Lecture notes and teaching

My teaching

Commutative rings and Homological algebra (Spring 2018) Main reference: Commutative ring theory, by Hideyuki Matsumura.
Applied Functional Analysis (Fall 2018) Main references: Functional Analysis, by Walter Rudin, and Real and Functional Analysis by Serge Lang
Commutative rings and Homological algebra (Spring 2019) Main reference: Commutative ring theory, by Hideyuki Matsumura.
Applied Functional Analysis (Fall 2019) .
Commutative rings and Homological algebra (Spring 2020) Main reference: Commutative ring theory, by Hideyuki Matsumura.
Applied Functional Analysis (Fall 2020).
Commutative rings and Homological algebra (Spring 2021).
Stochastic Methods (Spring 2021) : References: Stochastic Calculus And Financial Applications by Steele; Brownian Motion And Stochastic Calculus by Karatzas-Shreve (Springer). Lecture notes : Calcul Stochastique by. C. Breton.
Elementary Number Theory (Fall 2021): Reference: An Introduction to the Theory of Numbers Sixth Edition by Hardy & Wright.
Functional Analysis and Partial Differential Equations. Reference: Numerical analysis and optimization, An introduction to mathematical modeling and numerical simulation by Gregoire Allaire.
Applied Functional Analysis (Fall 2021).
Commutative rings and Homological algebra (Spring 2022).
Numerical Methods for Partial Differential Equations (Spring 2022).
Stochastic Methods (Spring 2022). References: Stochastic Calculus And Financial Applications by Steele; Brownian Motion And Stochastic Calculus by Karatzas-Shreve. Lecture notes : Calcul Stochastique by. C. Breton.
Finite Fields and Cryptography (Spring 2022).
Probability and statistics (Fall 2022).
Applied Functional Analysis (Fall 2022).
Commutative rings and Homological algebra (Spring 2023).
Numerical Methods for Partial Differential Equations (Spring 2023).
Probability and statistics (Fall 2023).
Applied Functional Analysis (Fall 2023).

Notes on Diophantine Geometry and transcendental numbers

1. Lindemann-Weierstarss theorem and the transcendence of $\pi$.
2. Heights

Introduction to the Minimal Model Program (Mori's program): My notes written in 2007, updated in 2022.

Notes on Minimal Model Program

Lectures on Algebraic Geometry and Introduction to Etale cohomology: every Thursday from 14:00 to 16:00 room 536.

(References: EGA 1 and 2, and SGA4, A. Grothendieck (IHES))

- An overview of the theory of (additive/abelian/..) categories (Sur quelques points d'Algebre Homologique, A. Grothendieck. Tohoku).
- Derived functors (Tohoku)
  - Presheaves and sheaves with values in a category. Direct and inverse image (EGA1).
- Ringed spaces (EGA1).
- Quasi-coherent and coherent sheaves (EGA1).
- Affine schemes, schemes (EGA1).
- Affine morphisms and Vector bundles (EGA2).
- Projective schemes.
- Grothendieck topologies-1.

Lectures on Algebraic Geometry (Fall 2019) (Monday 15:00-17:00 Room 437)

Constructible sets and construcible functions. A review of theory of Categories
The Quasi-coherent sheaves on the Proj of a graded ring.
Vector bundles and locally free sheaves. Henselian rings.