I am a CONACYT
Research fellow in Mathematics at CIMAT, in the City of
Guanajuato, Mexico, since may 2019. I belong to the CIMAT's Commutative Algebra and Algebraic Geometry
Academic Cluster.
I studied at the Institut de
Mathématiques de Jussieu (now Institut
de Mathématiques de Jussieu-Paris Rive Gauche) of the Pierre
and Marie Curie University (also known as UPMC, Paris 6, and now Sorbonne
University) from 2008 to 2015, under the joint direction of
Erwan
Brugallé and Jean-Jacques Risler.
I was a member of the research team
Analyse
Algébrique. My PhD thesis (Tropical intersection theory,
and real inflection points of real algebraic curves) can be
downloaded from here.
Awards and distinctions
I am a co-organizer of:
Seminars
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Upcoming
meetings
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French connection
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My connection to the French research environment can be
tracked with my scanR profile page. |
My areas of interest include:
- Algebraic and Analytic (non-Archimedean)
Geometry (Real Algebraic, Tropical Algebraic, Rigid
Algebraic and non-Archimedean Algebraic).
- Combinatorics (Matroids, Infinite Matroids,
Tropical mathematics).
- Differential and Tropical Differential Algebraic
Geometry.
- Inflection phenomena in Algebraic Geometry.
Right now I am very interested in the third subject. You can find
a comprehensive introduction to the state of the art on the
subject in our recent preprint Exploring tropical differential equations,
which grew up from the previous friendly introduction that can be
found here. (first version : march 2020)
More details on some of my ongoing research projects are
available in my Research Gate site.
Journal articles
- F. Aroca, C. Garay and Z.
Toghani, The fundamental theorem of tropical
differential algebraic geometry. Pacific Journal of
Mathematics Vol. 283 (2016), No. 2, 257-270
- I Biswas, E Cotterill and C.
Garay, Real inflection points of real
hyperelliptic curves. Transactions of the American
Mathematical Society 372 (2019), no. 7, 4805-4827.
- E. Cotterill and C. Garay, Real inflection points of real linear
series on an elliptic curve. Experimental
Mathematics (Taylor & Francis, 2019).
- S Falkensteiner, C. Garay, M
Haiech, et. al., On Initials and the Fundamental Theorem of
Tropical Partial Differential Geometry. Journal of
Symbolic Computation (Elsevier, 2023), ISSN 0747-7171,
https://doi.org/10.1016/j.jsc.2022.08.005.
- E. Cotterill, C. Garay and J. Luviano, Exploring tropical differential equations.
Advances in Geometry https://doi.org/10.1515/advgeom-2023-0019.
- P. L. del Angel, E. J. Elizondo, C. Garay, F. Zaldívar. On
T-invariant subvarieties of symplectic Grassmannians and
representability of rank 2 symplectic matroids over C.
Journal of Algebra, Volume 640, 2024,300-325, ISSN 0021-8693,
https://doi.org/10.1016/j.jalgebra.2023.10.031.
Proceedings articles
- S Falkensteiner, C Garay-López, M
Haiech, et. al. The Fundamental Theorem of Tropical
Partial Differential Algebraic Geometry, In
Proceedings of the 45th International Symposium on Symbolic and
Algebraic Computation (ISSAC '20). Association for Computing
Machinery, New York, NY, USA, 178-185.
- E. Cotterill and C. Garay, Inflection divisors of linear series on an
elliptic curve. Matemática Contemporânea, Vol. 47
(2020), 73-81. Moduli Spaces in Algebraic Geometry and
Applications.
Submitted
- L. Bossinger, S. Falkensteiner, C. Garay-López, M.-P.
Noordman, Tropical initial degeneration for systems of
algebraic differential equations. arXiv eprint: 2309.10761.
- F. Aroca, L. Bossinger, S. Falkensteiner, C. Garay, et.al. Infinite
matroids in tropical differential algebra. arXiv eprint: 2305.04784.
- F. Baril and C. Garay, Tropicalization of Schemes and
Sheaves. arXiv
eprint: 2304.04872.
- E. Cotterill, I. Darago, C. Garay, C. Han and T. Shaska, Arithmetic
inflection of superelliptic curves. arXiv eprint: 2110.04813
Preprints
- E. J. Elizondo, C. Garay and A. Fink, Matroids and the
space of torus-invariant subvarieties of the Grassmannian with
given homology class. arXiv eprint: 2112.15334
The index of my preprints available on arXiv is here. One more index of (different) material
available on Archive Ouverte HAL (in french) is here.
Expository pieces
- C. Garay, Introducción a las ecuaciones diferenciales
tropicales. Mixba'al, Revista Metropolitana de
Matemáticas. Vol.13, No.1 (2022), p.p 11-28.
DOI: www.doi.org/10.24275/uami/dcbi/mix/v13n1/cgaray
In preparation
- Bitangents of real algebraic curves: signed count and
constructions. Joint with T. Blomme and E. Brugallé.
- Matroids over a scheme. Joint with A. Fink and L. Moci.
- Geometría de Estructuras algebraicas cercanas a anillos
conmutativos. Ver más.
- Métodos algebraicos y tropicales para resolver ecuaciones
diferenciales algebraicas. Ver
más.
Click here to access some
resources for students
Past students and
duties
| BSc |
- Víctor Torres (ESFM-IPN)
- Saul Aranda (UGto)
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| MSc |
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| PhD |
Alejandro Martínez (joint with
O. Lorscheid, Rijksuniversiteit
Groningen) |
| Other (tutorial committee) |
Oscar Castañon (Ph.D., IM-UNAM Cuernavaca)
Sebastian Velasco Rodríguez (Bs.C., UIA, CDMX) |
Postdoc
- Otto Romero (Conacyt, joint with Manuel González Villa, CIMAT
Guanajuato). October 2021-Present
- Seminario DiferenciaHable en Geometría. Facultad de Ciencias,
UNAM. 30 Noviembre 2023
- Seminario (TBH), Universidad Iberoamericana. Ciudad de México,
01 Diciembre 2023
- 8 Congreso de Investigación Científica. UNAH-VS Honduras, 3-7 Diciembre 2023.
- Escuela Temática de Álgebra y Geometría
Algebraica, CIMAT, 11-15 Diciembre 2023
Past events
Visitors
Past visitors
(O) Means Online participation. (H)
Means Hybrid participation. Default is "in person".
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