On Zagier-Hoffman's conjectures in positive characteristic

Thời gian: 14:00 đến 15:00 Ngày 02/11/2022

Địa điểm: C102, VIASM

Báo cáo viên: Ngô Đắc Tuấn, Université de Caen Normandie, France

Tóm tắt:

Multiple zeta values (MZV’s) are positive real numbers investigated by Euler in the late eighteenth century. Surprisingly, these numbers are ubiquitous in many mathematical and physical theories such as number theory, mixed Tate motives, and quantum field theory. They were studied by Broadhurst, Brown, Deligne–Goncharov, Goncharov, Hoffman, Ihara-Kaneko–Zagier, Tsumura, Yamamoto, Zagier among others. By a well-known analogy between the arithmetic of number fields and that of function fields of positive characteristic, Thakur introduced a theory of positive characteristic multiple zeta values associated to the projective line in 2004. In this talk, we study Todd-Thakur’s analogues of Zagier-Hoffman’s conjectures in positive characteristic. We first establish the algebraic part of these conjectures which is the analogue of Brown’s theorem and those of Deligne-Goncharov and Terasoma. We then give two results towards the transcendental part of these conjectures.