about

Hello and welcome to my personal webpage, with mostly math content. My interests revolve around combinatorial questions that arise 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 Frankfurt and at Nantes with the SNF project 200142. Before, I did my phd at the university of Bern. A detailed CV is available upon request. See also my ORCID profile https://orcid.org/0000-0002-2733-1868.

contact

Address: Université de Nantes
Laboratoire de Mathématiques Jean Leray - UMR 6629
2 Chemin de la Houssinière
BP 92208
F-44322 NANTES Cedex 3
Office 104
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)
• Catalan-many tropical morphisms to trees; Part III: The real story
  (with Erwan Brugallé)
• Catalan-many tropical morphisms to trees; Part II: A space and a count

preprints

• 7. Combinatorics of higher dimensional tropical covers
     arXiv: 2305.03220
• 6. Buildings, valuated matroids, and tropical linear spaces
     arXiv: 2304.09146 (with Luca Battistella, Kevin Kühn, Arne Kuhrs, Martin Ulirsch)
• 5. One-quasihomomorphisms from the integers into symmetric matrices
     arXiv: 2302.01611 (with Tim Seynnaeve, Nafie Tairi)
     Here is a poster associated to this paper.

published

• 4. On the gonality of metric graphs
     Notices of the AMS, May 2021, Pages 687 - 695
     (with Jan Draisma)
• 3. 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 )
• 2. 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)
• 1. 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)

talks

to come:

• 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.

recent:

• 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.

Past Ones

attending upcoming events

• Research visit to the non-linear algebra group in MPI:MiS Leipzig. Working with Stefano Mereta on the topic of Tropical differential equations [17.04.23 - 21.04.23. Leipzig, DE]
• 4th Graduate Student Meeting on Applied Algebra and Combinatorics [26.04.23 - 28.04.23. Stockholm, SE].
• Algebraic and Tropical Methods for Solving Differential Equations [ 12.06.2023 - 23.06.2023]
• SIAM Conference on Applied Algebraic Geometry (AG23) [10.07.23 - 14.07.23. Eindhoven, NL].

Past Ones

Useful links