about
Hello and welcome to my personal math webpage.
I am interested in combinatorial questions arising in the context of algebraic geometry and commutative algebra,
e.g. questions about graphs, posets, matroids, simplicial complexes, Bruhat-Tits buildings.
Most of my research is in the sunny field of tropical geometry.
Currently, I am a postdoc at the University of Warwick.
A detailed CV is available upon request
and my ORCID is https://orcid.org/0000-0002-2733-1868.
contact
Address:
Mathematics Institute,
University of Warwick
Coventry, CV4 7AL
United Kingdom.
Email: alejandro [at] vargas.page
articles
Feel free to email me for previews of articles in preparation, or broken links. See here for my papers on arXiv.
in preparation
- Polyhedral geometry of tropical solution sets associated to ODE’s
(with Stefano Mereta) - Multiplicities for tropical real gonality
(with Erwan Brugallé) - Catalan-many tropical morphisms to trees; Part II: A space and a count
preprints
published
-
- Buildings, valuated matroids, and tropical linear spaces
Journal of the London Mathematical Society 109, no. 1 (2024): e12850.
(with Luca Battistella, Kevin Kühn, Arne Kuhrs, Martin Ulirsch)
- Buildings, valuated matroids, and tropical linear spaces
-
- On the gonality of metric graphs
Notices of the AMS, May 2021, Pages 687 - 695
(with Jan Draisma)
- On the gonality of metric graphs
-
- Catalan-many tropical morphisms to trees; Part I: Constructions
Journal of Symbolic Computation, Volume 104, May–June 2021, Pages 580-629
arXiv: 1909.12924 (with Jan Draisma)
- Catalan-many tropical morphisms to trees; Part I: Constructions
-
- A short note on Cayley-Salmon equations
Le Matematiche, Vol 75 No 2 (2020), Pages 559-574
arXiv: 1912.01464 (with Marvin Hahn and Sara Lamboglia )
- A short note on Cayley-Salmon equations
-
- Group structures on families of subsets of a group
Pi Mu Epsilon Journal, Vol. 14, No. 5 (Fall 2016), pp. 323-326
arXiv: 1604.01119 (with Mario Gómez, Sergio López-Permouth, Fernando Mazariegos and Rigoberto Zelada)
- Group structures on families of subsets of a group
talks
recent:
- Valuated Matroids, Tropicalized Linear Spaces and the Affine Building of PGL_{r+1}(K)
at the Latin American Geometria Algebraica Real y TrOpical Seminar
See here for slides and here for abstract. - Valuated Matroids, Tropicalized Linear Spaces and the Affine Building of PGL_{r+1}(K) at the Seminar on Nonlinear Algebra of the Max Planck Institute for Mathematics in the Sciences See here for slides and here for abstract.
- Counting tropical morphisms from metric graphs to metric trees at the Séminaire de topologie, géométrie et algèbre of the Laboratoire de Mathématiques Jean Leray. See here for slides and here for abstract.
- Examples of Bruhat-Tits buildings at the GAUS AG Buildings - WS22/23 reading seminar.
- A moduli space of tropical covers that witnesses the gonality bound of metric graphs at the Young Reseachers’ Conference on Non-Archimedean and Tropical Geometry.