Abstract: 

I'll describe some concrete questions of linear algebra arising from the dynamics of mapping class group actions on character varieties. Variants of these questions go back to work of Painlevé, Fuchs, Gambier, and Schlesinger at the beginning of the 20th century, but their (partial) answers depend on modern techniques from algebraic and arithmetic geometry. I'll describe how this work resolves (arithmetic) conjectures of Esnault-Kerz, Budur-Wang, Kisin, and Whang, and makes progress towards a (topological) conjecture of Putman-Wieland. Everything is joint with Aaron Landesman.

Speaker:

Daniel Litt is an Assistant Professor of mathematics at the University of Toronto. He was in a similar position at the University of Georgia from 2019-2022. He completed his PhD at Stanford in 2015; from 2015-2018 he was an NSF Postdoc at Columbia; and from 2018-2019 he was a member at the Institute for Advanced Study. Broadly speaking, he is interested in the interplay between algebraic geometry and number theory (and, to a lesser extent, topology).

Video: http://archive.ymsc.tsinghua.edu.cn/pacm_lecture?html=Canonical_tuples_of_matrices.html