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
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
Brugallé and Jean-Jacques Risler.
I was a member of the research team
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:
|| My connection to the French research environment can be
tracked with my scanR profile page.
My areas of interest include:
- Algebraic and Rigid Algebraic Geometry (Real
Algebraic, Tropical Algebraic, Rigid and non-Archimedean
- Combinatorics (Matroids, Tropical
- Differential and Tropical Differential Algebraic
- 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.
- 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,
- 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, 178â€“185.
- E. Cotterill and C. Garay, Inflection divisors of linear series on an
elliptic curve. Matemática ContemporÃ¢nea, Vol. 47
(2020), 73â€“81. Moduli Spaces in Algebraic Geometry and
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.
- 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
- E. Cotterill, I. Darago, C. Garay, C. Han and T. Shaska, Arithmetic
inflection of superelliptic curves. arXiv eprint: 2110.04813
- E. Cotterill, C. Garay and J. Luviano, Exploring tropical
differential equations. arXiv eprint: 2012.14067.
- C. Garay, Introducción a las ecuaciones diferenciales
tropicales. Mixba'al, Revista Metropolitana de
Matem\'aticas. Vol.13, No.1 (2022), p.p 11-28.
- Matroids over a scheme. Joint with Alex Fink and Luca
Click here to access some
resources for students
- Geometría de Estructuras algebraicas cercanas a anillos
conmutativos. Ver más.
- Métodos algebraicos y tropicales para resolver ecuaciones
diferenciales algebraicas. Ver
Past students and
- Otto Romero (Conacyt, joint with Manuel González Villa, CIMAT
Guanajuato). October 2021-Present
- Gurvan Mével (Nantes Université). May 2023
Vargas (Nantes Université). October 2023
(O) Means Online participation