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SUMMARY:Nathan Broomhead (Plymouth)
DTSTART:20260225T160000Z
DTEND:20260225T170000Z
DTSTAMP:20260421T154107Z
UID:UEAPS/70
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UEAPS/70/">C
 onvex geometry for fans of triangulated categories</a>\nby Nathan Broomhea
 d (Plymouth) as part of ANTLR seminar\n\nLecture held in EFRY 01.02.\n\nAb
 stract\nFans and other convex-geometric objects have recently appeared in 
 homological algebra in several related contexts. For example\, as g-fans i
 n the silting theory of finite-dimensional algebras and as scattering diag
 rams in Bridgeland stability theory. I will discuss joint work with David 
 Pauksztello\, David Ploog and Jon Woolf on a general construction which we
  hope will provide a natural and unifying framework.\n\nStarting with a tr
 iangulated category D and a finite rank quotient lattice L of its Grothend
 ieck group\, we show that each heart H in D determines a closed convex `he
 art cone' in the dual vector space V=Hom(L\,R). The heart cones of H and a
 ll its forward tilts form a `heart fan' in V. If H is `algebraic'\, i.e. i
 s a length category with finitely many simple objects\, then the heart con
 e is simplicial and the heart fan is complete.\n
LOCATION:https://researchseminars.org/talk/UEAPS/70/
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