Academic at the Department of Mathematics of the Universidad Técnica Federico Santa María, Valparaíso, Chile.

Beijing

Research

I am mainly interested in birational geometry. More precisely, in asymptotic invariants and positivity in algebraic geometry (such as Newton-Okounkov bodies) and the use of techniques from the Minimal Model Program to the classification of algebraic varieties (e.g. Fano varieties). I am also interested in algebraic group actions on algebraic varieties.

(Pre)publications

Here you can find my research articles.

"On singular Fano varieties with a divisor of Picard number one" (arXiv:1605.08307)
Annali della Scuola Normale Superiore di Pisa (5), XIX (2), pages 567–600, 2019.
DOI: 10.2422/2036-2145.201609_018.
"Newton-Okounkov bodies on projective bundles over curves" (arXiv:1703.06828)
Mathematische Zeitschrift, 291 (3–4), pages 1357–1379, 2019.
DOI: 10.1007/s00209-018-2173-3.
"Fano threefolds as equivariant compactifications of the vector group" (arXiv:1802.08090)
Joint with Zhizhong Huang at Hannover.
To appear in Michigan Mathematical Journal.
"A characterization of some Fano 4-folds through conic fibrations" (arXiv:1803.09129)
Joint with Eleonora Anna Romano at Warsaw.
To appear in International Mathematics Research Notices.
"Equivariant compactifications of vector groups with high index" (arXiv:1806.02010)
Joint with Baohua Fu at Beijing.
Comptes Rendus Mathématique, 357 (5), pages 455–461, 2019.
DOI: 10.1016/j.crma.2019.05.002.

About me

A brief CV

Born on February 28th, 1991 in Copiapó (Chile)

Since December 2018 : Academic (Profesor Instructor) at the Department of Mathematics of the Universidad Técnica Federico Santa María, Valparaíso, Chile.
2018 : Postdoctoral Researcher at AMSS in the Chinese Academy of Sciences, Beijing.
2017 : ATER at Université Grenoble Alpes, Grenoble.
2014-2017 : Université Grenoble Alpes, Grenoble, PhD in Mathematics.
2013-2014 : Université Joseph Fourier, Grenoble, Master 2 Research in Mathematics.
2011-2013 : Universidad Técnica Federico Santa María, Valparaíso, Master in Mathematics.
2009-2011 : Universidad Técnica Federico Santa María, Valparaíso, Undergraduate degree in Mathematics.
2008 : Colegio Salesiano Valparaíso, Valparaíso, scientific formation.

Theses in mathematics

  • PhD thesis: « Geometry of singular Fano varieties and projective bundles over curves » .
    Advisors : Stéphane Druel and Catriona Maclean. Institut Fourier, Grenoble.
    Thesis defence : october 2017.

    • Master 2 thesis: « Rationnally connected varieties and their behavoir in family » .
      Advisor : Catriona Maclean. Institut Fourier, Grenoble.
      Thesis defence : june 2014.

    • Master thesis: « On the automorphism group of complete intersections of type (2,3) ».
      Advisor : Víctor González-Aguilera. Universidad Técnica Federico Santa María, Valparaíso.
      Thesis defence : july 2013.

    • Undergraduate thesis: « Complex algebraic surfaces of type K3 ».
      Advisor : Víctor González-Aguilera. Universidad Técnica Federico Santa María, Valparaíso.
      Thesis defence : july 2011.

    My recent activities

    Here is a list of some of my recent activities.

    Working groups

    This year, Gonzalo Manzano (USACH) and I, we organize a reading group on algebraic geometry. During the semester 2019-1 we will discuss the basics on algebraic geometry and we will follow the lecture notes of Joseph Le Potier. For further information, click here (in spanish).

    I organized, along with Louis-Clément, our own working group for PhD students. The goal was to read a book together and give a talk each week. Every year we worked on a quite large topic around complex algebraic geometry.

    Recent talks

    • Brazil-Chile-Mexico 4th meeting on singularities, Universidad de Talca, Talca, Chile. March 2019.
    • LXXXVII Encuentro Anual de la Sociedad Matemática de Chile, Universidad de O’Higgins, Rancagua, Chile. December 2018.
    • Algebraic Geometry Seminar, Pontificia Universidad Católica de Chile, Santiago, Chile. August 2018.
    • Seminar on Arithmetic and Geometry, Valparaiso, Chile. August 2018.
    • Geometry Seminar, Universidad de la Frontera, Temuco, Chile. August 2018.
    • Workshop on Algebraic Geometry, Morningside Center of Mathematics, Beijing, China. June 2018.

    Recent conferences attended

    • (upcoming) «Brazil-Chile-Mexico 4th meeting on singularities » . Universidad de Talca, Talca, Chile. March 2019.
    • «LXXXVII Encuentro Anual de la Sociedad Matemática de Chile » . Universidad de O'Higgins, Rancagua, Chile. December 2018.
    • «Workshop for Birational Geometry and Related Topics » . Fudan University, Shanghai, China. November 2018.
    • «Varieties and Group Actions » . Polish Academy of Sciences, Warsaw, Polando. September 2018.

Contact

E-mail : pedro [dot] montero [at] usm [dot] cl
Phone : (+56) 32 2654640
Office F247

Departamento de Matemática
Universidad Técnica Federico Santa María
Avenida España 1680, Valparaíso, Chile


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