SEAMS school “Arithmetic, Geometry and Model Theory”

Institute of Mathematics (VAST), Hanoi Vietnam

17 – 28 February 2020

**Description**

Recent years have seen a flourishing interaction between model theory, arithmetic geometry and number theory. The IHM-SEAMS school aims to familiarize advanced undergraduate students, graduate students and young researchers to basic concepts and techniques of model theory and main notions of algebraic geometry and number theory. This school will be an activity aiming to boost the interaction and collaboration between Asian and European researchers in mathematics. **Program**

The school is two week long from 17 February to 28 February 2020, with free Wednesday afternoons. There are three mini-courses, each consists of 6 x 120-minute lectures. There will be at least one tutorial session every day (11h00-12h00 and / or 16h00-17h00). Though the audience is expected to have a basic mathematical background, knowledge of technical terminology is not assumed.

**Introduction to Model Theory**given by Pablo Cubides Kovacsics (TU Dresden) and Le Quy Thuong (VNU Hanoi).

The aim of this course is to introduce the students to the basics of model theory with a particular emphasis towards potential algebraic and arithmetic applications. In particular, o-minimality will be defined and some of its main properties will be discussed.**Introduction to Algebraic Curves**given by Nguyen Chu Gia Vuong and Ha Minh Lam (IMH Hanoi).

Algebraic geometry is a highly developed field in mathematics. The aim of this course is to give an introduction to algebraic geometry via algebraic curves. We will introduce basic notions and theorems of algebraic geometry, especially those related to curves: affine varieties, projective varieties, affine plane curves, projective plane curves, local invariants, intersection numbers, Bezout’s theorem, Noether’s theorem, divisors and Riemann-Roch theorem. Note that, the materials covered here are closely related to Angles’ course. The students are supposed to have some background on commutative algebra: rings, algebras, ideals, Hilbert basis theorem, modules.**Introduction to Algebraic Number Theory**given by Bruno Angles (Univ. Caen) and Ta Thi Hoai An (IMH Hanoi).

This course introduces the student to the main arithmetic objects of algebraic number theory: zeta values and ideal class groups. We will introduce basic notions of algebraic number theory: ring of integers, ideal class groups and ramification and study them in the case of quadratic fields and cyclotomic fields. Then we will present the basic properties of L-series attached to Dirichlet characters and see how the values at negatives integers of such Dirichlet L-series are connected to Bernoulli numbers. Finally, we introduce the basic properties of Gauss and Jacobi sums and prove the Stickelberger Theorem and the celebrated Herbrand-Ribet’s Theorem.

Website: http://math.ac.vn/conference/seams2020

**Registration**

- There are no registration fees and no additional fees.
- If you are interested in participating in the school, please register online here

The deadline for registration is 15 January 2020. However, the deadline for the financial support is December 31.

**Financial support**

- We can cover local expenses for selected participants.
- Travel support for up to 12 students from Asean and neighboring countries and 10 domestic students is available
- If you apply for travel support, please fill out the corresponding section carefully.

**The application should include**

- a copy of the academic transcript;
- a recommendation letter.

**Contact**: