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SUMMARY:Aaron Pixton (University of Michigan)
DTSTART:20231201T220000Z
DTEND:20231201T230000Z
DTSTAMP:20260423T024718Z
UID:MAAGC2023/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MAAGC2023/2/
 ">Tautological rings and competing conjectures</a>\nby Aaron Pixton (Unive
 rsity of Michigan) as part of MAAGC 2023\n\nLecture held in Temple 1160 VC
 U Monroe Park Campus.\n\nAbstract\nLet M_g be the moduli space of smooth c
 urves of genus g.  The tautological ring is a subring of the cohomology of
  M_g that was introduced by Mumford in the 1980s in analogy with the cohom
 ology of Grassmannians. It is a graded ring with one generator in each deg
 ree\, but the ideal of relations between these generators is unknown in ge
 neral. Work of Faber and Faber-Zagier in the 1990s led to two conjectures\
 , each proposing a full description of the structure of the tautological r
 ing. Both conjectures are true for g < 24\, but they contradict each other
  for g >= 24. Although these competing conjectures are both still open\, I
  will discuss some recent evidence favoring one of them over the other.\n
LOCATION:https://researchseminars.org/talk/MAAGC2023/2/
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