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Abstract We geometrize the modpSatake isomorphism of Herzig and Henniart–Vignéras using Witt vector affine flag varieties for reductive groups in mixed characteristic. We deduce this as a special case of a formula, stated in terms of the geometry of generalized Mirković–Vilonen cycles, for the Satake transform of an arbitrary parahoric modpHecke algebra with respect to an arbitrary Levi subgroup. Moreover, we prove an explicit formula for the convolution product in an arbitrary parahoric modpHecke algebra. Our methods involve the constant term functors inspired from the geometric Langlands program, and we also treat the case of reductive groups in equal characteristic. We expect this to be a first step toward a geometrization of a modpLocal Langlands Correspondence.
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Frequency comb generation with lasers near exceptional points
We show that exceptional points and the nonlinearity of a laser can induce an oscillating population inversion, creating a frequency comb. We develop anab-initiotheory describing all steady-state properties of such lasers.
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- Award ID(s):
- 2146021
- PAR ID:
- 10497745
- Publisher / Repository:
- Optica Publishing Group
- Date Published:
- ISBN:
- 978-1-957171-23-4
- Page Range / eLocation ID:
- Tu1A.3
- Format(s):
- Medium: X
- Location:
- Honolulu, Hawaii
- Sponsoring Org:
- National Science Foundation
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