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数学前沿群论及泛函分析会议
中国 • 天津市 2018年07月15日－2018年07月17日
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主题报告
报告题目：
Some aspects of projective spectrum
报告摘要：
Projective spectrum is a relatively new notion of joint spectrum for several elements A_1, A_2, ..., A_n in a unital Banach algebra. It is defined as the set of complex numbers z_1, z_2, ..., z_n such that the linear combination A(z)=z_1A_1+z_2A_2+...z_nA_n is not invertible. In these two talks I will present some examples and theories centered around projective spectrum. A most notable case is when A_1, A_2, ..., A_n are generators of a group C^*algebra, in which projective spectrum reveals much information about the group and its representations. Some connections with topology and complex geometry will also be described.
报告人：
Rongwei Yang
报告人单位：
The State University of New York Albany, NY, USA
个人介绍：
https://www.researchgate.net/profile/Rongwei_Yang3
报告题目：
Groups of intermediate growth and around
报告摘要：
In two lectures I will give a short account of the notion of growth in group theory and more generally in algebra. After a quick discussion of the cases of polynomial growth and exponential growth (which will include the famous theorem of M. Gromov on structure of groups of polynomial growth) I will focus on groups of intermediate (between polynomial and exponential) growth. Such groups respond to the Problem of J. Milnor formulated in 1968 and to some other problems formulated by various mathematicians that were solved in the last three decades. Among applications of groups of intermediate growth I will explain how they lead to the solution of M. Day problem on non elementary amenability. Also applications to geometry, random walks, spectral theory of groups and graphs will be demonstrated. It will also be discussed the following cases: selfsimilar groups, automaton groups, fractal groups and branch groups as they constitutes the main base for the construction of groups of intermediate growth. These groups have interesting algebraic, algorithmic and dynamical properties, some of which will be mentioned as well. The talks are selfcontained.
报告人：
Rostislav Grigorchuk
报告人单位：
Texas A&M University
职务：
Distinguished Professor
个人介绍：
https://en.wikipedia.org/wiki/Rostislav_Grigorchuk
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