Tuesday, April 12, 2022
Time | Items |
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All day |
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4:00pm |
04/12/2022 - 4:15pm Quasi-Fuchsian manifolds are hyperbolic manifolds of topological type Σ × R with well-behaved ends. They provide a setting where the underlying topology is simple but the geometry can be very intricate. Uhlenbeck defined a sub-class of quasi-Fuchsian manifolds M that contain minimal surfaces with maximum principal curvature λ_0 < 1, proved that any such surface is unique, and gave a way of parametrizing this sub-class in terms of data attached to this unique minimal surface. Such M are called almost-Fuchsian and have been well-studied since. After describing the basic landscape I will talk about joint work with Zeno Huang that constructs a compactification of the almost Fuchsian space. As a corollary we can prove a gap theorem for the geometry of minimal surfaces in hyperbolic 3-manifolds M that fiber over the circle. I will go over some aspects of the proofs and the much that remains to be understood. Location:
https://yale.zoom.us/j/94256436597
04/12/2022 - 4:30pm In this talk, we will discuss the local gamma factors that appear in the functional equations of local $L$ factors in the framework proposed by Braverman and Kazhdan. We will introduce some of the basic objects of this theory, focusing on the proposed generalization of the standard Fourier transform. The descent of this Fourier transform along parabolic subgroups allows us to establish multiplicativity for gamma factors. If time permits we also discuss the action of the generalized Fourier operator on representations in the test case where $G=\mathrm{GL}(2)$. Location: |