About me
I am currently a Postdoc in the Complex Geometry and Holomorphic Foliations group of IMPA, working with Hossein Movasati.
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.
Here you can find my CV.
Articles
- Periods of Complete Intersection Algebraic Cycles. Preprint.
- Integral Hodge conjecture for Fermat varieties (with E. Aljovin, H. Movasati). Journal of Symbolic Computation, Vol. 95 (2019), pp. 177--184.
- Periods of linear algebraic cycles (with H. Movasati). Pure and Applied Mathematics Quarterly, Vol. 14, No. 3-4 (2018), pp. 563--577.
Thesis
- Periods of Algebraic Cycles. 19.03.19. IMPA. Slides.
Teaching
Instructor
- Hodge Theory. Spring Term 2019. Recorded lectures at IMPA YouTube channel. Exercises: List 1, List 2, List 3. Detailed content of the course.
- An Introduction to Algebraic de Rham Cohomology and Infinitesimal Variations of Hodge Structures. Spring Term 2018. IMPA.
- Introduction to Number Theory. Summer Term 2017. Together with H. Movasati and M. Torres. IMPA. Detailed content of the course. My lecture notes.
Graduate TA
- 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.
Undergraduate TA
- 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.
Notes and Videos
Recorded Talks
- 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.
Notes
- A Course in Hodge Theory: Periods of Algebraic Cycles. This is a book in progress with Hossein Movasati (second volume of Hossein's book A Course in Hodge Theory: With Emphasis on Multiple Integrals).
- Supplement to: Periods of Complete Intersection Algebraic Cycles.
- La recta projectiva real en olimpiadas.