中科院数学与系统科学研究院
数学研究所
学术报告
表示论研讨班
报告人: 何旭华教授(香港大学)
题 目：Affine Deligne-Lusztig varieties and affine Lusztig varieties I
时 间：2024.06.06（周四）下午14:30--15:30
地 点：N818
摘 要：Roughly speaking, an affine Deligne-Lusztig variety describes the intersection of a given Iwahori double coset with a Frobenius-twisted conjugacy class in the loop group; while an affine Lusztig variety describes the intersection of a given Iwahori double coset with an ordinary conjugacy class in the loop group. The affine Deligne-Lusztig varieties provide a group-theoretic model for the reduction of Shimura varieties and play an important role in the arithmetic geometry and Langlands program. The affine Lusztig varieties encode the information of the orbital integrals of Iwahori-Hecke functions and serve as building blocks for the (conjectural) theory of affine character sheaves. In this talk, I will explain a close relationship between affine Lusztig varieties and affine Deligne-Lusztig varieties, and consequently, provide an explicit nonemptiness pattern, dimension formula and the number of irreducible components for affine Lusztig varieties in most cases. This talk is based on my preprint arXiv:2302.03203, and my joint project in progress with my postdoc Ruben La.
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题 目：Affine Deligne-Lusztig varieties and affine Lusztig varieties II
时 间：2024.06.06（周四）下午15:45--16:45.
地 点：N818
摘 要：Roughly speaking, an affine Deligne-Lusztig variety describes the intersection of a given Iwahori double coset with a Frobenius-twisted conjugacy class in the loop group; while an affine Lusztig variety describes the intersection of a given Iwahori double coset with an ordinary conjugacy class in the loop group. The affine Deligne-Lusztig varieties provide a group-theoretic model for the reduction of Shimura varieties and play an important role in the arithmetic geometry and Langlands program. The affine Lusztig varieties encode the information of the orbital integrals of Iwahori-Hecke functions and serve as building blocks for the (conjectural) theory of affine character sheaves. In this talk, I will explain a close relationship between affine Lusztig varieties and affine Deligne-Lusztig varieties, and consequently, provide an explicit nonemptiness pattern, dimension formula and the number of irreducible components for affine Lusztig varieties in most cases. This talk is based on my preprint arXiv:2302.03203, and my joint project in progress with my postdoc Ruben La.
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