b-Lab in October 2020. I first stayed a couple of months as a postdoc at the UPC and then pursued my research as a postdoc at the ENS in Lyon under the supervision of Prof. Marco Mazzucchelli.
I am currently a Post-doc at the BCAM in Bilbao under the supervision of Prof. Javier Fernandez de Bobadilla.
My research interests lie in between symplectic and Poisson geometry: so-called b-symplectic structures are symplectic away from a hypersurface, but they admit a singularity along this hypersurface. Those appear to be related to classical problems coming from celestial mechanics - and make applications of dynamical results on those problems, especially appealing! I am thus interested in generalizing the known results from symplectic and contact topology to the setting of geometric structures with singularities. This includes Floer homology (on the side of b-symplectic manifolds) and methods of chasing periodic Reeb orbits (for b-contact manifolds).
I am also interested in hydrodynamics (more precisely, stationary Euler solutions) and its relation to contact geometry. And as you might wonder, particularly in the presence of singularities.
Click here for my CV and here for a copy of my PhD thesis.
In COVID times, YouTube presentations almost served as business cards. Here you have mine.
Besides my mathematical interests, I enjoy learning languages - the last one being Euskera, the language spoken in the Basque territory. This is one of the few non-Indo-European languages that exists in Europe. Its origin remains unclear nowadays - but as a surprising fact: it is older than Roman! There are many conjectures about the origin, but proving them (similar to mathematics) is hard!
Research.
Research.
An Invitation to Singular Symplectic Geometry, published in International Journal of Geometric Methods in Modern Physics, Vol. 16, No. supp01 (2019), with R. Braddell, A. Delshams, E. Miranda, A. Planas
Do overtwisted contact manifolds admit infinitely many periodic Reeb orbits?, Extended Abstract, Birkhäuser.
The singular Weinstein conjecture, with E. Miranda, Advances in Mathematics 389 (2021): 107925.
On the singular Weinstein conjecture and the existence of escape orbits for $b$-Beltrami fields, with E. Miranda and D. Peralta--Salas, Communications in Contemporary Mathematics 24.07 (2022): 2150076.
Morse functions and contact convex surfaces, with R. Cardona, Journal of Geometry and Physics 191 (2023) 104886
The geometry and topology of contact structures with singularities, with E. Miranda, to appear in Journal of Geometry and Physics.
2N or infinitely many escape orbits, with J. Fontana, E. Miranda and D. Peralta-Salas, Regular and Chaotic Dynamics, DOI 10.1134/S1560354723520039.
The Arnold conjecture for singular symplectic manifolds, with J. Bruguès and E. Miranda, J. Fixed Point Theory Appl. 26, 16 (2024). https://doi.org/10.1007/s11784-024-01105-y, see here.
A counterexample to the singular Weinstein conjecture, with J. Fontana-McNally, E. Miranda and D. Peralta-Salas, Advances in Mathematics, Volume 458, Part B, December 2024, 109998
Preprints:
Existence and classification of $b$-contact structures, with R. Cardona, preprint.
Summer School on Geometry, Dynamics and Field Theory
Summer School on Geometry, Dynamics and Field Theory
These are expanded notes from the author's minicourse at the International ICMAT Summer School on Geometry, Dynamics and Field Theory that was held at Miraflores de la Sierra in Madrid, Spain, June 20-25, 2024. These notes are intended to be accessible to undergraduate students.
You can find the lecture notes on $b$-Reeb dynamics here.
For the exercises, click here.
The lecture notes can be found here. I am currently working on a polished version, so the file will be updated on a regular basis during the semester. The above exercises can be found in the respective chapters in the book.
I offer remuneration in form of chocolate in exchange for pointing out typos!
Contact me.
Contact me.
☎ BCAM Bilbao Center of Applied Math
Mazarredo Zumarkalea, 14, Abando,
✉ cXYZ@bcamath.org (replace XYZ by last name)
Google Sites
Report abuse