Learning seminar on multiple zeta values

报告人 Speaker:余成龙
组织者 Organizer:Cezar Lupu, 赖力,余成龙,郑志伟
时间 Time:Fri 1:30-3:30pm,2022-3-18
地点 Venue:Ning Zhai W11

Upcoming Talks

Seminar 6      

Title: Picard-Fuchs equations and Frobenius constants      

Speaker: 余成龙

Time: 1:30pm-3:00pm,  2022-3-18

Place: 宁斋 Ningzhai W11

Abstract: I will continue the topic last time and introduce Frobenius constants associated to an ODE. The main reference is Bloch and Vlasenko’s paper “Gamma functions, monodromy and Frobenius constants”.

Past Talks

Seminar 5

Title: Picard-Fuchs equations related to irrationality of zeta values
     Time: 1:30pm-3:00pm,2022-3-11
     Place: 宁斋 Ningzhai W11
     Abstract: In this talk, I will discuss the geometric constructions and Picard-Fuchs equations related to Apéry's proof for irrationality of zeta(2) and zeta(3).

Seminar 4: Linear forms in Riemann zeta values and MZVs
       Speaker: Li Lai
       Time: January 7th, 2022, Friday 13:30-15:00
       Location: Ning Zhai W11
This talk consists of three parts. First, we breifly introduce Siegel's and Nesterenko's linear independence criteria. Then, we explore their applications to the irrationality of Riemann zeta values (I will explain key ideas of the Ball-Rivoal theorem and go a little beyond that). Finally, we discuss the possibility and difficulty of generalizing the irrationality results from Riemann zeta values to MZVs.

Seminar 3:Multiple zeta values. Basic properties and identities II.

Speaker:Cezar Lupu


Abstract:In this third talk, we explore more the integral representation of Kontsevich of MZV's. Also, using this integral representation we immediately derive Drinfeld's duality as well as other evaluations of families of MZV's. Moreover, we introduce some special functions such as multiple polylogarithms or Gauss hypergeometric and using generating functions we prove identities for multiple zeta values such as Hoffman-Zagier and Broadhurst-Zagier theorems. Briefly, we discuss the notion of period in the sense of Kontsevich and Zagier and some examples.

Seminar 2:Multiple zeta values. Basic properties and identities.

Speaker:Cezar Lupu


Join Zoom Meeting:https://zoom.us/j/93596239802?pwd=cVdCWS8xU0NSRy9IaWNxUDN6Skt2Zz09

Meeting ID:935 9623 9802


Abstract:In this second talk, we explore more the linear relations among multiple zeta values and we study a little bit more the $\mathbb{Q}$-vector space of multiple zeta values of a given weight. Also, using generating functions and properties of special functions, we prove some well-known identities for MZV's in the literature.

Seminar 1:An introduction to the Riemann and multiple zeta functions and their special values.

Speaker:Cezar Lupu, Yanqi Lake BIMSA


Abstract:In this first talk, we introduce the multiple zeta functions and their values. We explore the basic properties such as convergence, analytic continuation, their relations and some special values. This talk is also suitable for graduate students and advanced undergraduate students.