RESEARCH ARTICLES
- The motive of a variety with cellular resolution of singularities. August 2024. Preprint.
- The cotangent complex and Thom spectra, joint with Nima Rasekh. First version: May 2020. Published in Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, January 2021, https://doi.org/10.1007/s12188-020-00226-8
- Thom spectra, higher THH and tensors in ∞-categories, joint with Nima Rasekh and Gabriel Valenzuela. First version: November 2019. Published in Algebraic & Geometric Topology, October 2022, https://doi.org/10.2140/agt.2022.22:4
- Higher topological Hochschild homology of periodic complex K-theory. First version: December 2017. Published in Topology and its Applications, August 2020, https://doi.org/10.1016/j.topol.2020.107302
- Graded multiplications on iterated bar constructions. First version: February 2017. Published in An Alpine Bouquet of Algebraic Topology, Contemporary Mathematics, vol. 708, Amer. Math. Soc., Providence, RI, 2018, pp. 245-274, https://doi.org/10.1090/conm/708
DISSERTATIONS
- PhD dissertation (December 8, 2017): On higher and iterated topological Hochschild homology (slides). Université Paris 13. Supervisor: Christian Ausoni.
- Master’s dissertation (2014): An algebraic description of the algebraic K-theory groups. Université Paris 13. Supervisor: Christian Ausoni.
- Bachelor’s dissertation (2012): Functores adjuntos y teoremas de adjunción. In Spanish (slides) (addenda). Universidad de la República (Uruguay). Supervisor: Walter Ferrer Santos.
COURSE MATERIAL
- Introduction to Stable Homotopy Theory. 104 pages. Notes for a one-semester course, 2 hours a week. Spring 2022. Exercise sheet 1 , Exercise sheet 2, Exercise sheet 3, Exercise sheet 4, Exercise sheet 5, Exercise sheet 6, Exercise sheet 7
NOTES
- Lurie’s construction of the smash product of spectra (notes for an expository talk. November 2022)
- Monoids (notes for a talk at the quasicategories study seminar at University of Warsaw, motivating the concept of a symmetric monoidal quasicategory. November 2017)
- Homotopy, homology, and the Dold-Thom theorem (sketchy notes for two talks at the PhD student seminar in Université Paris 13. March 2016)
- Fiber bundles and characteristic classes (notes for a talk series at the 2015 summer school “Małe Ciche Niskowymiarowe”)
- Higher and iterated topological Hochschild homology (notes for a talk at the 2015 European Talbot)
- A construction of the K-theory spectrum of a ring (for a course examination, 2014)
- El proceso de formalización de la lógica matemática – la crisis de la geometría euclídea (examination for an Epistemology kind of course, 2011. In Spanish.)
COURSE NOTES (or more accurately, notes more or less inspired by courses I took as a student. In Spanish.)
- Cálculo III (Differentiable manifolds and differential forms; geometry of curves and surfaces)
- Introducción a la geometría diferencial (Differential topology, Gauss-Bonnet theorem, introduction to Riemannian geometry)
- Álgebra II (group theory, fields and Galois theory, representations of finite groups)
OLD STUFF (mostly memory dumps: use at your own risk! In Spanish.)
- Hacia la arcada del álgebra homológica (una introducción a las categorías abelianas)
- Empalme-factorización de sucesiones exactas y exactitud de functores
- Una breve introducción a los espacios uniformes