Hopf algebras and multiple zeta values in positive characteristic

Multiple zeta values (MZVs) were first considered by L. Euler and have since been studied in various mathematical contexts. The Hopf algebra of classical MZVs was introduced by M. E. Hoffman in the late 1990s, which provides a powerful framework for the study of these special numbers. In the function field setting, D. S. Thakur introduced an analogue of MZVs, which raises the natural question of whether a Hopf algebra structure exists for MZVs in this context. Working on this question, S. Shi proposed several conjectures for the Hopf algebra of MZVs in the function field setting in her Ph.D. thesis (2018). This talk will provide an introduction to Hopf algebras, discuss the Hoffman algebra of classical MZVs, and present our recent results towards Shi's conjectures. This is a joint work with B.-H. Im, H. Kim, T. Ngo Dac, and L. H. Pham.