On Zagier-Hoffman's conjectures in positive characteristic

The aim of the talk is to introduce multiple zeta values (MZV's) and discuss our recent result for the Zagier-Hoffman's conjectures in positive characteristic. This is a joint work with Bo-Hae Im, Hojin Kim, Lan Huong Pham and Tuan Ngo Dac. We shall focus on the algebraic part of the conjecture and give some ideas for the transcendental part. If time permits, we shall introduce some variants of MZV's in positive characteristic.