2018.7.13-7.19 学术活动预告
2018/7/12 13:51:53 中国科学院数学与系统科学研究院
Speaker:
Dr. Chen Wan, Institute for Advanced Study, Princeton
Title:
The local and global problems for the Ginzburg-Rallis model
Time & Venue:
2018.7.13 14:00-16:00 N109
Abstract:
I will discuss the local multiplicity and the global period integral for the Ginzburg-Rallis model. Locally, by proving a local trace formula for the model, I prove a multiplicity formula for all the tempered representations, which implies that the summation of the multiplicities for the Ginzburg-Rallis model is always equal to 1 over every tempered local Vogan L-packet. Globally, by studying a G_2-period of a Fourier coefficient of an Eisenstein series of E_6, we can show that if the period integral of the Ginzburg-Rallis model is nonzero, then the exterior cube automorphic L-function is nonzero at 1/2. The global result is a joint work with Aaron Pollack and Michal Zydor.
Speaker:
Distinguished Prof. Rostislav Grigorchuk，Texas A & M University
Title:
Interesting example of computation of spectrum of certain group of intermediate growth
Time & Venue:
2018.7.14 10:30-11:30 N913
Abstract:
I will explain computation of the spectrum of the Cayley graph of a group of intermediate growth constructed by me in 1980. It is based on the use of the spectrum of associated Schreier graph and on the computation of a joint spectrum of a pencil of operators associated with a regular representation of infinite dihedral group. A short overview of the problematic of computation of spectra of infinite groups and graphs will be done as well.
报告人简介：Rostislav Grigorchuk教授的主要研究领域为几何群论，群上的随机游走，动力系统等。其最著名的工作是1984年首次构造了具有过渡性增长阶的有限生成群，现在被国际上称为Grigorchuk群。Grigorchuk教授因其杰出学术贡献，于1990年在国际数学家大会上被邀请做45分钟报告。2015年获得美国数学会Steele奖。
Speaker:
Prof. Nakao Hayashi, Department of Mathematics, Graduate School of Science, Osaka University, Japan
Title:
Boundary value problem for nonlinear Schrodinger equations
Time & Venue:
2018.7.16 16:00-17:00 N702
Abstract:
We consider the inhomogeneous Dirichlet-boundary value problem for nonlinear Schrodinger equations with power nonlinearities on the half line. We present sufficient conditions of initial and boundary data which ensure asymptotic behavior of small solutions to the target equations. We improve the time decay condition of the boundary data which was assumed in the previous work.
Speaker:
Prof. Yunping Jiang，The City University of New York and NSF，USA
Title:
Order of Oscillating Sequences, MMA-MMLS, and Sarnak's Conjecture
Time & Venue:
2018.7.17 16:00-17:00 N913
Abstract:
In this talk, I will explain several concepts, a log-uniformly oscillation sequence, an oscillation sequence, an oscillation sequence of higher order, a minimal mean attractable (MMA) dynamical system, a minimal mean-L-stable (MMLS) dynamical system. Equicontinuous dynamical systems are clearly MLS. Feigenbaum dynamical systems are not equicontinuous globally but when they are restricted on minimal sets still equicontinuous. Furthermore, in this talk I will give two non-trivial examples of dynamical systems which are not equicontinuous even when they are restricted on minimal sets but MMLS. We will prove that any oscillating sequence is linearly disjoint with all MMA and MMLS dynamical systems. One of the consequences is that Sarnak’s conjecture holds for all MMA and MMLS dynamical systems. There are dynamical systems which are not MMLS. Therefore, we need to use the concept of an oscillation sequence of higher order. The Mobius sequence is an example of an oscillation sequence of higher order due to a result of Hua. In this talk, I will give another interesting example of an oscillation sequence of higher order. Furthermore, I will prove that any oscillation sequence of order $d\geq 2$ is linearly disjoint with all affine distal maps of the $d$-torus.
来源：中国科学院数学与系统科学研究院
中国科学院数学与系统科学研究院
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