I did my PhD in the arithmetic geometry research group at the Mathematical Institute of FU Berlin, supervised by Hélène Esnault.

I am interested in the topology of conjugate Berkovich spaces. Here you can check my Exposé. Before I did my master on the Grothendieck-Ogg-Shafarevich formula for l-adic sheaves.

My academic CV (pdf, TeX).

Contact

Mail: castillejo@zedat.fu-berlin.de

Articles

• (PhD thesis) The topology of conjugate Berkovich spaces (English). 2020.
• (Master thesis) The Grothendieck-Ogg-Shafarevich formula for l-adic sheaves (English. Pdf, TeX). 2016.
• (with V. Arnaiz and A. González) Sobre el problema de Flavio Josefo (Spanish. Pdf, TeX). Ponencias de jóvenes investigadores (I) (Colección Cuadernos del I.N.I.C.E.. Investigación juvenil; n. 96). 2010.

Talks

Upcoming:

Past:

• Periods and the conjectures of Grothendieck and Kontsevich-Zagier (Video, pdf, TeX). PhD defense, June 10, 2020.
• The topology of conjugate Berkovich spaces (Video, pdf, TeX). PhD defense, June 10, 2020.
• Proof of the Hodge-Tate filtration. p-adic Hodge Theory, November 19, 2018.
• Period mappings and Galois representations I. A New Proof of Mordell Conjecture, after Lawrence-Venkatesh, November 1, 2018.
• Ramification of curves: from Hurwitz formula to the Grothendieck-Ogg-Shafarevich formula. Abhyankar's conjecture, April 23, 2018.
• Tempered fundamental group and covers (Notes). JAVA, September, 2017
• Galois cohomology and logarithmic geometry. p-adic Hodge Theory, May 15, 2017.
• The de Rham-Witt complex. Crystalline Cohomology, January 16, 2017.
• Skeleton (Notes, TeX). Berkovich spaces, birational geometry and motivic zeta functions, December 1, 2016.
• Periods and the conjectures of Grothendieck and of Kontsevich-Zagier (Notes, TeX). Motivic Galois Groups and Periods, June 23, 2016.
• The Riemann-Hilbert correspondence (Notes -by Wouter). D-Modules, May 23, 2016.
• l-adic sheaves and the Grothendieck-Ogg-Shafarevich formula (Notes of first, second, third and fourth lecture). Mini course (8 hours), FU Berlin, April 14-15, 2016.
• Crystalline cohomology (Notes, TeX). Supersingular K3 Surfaces, FU Berlin, October 22, 2015.
• Chow ring (Notes). Intersection theory, FU Berlin, October 12, 2015.
• Cohomology of the multiplicative group scheme on a curve (Notes). Étale Cohomology, FU Berlin, June 29, 2015.
• Category of sheaves on the étale site (Notes). Étale Cohomology, FU Berlin, June 29, 2015.
• Introduction to stacks (Notes, TeX). Rational Sections and Serre's Conjecture, FU Berlin, April 23, 2015.
• Homotopy, contractibility and deformation retractions (Notes). Algebraic Topology II, FU Berlin, February 4, 2015.
• Theorem of the cube (Notes, TeX). Abelian varieties, FU Berlin, May 27, 2014.
• Ruled quartic surfaces (Notes, TeX). Algebraic Geometry Seminar, FU Berlin, January 8, 2014.

Seminars

Upcoming:

Past:

• Brill-Noether theory: geometric, tropical and singularity theory aspects, Berlin, November 5-7, 2019.
• Conference on Varieties, Polyhedra, Computatio, Berlin, October 7-11, 2019.
• Fall school on Varieties, Polyhedra, Computation, Berlin, September 30 - October 4, 2019.
• Non-Archimedean and Tropical Geometry, Regensburg, July 28 - August 2, 2019.
• Periods and motives, Berlin, July 8-12 , 2019.
• Network Games, Tropical Geometry, and Quantum Communication, Berlin, June 3-7, 2019.
• Optimization and Tropical Geometry, TU Berlin, Summer Semester 2019.
• Algebraic curves: enumerative, combinatorial and computational aspects, HU Berlin, Summer Semester 2019.
• Algebraic Geometry and Complex Geometry, CIRM (Marseille), December 17-21, 2018.
• p-adic Hodge Theory, FU Berlin, Winter Semester 2018-19.
• A New Proof of Mordell Conjecture, after Lawrence-Venkatesh, FU Berlin, Winter Semester 2018-19.
• Arithmetic Geometry guest seminar, FU Berlin, 2014-2019.
• Berkovich Spaces: 30 years, Paris, July 9-13, 2018.
• Abhyankar's conjecture, FU Berlin, Summer Semester 2018.
• de Rham epsilon factors \E0 la Beilinson-Bloch-Esnault, FU Berlin, Summer Semester 2018.
• Formal geometry and deformation theory, FU Berlin, Winter Semester 2017-18.
• Period mappings: from complex to p-adic, Tatihou Island, September 24-29, 2017.
• Motives for periods (Notes), FU Berlin, August 28 - September 1, 2017.
• Models of curves and abelian varieties, FU Berlin, Summer Semester 2017.
• p-adic Hodge Theory, FU Berlin, Summer Semester 2017.
• Langlands correspondence for function fields, FU Berlin, Summer Semester 2017.
• p-adic Analytic Geometry and Differential Equations, Luminy, March 27 - 31, 2017.
• Berkovich spaces, singularity theory and birational geometry, FU Berlin, Winter Semester 2016-17.
• Crystalline Cohomology, FU Berlin, Winter Semester 2016-17.
• Seminar of the HBS, Hattingen, January 30 - February 3, 2017.
• Motivic Galois Groups, FU Berlin, Summer Semester 2016.
• D-modules, FU Berlin, Summer Semester 2016.
• Berkovich Spaces, HU Berlin, Summer Semester 2016.
• Algebraization theorems, From GAGA to foliations over number fields (Notes), Tatihou island (Normandy), July 4-8, 2016.
• Day of Algebraic and Arithmetic Geometry, Berlin-Brandenburgische Akademie der Wissenschaften, May 20, 2016.
• Motivic Homotopy Theory, FU Berlin, March 7, 2016.
• Supersingular K3 Surfaces, FU Berlin, Winter Semester 2015-16.
• Intersection Theory, FU Berlin, Winter Semester 2015-16.
• Perfectoid Spaces, Bressanone, August 31-September 4, 2015. Photo.
• AMS Summer Institute in Algebraic Geometry, Salt Lake City, July 12-August 1, 2015.
• Étale Cohomology, FU Berlin, Summer Semester 2015.
• Rational Sections and Serre's Conjecture, FU Berlin, Summer Semester 2015.
• Day of Arithmetic and Algebraic Geometry, Berlin, March 12, 2015.
• Topics in Characteristic p > 0 and p-Adic Geometry, Łukęcin, September 8-12, 2014. Photo.
• VBAC 2014, Berlin, September 1-5, 2014.
• CMI Summer School: Periods and Motives, Madrid, June 30-July 25, 2014.
• Escuela JAE de Matemáticas, Madrid, July 2-27, 2012.
• Escuela JAE de Matemáticas, Madrid, July 4-22, 2011.

Activity

As a webmaster:

• Arithmetic Geometry group at FU Berlin, since December 2016.

As a teaching assistant in HU Berlin:

• Lineare Algebra und Analytische Geometrie II, Summer Semester 2014.
• Lineare Algebra und Analytische Geometrie I, Winter Semester 2013-14.

Organization:

• Seminar of Formal geometry and deformation theory (with Tanya Kaushal Srivastava), Winter Semester 2017-18.
• Seminar of Intersection Theory (with Yun Hao), Winter Semester 2015-16.
• Seminar of Étale Cohomology (with Elena Lavanda), Summer Semester 2015.
• Conferences "Logic and Godel", UCM Madrid. Poster. April 2012
• Conferences "Mathematics and science", UCM Madrid. Poster and videos. May 2011.
• Matgazine, the mathematics magazine of the students (in Spanish). Founded in October 2010, director October 2010-June 2012.

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Last update: 04.2017