BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Sebastian Opper (Charles University\, Prague)
DTSTART:20250513T060000Z
DTEND:20250513T070000Z
DTSTAMP:20260423T021222Z
UID:OISTRTS/70
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OISTRTS/70/"
 >Autoequivalences of triangulated categories via Hochschild cohomology</a>
 \nby Sebastian Opper (Charles University\, Prague) as part of OIST represe
 ntation theory seminar\n\n\nAbstract\nI will talk about a general tool whi
 ch allows one to study symmetries of (enhanced) triangulated categories in
  the form of their derived Picard groups. In general\, these groups are ra
 ther elusive to computations which require a rather good understanding of 
 the whole category at hand. A result of Keller shows that the Lie algebra 
 of the derived Picard group of an algebra can be identified with its Hochs
 child cohomology equipped with the Gerstenhaber Lie bracket. Mimicking the
  classical relationship between Lie groups and Lie algebras\, I will expla
 in how to "integrate'' elements in the Hochschild cohomology of a dg categ
 ory over fields of characteristic zero to elements in the derived Picard g
 roup via a generalized exponential map. Afterwards we discuss properties o
 f this exponential and a few applications. This includes necessary conditi
 ons for the uniqueness of enhancement of triangulated functors and uniquen
 ess of Fourier-Mukai kernels. Other applications concern derived Picard gr
 oups of categories arising in algebra and geometry such as derived categor
 ies of graded gentle algebras and their corresponding partially wrapped Fu
 kaya categories.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/70/
END:VEVENT
END:VCALENDAR