Research Paul Kiefer

Abstract

In the proposed project, we study special cycles on locally symmetric spaces of orthogonal type. Locally symmetric spaces are interesting highly symmetric manifolds. Remarkably, in many cases, they are quasi-projective varieties and even possess a moduli interpretation. Special cycles are submanifolds of these spaces and their study is important for the understanding of the arithmetic and geometric properties of locally symmetric spaces. An important tool in this area is the Kudla-Millson theta form and its generalization by Funke-Millson, whose study is part of the Kudla program. In this proposal, we will mainly use the Funke-Millson theta form to study locally symmetric spaces. We will investigate the modular properties of the generating series of degrees of special cycles and of cycle integrals of meromorphic differential forms. Furthermore, we will construct p-adic families of geometric theta functions to improve our understanding of the emerging p-adic Kudla program. Lastly, we will study the cohomology of locally symmetric spaces of orthogonal type using the Kudla-Millson and Funke-Millson lift. As an important milestone, we aim to generalize the injectivity results of the Funke-Millson lift in low genus to arbitrary genus, to obtain dimension formulas for the cohomology of locally symmetric spaces.

Researcher(s)

• Promoter: Barros Ignacio
• Fellow: Kiefer Paul

Research team(s)

• Fundamental Mathematics01/10/2026 - 30/09/2029

Funding

• FWO

Project type(s)

• Research Project