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Wed, Nov 11, 2026 Lie Groups Seminar 3:30 PM MSCS 509 Analysis and geometry on $\mathrm{SU}(2,1)/P$, Part II Sean Curry, OSU Abstract ⌄ PDF Abstract: Continuing from our previous discussion of Cartan geometries and parabolic geometries, we will discuss the concrete case of $S^3 = \mathrm{SU}(2,1)/P$ and its deformations. The underlying geometry of spaces modelled on $\mathrm{SU}(2,1)/P$ is 3-dimensional Cauchy-Riemann (CR) geometry, a notion which attempts to characterize abstractly what it means to be a hypersurface in $\mathbb{C}^2$ (or, more generally, in a complex surface); the CR geometry of $S^3 = \mathrm{SU}(2,1)/P$ is that coming from its standard realization as the unit sphere in $\mathbb{C}^2$. I will discuss work on characterizing when an abstract deformation of $S^3 = \mathrm{SU}(2,1)/P$ is realizable as a deformation of the unit sphere in $\mathbb{C}^2$ and apply this to prove a rigidity result for a certain nonlinear geometric partial differential equation arising from complex analysis and from physics.

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