CV
•2024- 2025 Posdoctoral research, DISMA, Dipartimento di SCIENZE MATEMATICHE "Giuseppe Luigi Lagrange", Politecnico di Torino.
Education
• 2016 - 2020 Ph.D. in Mathematics, Pontificia Universidad Católica de Chile, Thesis " On The Geography of Surfaces of General Type with fixed Fundamental Group" under the supervision of Giancarlo Urzua.
• 2014 - 2016 Master in Mathematics, Pontificia Universidad Católica de Chile, Thesis on "Geometry of Hilbert and Quot schemes of points on smooth curves and smooth surfaces" under the supervision of Sukhendu Mehrotra.
• 2008- 2013 Bachelor’s degree in Mathematics, Universidad del Valle, Colombia. Under the supervision of Roberto Ruiz.
Position Held
2024- 2025 Posdoctoral research, DISMA, Dipartimento di SCIENZE MATEMATICHE "Giuseppe Luigi Lagrange", Politecnico di Torino.
2021- 2024 Posdoctoral research, Department of mathematics Universidad Federico Santa María.
2021 Full Time professor, Department of sciences, Universidad de la Costa.
Teaching
2022 - Matemáticas 3, Calculus in several variables, Universidad Técnica Federico Santa Maria , Valparaíso, Chile
2021 - Differential equations, Universidad de la Costa, Barranquilla, Colombia.
2020 - Short course on Algebraic Geometry, Universidad Central de Ecuador, Quito, Ecuador.
Participation in Conferences
Variedades Exóticas y algo más. Universidad del Valle, Cali (Colombia) February 2024.
XXXI Congreso de Matemática Capricornio COMCA, Universidad Católica del Norte, Antofagasta (Chile) August 2023.
Roma Tre University, (Italy) June 14-17, 2022. On the occasion of Sandro Verra’s 70th birthday. Roma Tre University, (Italy) June 14-17, 2022.
Classical Elegance: the Geometry of Algebraic varieties, A Conference in honor of Rita Pardini’s 62th birthday. Palazzone di Cortona, (Italy) June 7th-10th, 2022
XXXIII Jornada Zona Sur Matemáticas 2021, UFRO Online (Chile), April 20th-24th, 2021.
Fourth LATIN AMERICAN SCHOOL on Algebraic Geometry and its Applications, Talca (Chile), December 2nd - 13th, 2019.
Thematic month Complex Geometry CIRM, Luminy-Marseille (France), February 2019.
ICTP-CIMPA: AGRA III Winter School, Córdoba (Argentine), July 2018.
LXXXV Encuentro anual Sociedad Matemática de Chile, SOMACHI, Talca (Chile), November 2017.
Talks
Variedades Exóticas y algo más. Universidad del Valle, Cali (Colombia), ¿Cuáles manifolds proyectivos admiten fibrado tangente Ulrich?, February 2024.
Rational points: new dimensions; consortium based at the Universities of Groningen, Leiden, and Utrecht, Utrecht University (The Netherlands), Elliptic fibrations on K3 surfaces admitting strictly elliptic involution, November 2023.
XXXI Congreso de Matemática Capricornio COMCA, Universidad Católica del Norte, Antofagasta (Chile), K3 surfaces vs DPN pair, August 2023.
Algebra Research group, Bernoulliborg, University of Groningen, Surfaces of General type, Groningen (The Netherlands), May 2023.
ICTP, Algebraic Geometry Seminar, Construction of Savage surfaces, Trieste (Italy), April 2023.
ENEMAT 1, Variedades Proyectivas que tienen fibrado Tangente Ulrich, Santiago (Chile), November 2022.
AGV Seminar, Universidad de Valparaíso, Pequeña Introducción a los fibrados de Ulrich, Universidad de Valparaíso (Chile), May 2022.
XXXIII Jornada Zona Sur Matemáticas 2021, On Geography of Surfaces of General Type, Online UFRO (Chile), April 2021.
SaNTAS, Santiago Number Theory and Algebra Seminar, Some results about Hilbert schemes and Quot schemes, Santiago (Chile), June 2018.
SOMACHI LXXXV, a section of Algebraic and Arithmetic Geometry, Some results about Hilbert schemes and Quot schemes, Universidad deTalca, Talca (Chile), November 2017.
Academic Visitis
•Internship at Aix-Marseille Université, from March 2019 to June 2019, with Xavier Roulleau.
• Visit at University of Groningen, at Bernoulliborg, Algebra Research Group , from February 2023 to May 2023, with Cecilia Salgado.
•ICTP (Italy), Group of Algebraic Geometry, April 2023, work with Yulieth Prieto.
• Visit at University of Groningen, at Bernoulliborg, Algebra Research Group , from September 2023 to November 2023, with Cecilia Salgado.
Students
•Edwin Fernando Cruz Días, Master, Universidad Central del Ecuador, Julio 2021- August 2023. Summa cum laude.
•José Ávila, Undergraduate, Universidad del Valle, Abril 2022-March 2023. Summa cum laude, Invariant Smooth Quartic Surfaces by all Finite Primitive Groups of PGL_4(C).
• Juan Sebastian Cruz, Undergraduate, Universidad del Valle, September 2023-Ongoing.
Research assistant :
•Emilio Oyanedel, at Universidad Federico Santa María, assistant research of the undergraduate research. Topic: K3 surfaces and Torelli Theorem. I-2022.
•Mario Alonso Pastrana, at Universidad Federico Santa María, assistant research of the undergraduate research. Topic: Algebraic Surfaces. II-2022.
•Sebastián Fuentes, at Universidad Federico Santa María, assistant research of the undergraduate research. Topic: Algebraic Surfaces. II-2022.
Publications
Savage Surfaces , JEMS, join Giancarlo Urzúa.
Projective manifolds whose tangent bundle is Ulrich, Journal of Algebra, join V. Benedetti, P. Montero, and Y. Prieto Montañez.
Invariant Smooth Quartic Surfaces by all Finite Primitive Groups of PGL_4(C), Journal of Pure and Applied Algebra, Join G. Ortiz, and J. Ávila.
Mathematical Service
Reviewer for the zbMATH Open, MathSciNet AMS, and referee of "Proyecciones, Journal of Mathematics".
Member of the undergraduate program committee, Universidad del Valle, 2021-2024.
Part of the scientific committee (Algebraic Geometry) Altencoa 9, Universidad del Valle.
Part of the organizing committee Variedades Exóticas y algo más, Universidad del Valle.
Fellowships, Grants, and Awards
“Geometria Algebrica Multilineare” approvato dal competente organo del Dipartimento di Scienze Matematiche "G. L. Lagrange," at Politecnico di Torino.
Postdoctorado Proyecto Fondecyt Anid 2021-2024 Folio 3210518.
Beca Doctorado Nacional - 2017, CONICYT, Chile 2017-2020.
M.Sc. Scholarship, Pontificia Universidad Católica de Chile, Vicerrectoría de Investigaciones, Chile, 2014-2016.
Pre-prints
On strictly elliptic K3 surfaces and del Pezzo Surfaces. Join with P. Comparin, P.Montero, Y. Prieto, submitted.