My teaching 

1. Commutative rings and Homological algebra (Spring 2018) Main reference: Commutative ring theory, by Hideyuki Matsumura.

2. Applied Functional Analysis (Fall 2018) Main references:    Functional Analysis, by Walter Rudin, and Real and Functional Analysis by Serge Lang

3. Commutative rings and Homological algebra (Spring 2019) Main reference: Commutative ring theory, by Hideyuki Matsumura.

4. Applied Functional Analysis (Fall 2019) .

5. Commutative rings and Homological algebra (Spring 2020) Main reference: Commutative ring theory, by Hideyuki Matsumura.

6. Applied Functional Analysis (Fall 2020).

7. Commutative rings and Homological algebra (Spring 2021).

8. 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. 

9. Elementary Number Theory (Fall 2021): Reference:  An Introduction to the Theory of Numbers Sixth Edition by  Hardy & Wright.

10. Functional Analysis and Partial Differential Equations. Reference:  Numerical analysis and optimization, An introduction to mathematical modeling and numerical simulation by Gregoire Allaire.

11. Applied Functional Analysis (Fall 2021).

12. Commutative rings and Homological algebra (Spring 2022).

13. Numerical Methods for Partial Differential Equations (Spring 2022).

14. 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. 

15. Finite Fields and Cryptography (Spring 2022).

16. Probability and statistics (Fall 2022).

17. Applied Functional Analysis (Fall 2022).

18. Commutative rings and Homological algebra (Spring 2023).

19. Numerical Methods for Partial Differential Equations (Spring 2023).

20. Probability and statistics (Fall 2023).

21. Applied Functional Analysis (Fall 2023).

22. Probability and Statistics (Spring 2024).

23. Mathematical Analysis (exercise sessions) (Spring 2024).

24. Probability and Statistics (Fall 2024).

25. Linear Algebra (Fall 2024).

26. Functional Analysis (Fall 2024).

27. Probability and Statistics (Spring 2025).

28. Linear Algebra (Spring 2025).

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) 

1. Constructible sets and construcible functions. A review of theory of Categories

2. The Quasi-coherent sheaves on the Proj of a  graded ring. 

3. Vector bundles and locally free sheaves. Henselian rings.