Université Grenoble Alpes

CS 40700

38058 Grenoble cedex 09

OFFICE 307

E-mail :

Algebraic Geometry

Presentation

I defended my thesis in September 2017. I am currently a teaching assistant at Grenoble Alpes University.

Ph.D.

Title

Picard Group of unipotent groups over a field

Ph.D. advisor

Date of defence

25 September 2017

Let k be any field. We study the Picard group of the (smooth connected) unipotent k-algebraic groups.

As every unipotent algebraic group is an iterated extension of forms of the additive group, we will study the Picard group of the forms of the additive group. In fact we study the Picard group of forms of the additive group and the affine line simultaneously using a geometric method. We obtain an explicit upper bound on the torsion of the Picard group of the forms of the affine line and their regular completion, and a sufficient condition for the Picard group of a form of the affine line to be nontrivial. We also give examples of nontrivial forms of the affine line with trivial Picard groups.

In general, a unipotent k-algebraic group is a form of the affine n-space. In order to study the Picard group of a form X of the affine n-space with a geometric method, we define a "restricted" Picard functor; we show that if X admits a regular completion then the "restricted" Picard functor is representable by a unipotent k-algebraic group (smooth, not necessarily connected). With this "restricted" Picard functor and geometric arguments we show that the Picard group of a unirational form of the affine n-space is finite. Moreover we generalise a result of B. Totaro: if k is separably closed and if the Picard group of a unipotent k-algebraic group is nontrivial then it admits a nontrivial extension by the multiplicative group.

Documents

Ph. D.

Picard Group of unipotent groups over a field (in French)

Publications

Picard group of the forms of the affine line and of the additive group,
Journal of Pure and Applied Algebra Volume 221, Issue 11, November 2017, Pages 2838-2860 (Science Direct link).

Other

My dissertation with Bertrand RÉMY on unipotents algebraic groups (in French).

My CV in pdf.

Notes of a lecture by Guido Pezzini entitled "Geometry and combinatorics of spherical varieties".

My CV in pdf.

Notes of a lecture by Guido Pezzini entitled "Geometry and combinatorics of spherical varieties".

Oral presentations

2017

Newcastle University, Workshop on pseudo-reductive groups and related topics.

Rennes University, seminar algebra and geometry.

Lille University, seminar algebraic geometry.

Bourgogne University, "Mini-Workshop Algebraic Geometry".

ESI Vienne, Winter school "Geometry and Representation Theory" (5min presentation).

2016

Institut Fourier, seminar algebra and geometry.

ENS, seminar rational varieties.

Conferences

2017

Workshop on pseudo-reductive groups and related topics, Newcastle-Upon-Tyne.

Workshop Algebraic Groups, Oberwolfach.

2016

Colloque tournant du GDR TLAG, Montpellier.

Colloque Inter’Actions, Lyon.

2015

Colloque Inter’Actions, Grenoble.

Summer School Reductive Groups, Schloß Schney.

2014

Colloque Inter’Actions, Lyon.

Formation

2017-now

Teaching Assistant at Grenoble Alpes university.

2014-2017

Ph.D. at the Fourier Institute under the supervision of Michel Brion.

2010-2014

Studies in mathematics at E.N.S. Lyon, speciality in algebraic geometry and number theory.

Research stages: unipotent algebraic with Bertrand RÉMY (2014), Algebraic number theory with Vincent PILLONI (2012), and L-function with Pierre CHAROLLOIS (2011).

“Agrégation” of mathematics with rank 56 (competitive exam for teaching, 2013).

Research stages: unipotent algebraic with Bertrand RÉMY (2014), Algebraic number theory with Vincent PILLONI (2012), and L-function with Pierre CHAROLLOIS (2011).

“Agrégation” of mathematics with rank 56 (competitive exam for teaching, 2013).

2017-2010

Preparatory classes (competitive school) at "Lycée Joffre", Montpellier.

Teaching and Popularisation.

2017

Lecture Mat102, Mathematics for Science and Engineering at Grenoble Alpes university.

2016

Lecture Mat103, mathematics for biology at Grenoble Alpes university.

Lecture Mat307, Parametric curves and differential equations for physics at Grenoble Alpes university.

2015

Lecture Mat11a, mathematics for biology at Joseph-Fourier university.

Popularisation of mathematics at high school "Stendhal", Grenoble (France) via math à modeler.

2014

Lecture Mat11a, mathematics for biology at Joseph-Fourier university.

2011-2012

Oral exam in mathematics at the competitive school "Jean Perrin", Lyon (France).

2010

Tutoring for students with academic difficulty at high school "Robert Doisneau" in Lyon (France) via the association trait d'union.

Other

Computer science

Latex, OCaml, Giac/Xcas, Maple, HTML, Magma, Singular.

Languages

French (mother language), English (TOEIC 955), Spanish (beginner), Chinese (beginner)

Links

chaos, a popularisation movies on chaos theory and dynamical systems.

dimension, a popularisation movies on geometry and dimensions.

image de math, a website for popularisation of mathematics (in French).

dimension, a popularisation movies on geometry and dimensions.

image de math, a website for popularisation of mathematics (in French).