Jantzen filtrations: AI-Assisted Mathematical Research Seminar Series

报告人：Dan Ciubotaru（英国牛津大学）

时  间：2026年9月16日14:00

地  点：Zoom ID: 841 3254 9527 (Password: 20260916)

内容摘要:

The Jantzen conjecture is a refinement of the Kazhdan-Lusztig conjectures describing the multiplicity of composition factors into the standard modules. In the classical setting of category O and in the category of (g,K)-modules of real reductive groups, the Jantzen conjecture was proved by Beilinson and Bernstein in 1993. My own interest in this result comes from the applications to the computation of signatures of invariant hermitian forms, as pioneered by Vogan. For p-adic groups, or in the equivalent setting of affine Hecke algebras, not a lot was known outside type A. Over this summer, I got AI (Chat GPT) to produce a proof for graded affine Hecke algebras with equal parameters. In this talk, I will explain the main ideas of the proof and talk about my journey in using AI for this project.

个人简介：

Dan Ciubotaru is Professor of Mathematics at the University of Oxford and the Diana Brown Fellow and Tutor in Pure Mathematics at Somerville College. He received his PhD from Cornell University in 2004 and held positions at MIT and the University of Utah before joining Oxford in 2014. His research focuses on the representation theory of reductive groups and affine Hecke algebras, with particular interests in unitary representations, the local Langlands correspondence, and Dirac operators in representation theory. His work has appeared in prestigious journals, including Ann. of Math., Acta Math., Invent. Math., Duke Math. J., and J. Eur. Math. Soc.

联系人：马家骏