Siegel Transforms on Homogeneous Spaces of Lattices: Moments and Applications (CONTRIBUTED TALK)
speaker: Jiyoung Han (KIAS, Korea Institute for Advanced Study)abstract: The Siegel transforms, a crucial concept in applying homogeneous dynamics to number-theoretic problems related to lattice counting, are defined based on the idea that sets of lattices in vector spaces become homogeneous spaces. The moment formulas for Siegel transforms and their applications were introduced and studied in the 1950s-60s, mainly by Rogers and Schmidt. Recently, these topics have gained renewed interest through the works of Athreya—Margulis, Kelmer—Yu, Ghosh—Kelmer—Yu, etc. In this talk, we introduce various Siegel transforms on homogeneous spaces of lattices, explore their moment formulas, and discuss their applications to lattice counting problems. The talk presents joint works with Mahbub Alam and Anish Ghosh, and with Samantha Fairchild.
timetable:
Fri 24 May, 10:00 - 10:30, Aula Dini
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