A polynomial basis for the stuffle algebra and applications

Time: 9:30 -- 11:00, April 17th, 2024

Venue: Room 612, A6

Abstract: Classical multiple zeta values were introduced and studied by Euler two centuries ago. After a seminal paper of Zagier these objects have been actively studied in various areas of mathematics and physics such as arithmetic geometry, knot invariants, quantum field theory and Witten’s zeta functions. Surprisingly, there are several connections with the well-known shuffle algebra and the stuffle algebra. In this talk, we explore these connections in the characteristic p setting. In particular, we show that the stuffle algebra in characteristic p is a polynomial algebra. As applications, we deduce a formula for the transcendence degree of the algebra generated by multiple zeta values of small weights. This is a joint work with Tuan Ngo Dac and Lan Huong Pham.