Aitor Iribar López (ETH Zürich)
Simplified Kudla-Millson construction abstract
Abstract:
In their celebrated work 30 years ago, Kudla and Millson constructed modular forms with values in the cohomology of locally symmetric spaces. For spaces that parametrize variations of Hodge structures of weight 2, a connection with work of Mathai and Quillen on superconnections was done by Garcia 10 years ago. A more careful examination of the work shows that the definition is in fact very simple. This simple formula allows us, in work with Garcia and Greer, to show modularity of Noether-Lefschetz cycles on $\\mathcal A_g$. In the talk, I will review the main ideas behind the proof of modularity of special cycles using Mathai-Quillen forms with an emphasis on the case of K3 surfaces. This will serve as a preparation for the next talk, where the proof with Garcia and Greer will be discussed.
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43