Speakers:  

1. Phạm Ngô Thành Đạt (Institut de Mathématiques de Jussieu-Paris Rive Gauche, CNRS)

2. Nguyễn Minh Đức (Université Paris-Saclay)

3. Đào Quang Đức (University of Science and Technology of Hanoi)

4. Nguyễn Kiều Hiếu (Université de Versailles Saint-Quentin-en-Yvelines)

5. Lê Xuân Hoàng (VNU University of Science)

6. Nguyễn Khánh Hưng (Humboldt-Universität zu Berlin)

7. Nguyễn Quang Khải (Institut Camille Jordan, Université Claude Bernard Lyon 1)

8. Nguyễn Mạnh Linh (Institut de Mathématiques de Jussieu-Paris Rive Gauche, CNRS)

9. Nguyễn Hoàng Long (VNU University of Science)

10. Trương Tuấn Nghĩa (École normale supérieure, PSL)

References:

• Robin Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics 52, Springer New York, NY, 1977.

• Marc Hindry and Joseph H. Silverman, Diophantine Geometry: An Introduction, Graduate Texts in Mathematics 201, Springer New York, NY, 2000.

• James S. Milne, Algebraic number theory, 2020 (available at https://www.jmilne.org/math/CourseNotes/ANT.pdf).

• James S. Milne, Fields and Galois theory, 2022 (available at https://www.jmilne.org/math/CourseNotes/FT.pdf).

• Joseph H. Silverman, The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics 106, Springer New York, NY, 2009.

Program:

1. An introduction to Diophantine geometry by Nguyễn Mạnh Linh (beamer and recording).

2. Heights on projective spaces by Nguyễn Hoàng Long (notes and recording).

3. Height machine à la Weil by Đào Quang Đức (beamer and recording).

4. Abelian varieties and Jacobian by Phạm Ngô Thành Đạt (beamer and recording).

5. Abelian varieties over number fields by Nguyễn Khánh Hưng (notes and recording).

6. Galois cohomology by Trương Tuấn Nghĩa (notes and recording).

7. Integral models and good reduction by Nguyễn Minh Đức (beamer and recording).

8. The Mordell–Weil theorem by Nguyễn Kiều Hiếu (notes and recording).

9. Diophantine approximation by Lê Xuân Hoàng (notes and recording).

10. Roth's theorem and Siegel's theorems by Nguyễn Quang Khải (beamer and recording).

Speakers: 

1. Nguyễn Minh Đức (Université Paris-Saclay)

2. Lê Xuân Hoàng (VNU University of Science)

3. Nguyễn Khánh Hưng (Humboldt-Universität zu Berlin)

4. Nguyễn Mạnh Linh (Institut de Mathématiques de Jussieu-Paris Rive Gauche, CNRS)

5. Nguyễn Hoàng Long (VNU University of Science)

6. Trương Tuấn Nghĩa (École normale supérieure, PSL)

7. Nguyễn Duy Phước (Hue University of Education)

References:

• William Fulton, Algebraic Curves: An Introduction to Algebraic Geometry, electronic version, 2008 (available at https://dept.math.lsa.umich.edu/~wfulton/CurveBook.pdf)

• Robin Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics 52, Springer New York, NY, 1977.

• James S. Milne, Algebraic Number Theory, 2020 (available at https://www.jmilne.org/math/CourseNotes/ANT.pdf).

• Michael Rosen, Number Theory in Function Fields, Graduate Texts in Mathematics 210, Springer New York, NY, 2002.

• Joseph H. Silverman, The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics 106, Springer New York, NY, 2009.

• Joseph H. Silverman, Rational Points on Elliptic Curves, Undergraduate Texts in Mathematics, Springer Cham, 2015.

Program:

1. Algebraic varieties by Nguyễn Duy Phước (notes and recording).

2. Algebraic curves by Trương Tuấn Nghĩa (notes and recording).

3. The Riemann–Roch theorem by Nguyễn Hoàng Long (notes and recording).

4. Elliptic curves by Trương Tuấn Nghĩa (notes and recording).

5. Elliptic curves over ℂ and complex tori by Nguyễn Mạnh Linh (beamer, notes, and recording).

6. Elliptic curves over ℚ and the Mordell–Weil theorem by Lê Xuân Hoàng (notes, complementary notes 1, complementary notes 2, and recording).

7. Number theory over global function fields by Nguyễn Khánh Hưng (notes and recording).

8. The Riemann hypothesis and the ABC conjecture by Nguyễn Minh Đức (beamer and recording).

Speakers: 

1. Nguyễn Minh Đức (Université Paris-Saclay)

2. Nguyễn Mạnh Linh (Insitut de Mathématiques de Jussieu-Paris Rive Gauche, CNRS)

3. Lê Hoàng Long (Laboratoire Analyse, Géométrie et Applications, Université Sorbonne Paris Nord)

4. Trương Tuấn Nghĩa (École normale supérieure, PSL)

5. Đặng Minh Ngọc (École normale supérieure, PSL)

6. Nghiêm Trần Trung (Université Claude Bernard Lyon 1)

References:

• Otto Forster, Lectures on Riemann Surfaces, Graduate Texts in Mathematics 81, Springer New York, NY, 1981.

• Phillip Griffiths and Joseph Harris, Principles of Algebraic Geometry, John Wiley & Sons, Inc., 2014.

• Daniel Huybrechts, Complex Geometry: An introduction, Universitext, Springer Berlin, Heidelberg, 2005.

Program:

1. Introductory talk: Complex analytic geometry according to Griffiths–Harris by Nghiêm Trần Trung (beamer).

2. Local theory: Holomorphic functions of several variables, I by Trương Tuấn Nghĩa (notes).

3. Interlude: Generalities on sheaves by Nguyễn Mạnh Linh (notes and beamer).

4. Local theory: Holomorphic functions of several variables, II by Trương Tuấn Nghĩa (notes).

5. Local theory: Complex and Hermitian structures by Đặng Minh Ngọc (notes).

6. Complex manifolds by Lê Hoàng Long (notes).

7. Sheaf cohomology by Nguyễn Mạnh Linh (notes and beamer).

8. Holomorphic vector bundles by Nguyễn Minh Đức (notes).

9. Divisors and line bundles by Trương Tuấn Nghĩa (notes).

10. Projective spaces and blow-ups by Trương Tuấn Nghĩa (notes).

11. Elliptic curves and one-dimensional complex tori by Nguyễn Mạnh Linh (notes).

12. The Riemann–Roch theorem by Nguyễn Minh Đức (notes).

Speakers: 

1. Hoàng Tuấn Dũng (École normale supérieure, PSL)

2. Ngô Quý Đăng (École normale supérieure, PSL)

3. Nguyễn Minh Đức (Université Paris-Saclay)

4. Nguyễn Mạnh Linh (Insitut de Mathématiques de Jussieu-Paris Rive Gauche, CNRS)

5. Lê Hoàng Long (Laboratoire Analyse, Géométrie et Applications, Université Sorbonne Paris Nord)

6. Trương Tuấn Nghĩa (École normale supérieure, PSL)

7. Đặng Minh Ngọc (École normale supérieure, PSL)

References:

• James E. Humphreys, Introduction to Lie Algebras and Representations Theory, Graduate Texts in Mathematics 9, Springer New York, NY, 1972.

Program:

1. Introductory talk by Nguyễn Mạnh Linh.

2. Definitions and examples by Ngô Quý Đăng.

3. Ideals and homomorphisms by Trương Tuấn Nghĩa.

4. Solvable and nilpotent Lie algebras by Đặng Minh Ngọc.

5. Theorems of Lie and Cartan by Hoàng Tuấn Dũng

6. Killing form by Lê Hoàng Long.

7. Complete reducibility and representations by Nguyễn Minh Đức.

8. Representations of 𝔰𝔩(2,F) by Đặng Minh Ngọc.

9. Root space decomposition by Hoàng Tuấn Dũng.

10. Axioms of root systems by Nguyễn Minh Đức.

11. Simple roots and Weyl group by Trương Tuấn Nghĩa.

12. Classification of irreducible root systems by Ngô Quý Đăng.