Seminari di Sistemi Dinamici 2022

Effective equidistribution of expanding translates in ASL_d(R)ASL_d(Z)

speaker: Wooyeon Kim (ETH Zurich)

abstract: In this talk, we discuss effective versions of Ratner’s theorems in the space of affine lattices. For d>= 2, Let Y=ASL_d(\mathbb{R})ASL_d(\mathbb{Z}), H be a minimal horospherical group of SL_d(\mathbb{R}) embedded in ASL_d(\mathbb{R}), and a_t be the corresponding diagonal flow. Then (a_t)-push-forwards of a piece of H-orbit become equidistributed with a polynomial error rate under certain Diophantine condition of the initial point of the orbit. This generalizes the previous results of Strömbergsson for d=2 and of Prinyasart for d=3.

timetable:
Thu 31 Mar, 14:00 - 15:00,
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