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On the equidistribution of translates of orbits of symmetric subgroups in Γ\G
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We use the method of Burger to study the rate of equidistribution for translates of orbits of symmetric subgroups in homogeneous spaces Γ\G for semisimple Lie groups G and lattices Γ.

National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-347857OAI: oai:DiVA.org:uu-347857DiVA, id: diva2:1196082
Available from: 2018-04-09 Created: 2018-04-09 Last updated: 2018-04-11
In thesis
1. Some applications of representation theory in homogeneous dynamics and automorphic functions
Open this publication in new window or tab >>Some applications of representation theory in homogeneous dynamics and automorphic functions
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of an introduction and five papers in the general area of dynamics and functions on homogeneous spaces. A common feature is that representation theory plays a key role in all articles.

Papers I-IV are concerned with the effective equidistribution of translates of pieces of subgroup orbits in quotient spaces of semisimple Lie groups by discrete subgroups. In Paper I we focus on finite-volume quotients of SL(2,C) and study the speed of equdistribution for expanding translates orbits of horospherical subgroups. Paper II also studies the effective equidistribution of translates of horospherical orbits, though now in the setting of a quotient of a general semisimple Lie group by a lattice subgroup. Like Paper II, Paper III considers effective equidistribution in quotients of general semisimple Lie groups, but now studies translates of orbits of symmetric subgroups. In all these papers we show that the translates equidistribute with the same exponential rate as for the decay of the corresponding matrix coefficients of the translating subgroup. In Paper IV we consider the effective equidistribution of translates of pieces of horospheres in infinite-volume quotients of groups SO(n,1) by geometrically finite subgroups, and improve the dependency on the spectral gap for certain known effective equidistribution results.

In Paper V we study the Fourier coefficients of Eisenstein series for generic non-cocompact cofinite Fuchsian groups. We use Zagier's renormalization of certain divergent integrals to enable use of the so-called triple product method, and then combine this with the analytic continuation of irreducible representations of SL(2,R) due to Bernstein and Reznikov.

Place, publisher, year, edition, pages
Uppsala: Department of Mathematics, 2018. p. 25
Series
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 107
Keywords
automorphic functions, effective equidistribution, Eisenstein series, homogeneous dynamics, horospheres, lattices, Lie groups, representation theory
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:uu:diva-347976 (URN)978-91-506-2698-8 (ISBN)
Public defence
2018-06-08, Häggsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2018-05-17 Created: 2018-04-11 Last updated: 2018-05-17

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Edwards, Samuel

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