公开课/COURSE

讨论班/SEMINAR

2022-07-05  

Elementary proofs of Zagier's formula for multiple zeta values and its odd variant

BIMSA-YMSC Tsinghua Number Theory Seminar

报告人 赖力 清华大学

时 间 16:00-17:00 Tue

地 点 1110

Zoom 361 038 6975（PW: BIMSA）

摘要

In 2012, Zagier proved a formula which expresses the multiple zeta values \[ H(a, b)=\zeta(\underbrace{2,2, \ldots, 2}_{a}, 3, \underbrace{2,2, \ldots, 2}_{b}) \] as explicit $\mathbb{Q}$-linear combinations of products $\pi^{2m}\zeta(2n+1)$ with $2m+2n+1=2a+2b+3$. Recently, Murakami proved an odd variant of Zagier's formula for the multiple $t$-values \[ T(a, b)=t(\underbrace{2,2, \ldots, 2}_{a}, 3, \underbrace{2,2, \ldots, 2}_{b}). \] In this talk, we will give new and parallel proofs of these two formulas. Our proofs are elementary in the sense that they only involve the Taylor series of powers of arcsine function and certain trigonometric integrals. Thus, these formulas become more transparent from the view of analysis. This is a joint work with Cezar Lupu and Derek Orr.

组织者：Cezar Lupu

2022-07-07 

The Tadpole Problem

Geometry and Physics Seminar 2022Spring

报告人 Iosif Bena IPhT, Saclay

时 间 16:30-17:30 Thu

地 点 1129B

Zoom 361 038 6975（PW: BIMSA）

摘要

The fluxes that stabilize the complex-structure moduli of string compactifications give rise to a nontrivial D3 charge, which needs to be canceled by other objects in the compactification. I will present arguments that this is impossible when the number of complex-structure moduli is large. This indicates that all String-Theory compactifications on manifolds with a large number of complex-structure moduli have massless scalars and hence are not suited for phenomenology.

组织者：Hossein Yavartanoo