Tianyuan Representation Theory Seminar- Counting points on Newton strata and a multiplicity-one phenomenon

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:2022-06-24 15:00


时  间:624日下午15:00

地  点:腾讯会议ID436-5742-3564(无密码)


Affine Deligne-Lusztig varieties play an important role in the theory of Shimura varieties. Their geometries are controlled by the Newton strata in Iwahori double cosets. In this talk, I will report a multiplicity-one phenomenon on the Newton strata of a large class of Iwahori double cosets, namely, these strata form a stratification and each of them is nonempty and irreducible. We prove it by counting rational points on the Newton strata. As a consequence, we show the corresponding affine Deligne-Lusztig varieties are explicit unions of classical Deligne-Lusztig varieties of Coxeter type. This is based on joint work in progress with X. He and Q. Yu.


聂思安,中国科学院数学与系统科学研究院副研究员。20126月在中国科学院数学与系统科学研究院获得博士学位。2012-2015年先后在法国高等科学研究所(IHES),德国 Max Planck数学研究所,瑞典Mittag-Leffler研究所做博士后。主要研究领域为代数群、仿射Hecke代数及其表示理论;仿射 Deligne-Lusztig簇的几何及其在算数几何中的应用。研究成果发表在《Duke Math. J.》《Ann. Sci. Éc. Norm. Supér.》、《Math.Ann.》、《Compos.Math.》、《Adv. Math.》、《Selecta Math.》、《Represent. Theory》等国际学术期刊。