My main area of research is Algebraic Geometry, with emphasis in Hodge Theory and algebraic cycles. I am interested in developing techniques to compute periods of Hodge cycles explicitly, and use this information to study algebraic varieties. I am particularly interested in the Hodge conjecture, and its variational version. My work have concentrated in the case of hypersurfaces, where we can associate to every non-trivial primitive Hodge cycle an Artinian Gorenstein algebra. Lately this relation has specially dragged my attention.
Here you can find my CV.
- Small codimension components of the Hodge locus containing the Fermat variety. Preprint.
- Periods of Complete Intersection Algebraic Cycles. Preprint.
- Integral Hodge conjecture for Fermat varieties Joint with E. Aljovin and H. Movasati. Journal of Symbolic Computation, Vol. 95 (2019), pp. 177--184.
- Periods of linear algebraic cycles Joint with H. Movasati. Pure and Applied Mathematics Quarterly, Vol. 14, No. 3-4 (2018), pp. 563--577.
- How to construct Hodge cycles on hypersurfaces? (Spanish). Seminario de Geometría Algebraica. 16.06.20. Universidad Católica de Chile. Online Seminar. Slides.
- Small codimension components of the Hodge locus and periods of the Fermat variety. Geometry, Arithmetics and Differential Equations of Periods Seminar. 12.06.20. IMPA. Online Seminar. Slides.
- On Variational Hodge Conjecture for Hypersurfaces (Spanish). Math Department Colloquium. 10.07.19. Universidad de Chile. Santiago, Chile.
- Artinian Gorenstein Algebras and Components of the Hodge Locus. Hodge Theory Day. 21.03.19. IMPA. Rio de Janeiro, Brazil.
- Periods of Complete Intersection Algebraic Cycles. Hodge and Noether Lefschetz Loci Seminar. 28.11.18. CMSA, Harvard University. Cambridge, US.
- Periods of Linear Cycles in Fermat Varieties. Worhshop: Picard-Fuchs Equations and Hypergeometric Motives. 26.03.18. HCM, Bonn University. Bonn, Germany.
- Hodge Theory. Recorded lectures at IMPA YouTube channel. Detailed content of the course. Exercises: List 1, List 2, List 3. Spring Term 2019. IMPA.
- An Introduction to Algebraic de Rham Cohomology and Infinitesimal Variations of Hodge Structures. Spring Term 2018. IMPA.
- Introduction to Number Theory. Joint with H. Movasati and M. Torres. Detailed content of the course. My lecture notes. Summer Term 2017. IMPA.
Research Schools TA
- Stable Birrational Invariants and the Stable Lüroth Problem. Prof. Claire Voisin. 02.12.2019 - 06.12.2019. Universidad de Talca. Fourth Latin American School of Algebraic Geometry and Applications.
- Topics in Hodge Theory Prof. Hossein Movasati. Spring Term 2017. IMPA.
- Introduction to Complex Geometry. Prof. Hossein Movasati. Fall Term 2017. IMPA. Exercises.
- Schemes and Cohomology. Prof. Karl-Otto Stöhr. Fall Term 2017. IMPA. Exercises.
- Introduction to Number Theory. Prof. Hossein Movasati. Summer Term 2017. IMPA. Exercises.
- Classical Algebraic Geometry. Prof. Karl-Otto Stöhr. Spring Term 2016. IMPA. Exercises.
- Classical Algebraic Geometry. Prof. Eduardo Esteves. Spring Term 2015. IMPA.
- Abstract Algebra. Prof. Carolina Araujo. Fall Term 2015. IMPA.
- Linear Algebra. Prof. Alejandro Maass. Spring Term 2012. Universidad de Chile. Exercises.
- Multivariable Calculus. Prof. Juan Dávila. Fall Term 2012. Universidad de Chile. Exercises.
- Graph Theory. Prof. Martín Matamala. Fall Term 2012. Universidad de Chile.
- Introduction to Calculus. Prof. José Soto. Spring Term 2011. Universidad de Chile. Exercises.
- Introduction to Algebra. Prof. Alejandro Maass. Spring Term 2011. Universidad de Chile. Exercises.
- A Course in Hodge Theory: Periods of Algebraic Cycles. Book in progress, joint with Hossein Movasati (second volume of Hossein's book A Course in Hodge Theory: With Emphasis on Multiple Integrals).