Wavefront Set and the Generic L-packet

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:2022-10-27 15:00


时  间:1027日下午15:00

地  点:腾讯会议ID587-154-242(无密码)


Fourier coefficients of automorphic forms have many applications in number theory such as counting the number of representations of a natural number as the sum of squares. Guided by the local-global principle, a necessary nonvanishing condition of such Fourier coefficients is determined by the wavefront set of the representations over local fields. In this talk, we use the  local Gan-Gross-Prasad conjecture and consecutive local descent theory to introduce a new invariant associated to the irreducible representations in the generic L-packets, so called arithmetic wavefront sets. And we conjecture that the arithmetic wavefront sets coincide the classical wavefront sets defined by the Harish-Chandra characters. This is a joint work with Dihua Jiang and Dongwen Liu.


张磊,新加坡国立大学数学系副教授。2005年本科毕业于北京大学,2011年博士毕业于明尼苏达大学,2014年入职新加坡国立大学。研究方向是数论和表示理论,主要包括Langlangs 纲领、自守形式、L-函数、拓扑群的表示等。相关文章发表在 Ann. of Math., Amer. J. Math., J.Eur.Math.Soc., Geom.Funct.Anal.,等杂志上。