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Seminar

Classification of horospherical invariant infinite measures February 23, 2026 (11:10 AM PST - 12:10 PM PST)
Parent Program:
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Speaker(s) Dongryul Kim (Simons Laufer Mathematical Sciences Institute (SLMath))
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Keywords and Mathematics Subject Classification (MSC)
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Classification of horospherical invariant infinite measures

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In this talk, I will present the classification of horospherical invariant Radon measures for Anosov subgroups of arbitrary semisimple real algebraic groups. This generalizes the works of Burger and Roblin in rank one to higher ranks. At the same time, this extends the works of Furstenberg, Veech, and Dani, and a special case of Ratner's theorem for finite-volume homogeneous spaces to infinite-volume Anosov homogeneous spaces.

Especially, this resolves the open problems proposed by Landesberg--Lee--Lindenstrauss--Oh and by Oh. Our measure classification is in fact for a more general class of discrete subgroups, including relatively Anosov subgroups with respect to any parabolic subgroups, not necessarily minimal. Our method is rather geometric, not relying on continuous flows or ergodic theorems.

If time permits, I will also discuss the corresponding measure classification result for subgroups of mapping class groups. This is based on joint work with Inhyeok Choi.

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Classification of horospherical invariant infinite measures