Commensurabilities Among Lattices in PU(1,n)

Watch a 38-minute mathematics research lecture exploring the commensurability relationships between subgroups in PU(1,n), presented at Harvard CMSA's Workshop on Representation Theory, Calabi-Yau Manifolds, and Mirror Symmetry. Delve into joint research with Zhiwei Zheng that investigates discrete subgroups arising from hypergeometric function monodromy, building upon foundational work by Deligne, Mostow, and Thurston. Learn how the study of higher-dimensional Calabi-Yau type varieties, rather than complex reflection groups, leads to new discoveries about commensurability indices for higher n values and provides novel proofs for existing pairs in n=2. Understand the connection to hyperbolic triangles when n=1 and examine how this research extends previous findings by Deligne-Mostow, Sauter, Kappes-Möller, and McMullen for n=2 cases.