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SUMMARY:On Compact Clifford-Klein Forms
DTSTART;VALUE=DATE-TIME:20200128T091500Z
DTEND;VALUE=DATE-TIME:20200128T101500Z
DTSTAMP;VALUE=DATE-TIME:20210730T175627Z
UID:indico-event-5595@indico.math.cnrs.fr
DESCRIPTION:In the talk I will present a mathematically challenging and di
fficult problem of the (non)existence of compact Clifford-Klein forms of h
omogeneous spaces G/H. These are quotients of such spaces by discrete su
bgroups of G acting freely\, properly and co-compactly. I will formulate t
he challenging Toshiyuki Kobayashi conjecture and present several partial
results supporting it. The results basically are negative in the sense tha
t I will prove the non-existence of compact Clifford-Klein forms for large
families of homogeneous spaces\, and the non-existence of standard compac
t Clifford-Klein forms for all homogeneous spaces of exceptional simple re
al Lie groups. The methods are purely Lie-theoretical. The approach is qui
te computational: after expressing the problem as some conditions on Lie s
ubalgebras\, we develop algorithms checking known obstructions to the exis
tence of compact Clifford-Klein forms. Algorithms are implemented in the c
omputer algebra system GAP and use classifying algorithms of semisimple Li
e subalgebras developed by Willem De Graaf. We use the works of Yosuke Mor
ita and Nicolas Tholozan. The talk is based on my joint work with Maciej B
ochenski and Piotr Jastrzebski.\n\nhttps://indico.math.cnrs.fr/event/5595/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/5595/
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