Models of uniformly 2-nondegenerate CR hypersurfaces - Part I

In this talk, I will focus on the normal form approach to model theory for uniformly 2-nondegenerate CR hypersurfaces. The 2-nondegenerate models are invariants naturally assigned to any 2-nondegenerate CR hypersurface with applications towards solving the biholomorphic equivalence problem of Levi degenerate CR hypersurfaces. I will show how to classify all of these models and present a complete classification of 2-nondegenerate models in $\mathbb C^4$.
–Based on joint work with David Sykes and Martin Kolář, published in Math. Ann. 392, 1615–1663 (2025) DOI: 10.1007/s00208-025-03138-1.