Seminars on the theory of multiple zeta values
Time: 2023-05-19
Published By: Yiyi Ye
Speaker(s): Jiangtao Li(Central South University)
Time: May 22 - June 1, 2023
Venue: Room 82J12
Abstract:
1.Multiple zeta values, double shuffle relations and other related relations
In this seminar, we will give the definition of multiple zeta values. We will show that multiple zeta values satisfy (regularized) double shuffle relations. Moreover, we will give the definition of Grothendieck-Teichmuller group and exlpain its deep connection with the theory of multiple zeta values. The references are:[1] H. Furusho, Double shuffle relation for associators, Annals of Mathematics, Vol. 174 (2011), No. 1, 341-360.
[2] K. Ihara, M. Kaneko, D. Zagier, Derivation and double shuffle relations for multiple zeta values, Compos. Math., (142), 2006, 307-338.
2.Mixed Tate motives and cyclotomic multiple zeta values
In this seminar, based on the theory of mixed motives, we will give the construct of mixed Tate motives over number fields and algebraic integer rings. We will explain the results of Deligne about the structure of motivic Lie algebra in cyclotomic case. Lastly, we will explain Brown’s results about mixed Tate motives over integers and show the application of mixed Tate motives to the theory of cyclotomic multiple zeta values. The references are:
[3] F. Brown, Mixed Tate motives over $\mathbb{Z}$, Ann. of Math., 175(2) (2012), 949-976.
[4] J. Burgos Gil, J. Fresán, Multiple zeta values: from numbers to motives, Clay Math. Proceedings, to appear.
[5] P.Deligne, Le groupe fondamental de la droite projective moins trois points, in: Galois groups over Q, Springer, MSRI publications 16 (1989), 72-297; “Periods for the fundamental group,” Arizona Winter School 2002.
[6] P. Deligne, Le groupe fondamental unipotent motivique de
$\mathbb{G}_{m}-\mu_{N}$, pour $N=2,3,4,6$ ou $8$, Publications Mathématiques de l'IHÉS, 112(1) (2010), 101-141.
3. The Grothendieck-Teichmuller group and motivic Galois group of level two
Recently, Minoru Hirose proved that the Grothendieck-Teichmuller group for level $N=2$ and the motivic Galois group over $\mathbb{Z}[1/2]$ is equal. In this seminar we will explain the idea of Hirose’s proof. The reference is:
[7] M. Hirose, The cyclotomic Grothendieck-Teichmuller group and the motivic Galois group, arXiv: 2301. 04064.
4. Unit cyclotiomic multiple zeta values
Recently, inspired by Zhao’s conjecture about unit cyclotomic multiple zeta values. The author showed that the cyclotomic multiple zeta values are generated by unit cyclotomic multiple zeta values for $N=2,3,4$. Furthermore, the author calculated the motivic Galois actions for the unit cyclotomic multiple zeta values. As an application, the explicit relations among unit cyclotomic multiple zeta values are given in substantial cases. The reference is:
[8] J. Li, Unit cyclotomic multiple zeta values for $\mu_2,\mu_3$ and $\mu_4$, arXiv: 2007.00173v2.
Time:
5/22 10:00-11:30
5/23 13:00-14:30
5/30 13:00-14:30
6/1 10:00-11:30
