Pedro Ángel Castillejo 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. ## ContactMail: castillejo@zedat.fu-berlin.de ## Articles- (PhD thesis)
*The topology of conjugate Berkovich spaces*(English). 2020. - (Master thesis)
*The Grothendieck-Ogg-Shafarevich formula for*(English. Pdf, TeX). 2016.*l*-adic sheaves - (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.(Notes of first, second, third and fourth lecture). Mini course (8 hours), FU Berlin, April 14-15, 2016.*l*-adic sheaves and the Grothendieck-Ogg-Shafarevich formula*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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