Địa điểm, Thời gian: Viện Toán học, ngày 05 tháng 11 năm 2025

Hình thức tổ chức: Trực tiếp.

Người chủ trì: PGS. TS. Trần Giang Nam.

Cơ quan tổ chức: Viện Toán học (Kết hợp giữa Phòng Đại số và Lý thuyết số và Trung tâm Nghiên cứu và Đào tạo toán học quốc tế).

Time: 9:00 - 10:00, November 05, 2025

Speaker: Prof. Takuro Mochizuki (Research Institute for Mathematical Sciences, Japan)

Venue: Room 612, A6, Institute of Mathematics-VAST

Title: Algebraic integrable connections with bounded irregularity

Abstract: According to the higher dimensional non-abelian Hodge theory, any algebraic vector bundle with an integrable connection on a quasi-projective complex variety underlies a wild harmonic bundle. In particular, an algebraic Lagrangian cover is attached to an integrable connection. It is useful to understand the irregularity of the integrable connection. In this talk, we shall discuss an application to the study of boundedness of the family of algebraic integrable connections with bounded irregularity.

Tea break: 10:00 - 10:30

Time: 10:30 - 11:30, November 05, 2025

Speaker: Prof. Christophe Ritzenthaler (Executive Director of CIMPA)

Venue: Room 612, A6, Institute of Mathematics-VAST

Title: Primes of bad reduction of certain genus 2 curves

Abstract: Given a curve over a number field, characterised by certain arithmetic conditions, it is a classical game to understand its reductions modulo a prime, even without explicitly knowing an equation for this curve. This has been done for complex multiplication (CM) curves of genus 1 and 2.
Here we study genus 2 curves whose Jacobian is the square of a CM elliptic curve. We will use the refined Humbert invariant introduced by Kani to bound and enumerate primes of bad reduction, then more sophisticated results from Kudla and Rapoport to control the exponents. Some related results on oriented supersingular curves or on the relations between invariants and modular forms may be discussed if time permits, but we will mainly try to highlight the many open questions that remain around this problem.