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SUMMARY:Yu-Wei Fan (UC Berkerley)
DTSTART:20210607T010000Z
DTEND:20210607T020000Z
DTSTAMP:20260423T022722Z
UID:IBSCGP/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IBSCGP/8/">S
 hifting numbers in triangulated categories</a>\nby Yu-Wei Fan (UC Berkerle
 y) as part of IBS-CGP weekly zoom seminar\n\n\nAbstract\nOne can consider 
 endofunctors of triangulated categories as dynamical systems\, and study t
 heir long term behaviors under large iterations. There are (at least) thre
 e natural invariants that one can associate to endofunctors from the dynam
 ical perspective: categorical entropy\, and upper/lower shifting numbers. 
 We will recall some background on categorical dynamical systems and catego
 rical entropy\, and introduce the notion of shifting numbers\, which measu
 re the asymptotic amount by which an endofunctor of a triangulated categor
 y translates inside the category. The shifting numbers are analogous to Po
 incare translation numbers. We additionally establish that in some example
 s the shifting numbers provide a quasimorphism on the group of autoequival
 ences. Joint work with Simion Filip.\n
LOCATION:https://researchseminars.org/talk/IBSCGP/8/
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