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数学学院、所系列学术报告(853场):美国纽约州立大学Albany分校 杨容伟教授

发表于: 2018-12-04 14:03  点击:

时间:2018.12.27 上午10:00-11:00


地点:吉林大学数学学院  数学楼第一报告厅


题目:Projective spectrum and finitely generated groups/

Complex dynamics and the infinite dihedral group


报告人: 杨容伟教授(美国纽约州立大学Albany分校)


摘要: For a tuple $A=(A_1,\ A_2,\ ...,\ A_n)$ of elements in a unital Banach algebra

${\mathcal B}$, its {\em projective joint spectrum} $P(A)$ is the collection of $z\in {\bf C}^n$ such that the multiparameter pencil $A(z)=z_1A_1+z_2A_2+\cdots +z_nA_n$ is not invertible. If ${\mathcal B}$ is the group $C^*$-algebra for a discrete group $G$ generated by $A_1,\ A_2,\ ...,\ A_n$ with respect to a representation $\rho$, then $P(A)$ is an invariant of (weak) equivalence for $\rho$. This series of talks present some recent work on the projective spectrum $P(R)$ of $R=(1,\ a,\ t)$ for the infinite dihedral group $D_{\infty}=<a,\ t\ |\ a^2=t^2=1>$ with respect to the left regular representation. Results include a description of the spectrum, a formula for the Fuglede-Kadison determinant of the pencil $R(z)=z_0+z_1a+z_2t$, the first singular homology group of the joint resolvent set $P^c(R)$, and dynamical properties of the spectrum. These results give new insight into some earlier studies on groups of intermediate growth. Moreover, they suggest a link between projective spectrum and the Julia set of dynamical maps. Time permitting, I will also go over some other aspects of the projective spectrum as related to group theory, topology, complex geometry and Lie algebras.


个人简介:杨容伟教授于19985月获得美国纽约州立大学石溪分校博士学位,1998.9月至2001.7月在美国乔治亚大学攻读博士后,现为美国纽约州立大学奥尔巴尼分校数学统计系教授.研究兴趣主要包括:多元算子理论、泛函分析、多变量复分析、群论、复几何、算子代数等。