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.
I am a co-organizer of:
Seminars
|
|
Upcoming
meetings
|
|
|
French connection
|
|
My connection to the French research environment can be
tracked with my scanR profile page. |
Areas of interest
- Algebraic and Analytic (non-Archimedean)
Geometry. Real Algebraic, Tropical Algebraic, Rigid
Algebraic and non-Archimedean Algebraic.
- Combinatorics. (Coxeter, infinite) Matroids,
Tropical mathematics, Ordered structures.
- Algebraic and tropical methods to solve algebraic
differential equations. Differential and Tropical
Differential Algebraic Geometry.
- Geometry of Algebraic Structures Close to Commutative Rings.
- Enumerative and Inflection phenomena in Real 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.
- Geometry of algebraic structures close to commutative rings. Details.
- Algebraic and tropical methods to solve algebraic differential
equations.
Currently an external participant in the Project "Existence
of rational solutions in the Busemann-von Karman-Tsien
boundary layer", directed by Carla Valencia. IBERO University, Mexico
City. Details.
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.
DOI:https://msp.org/pjm/2016/283-2/pjm-v283-n2-p01-s.pdf
- 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 Volume 31, Issue 2, 506-517 (Taylor & Francis,
2019).
- 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.
- S Falkensteiner, C. Garay, M
Haiech, et. al., On Initials and the Fundamental Theorem of
Tropical Partial Differential Geometry. Journal of
Symbolic Computation, Volume 115, March–April 2023, Pages 53-73
(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 (de Gruyter 2023).
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.
Submitted
- T. Blomme, E. Brugallé and C. Garay. Bitangents of real
algebraic curves: signed count and constructions. arXiv eprint: 2402.03993
- 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
- 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
Preprints
- E. Cotterill and C. Garay, Matroids and semirings attached
to toric singularity arrangements. arXiv eprint: 2403.15942
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
- Matroids over a scheme. Joint with A. Fink and L. Moci.
01/24 to 05/24 |
|
08/23 to 12/23 |
- Matemáticas discretas (Algebraic combinatorics).
Universidad de Guanajuato.
|
01/23 to 05/23 |
- Métodos Combinatorios en Geometría Enumerativa Real y
Compleja (O). Posgrado UNAM.
- Algebraic Geometry. Universidad de Guanajuato.
|
08/22 to 12/22 |
|
01/22 to 05/22 |
- Introducción a la Geometría Algebraica no Arquimedeana
y Tropical (O). Posgrado UNAM.
Temario y más información
- Calculus II. Universidad de Guanajuato.
|
01/21 to 05/21 |
|
08/20 to 12/20 |
|
01/20 to 05/20 |
- Rigid and tropical methods in Algebraic Geometry.
CIMAT
|
08/19 to 12/19 |
|
09/12 to 08/14 |
|
Current students
BSc |
- Víctor Torres (ESFM-IPN, Mexico City),
- Saul Aranda (UGto, Guanajuato),
- Crisanto Salazar (UAS, Sinaloa).
|
MSc |
- David Huerta (IM-UNAM, Mexico City)
|
PhD |
|
Other (tutorial committee) |
- Oscar Castañon (PhD., IM-UNAM Cuernavaca)
- Ruby Lizbeth Almazán Calzada (PhD., FC-UNAM)
- Omar Carbajal Bonal (MsC. CIMAT Guanajuato)
- Sebastian Velasco Rodríguez (BsC., UIA, Mexico City)
|
Past students and
duties
Click here to access some
resources for students
Postdocs
- Otto Romero (Conacyt, joint with Manuel González Villa, CIMAT
Guanajuato). October 2021-Present
Past events
Visitors
Past visitors
(O) Means Online participation. (H)
Means Hybrid participation. Default is "in person".
|