Geometry of Shimura varieties in positive characteristic

在之前与我的合作者Naoki Imai（东京大学）和Wushi Goldring（斯德哥尔摩大学）合作的基础上，我们在2022年完成了三份预印本。在这些论文中，我们给出了关于特征p上自同构形式权的一般猜想的实例。我们还证明了Shimura变的上同调的某些消失结果，这是对以前论文结果的改进。我们已经在同行评议的期刊上提交了预印本。我于2022年9月在新雪谷的一次会议上展示了这项研究。我还被邀请参加了志村变量的算术研讨会，在那里我与几位数学家讨论了我的研究，并计划了未来的研究项目。

Building up on previous work with my coauthors Naoki Imai (Tokyo University) and Wushi Goldring (Stockholm University), we completed three preprints in 2022. In those papers, we show instances of a general conjecture regarding the weight of automorphic forms in characteristic p. We also prove certain vanishing results for the cohomology of Shimura varieties, which improves on results from previous papers. We have submitted our preprints in peer-reviewed journals.I presented this research at a conference in Niseko in September 2022. I was also invited to a Oberwokfach workshop on the arithmetic of Shimura varieties, where I discussed my research with several mathematicians, and planned on future research projects.