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SUMMARY:Curve/Jacobian correspondence [Lecture]
DTSTART:20261102T140000Z
DTEND:20261102T144500Z
DTSTAMP:20261027T144700Z
UID:indico-event-1704@math-events.uni-bonn.de
DESCRIPTION:Speakers: Younghan Bae\n\n\nTo every smooth projective complex
  curve C of genus g\, one associates a g dimensional complex torus J(C)\, 
 called its Jacobian. Classical Abel-Jacobi theory reveals precise connecti
 ons between the geometry and topology of C and J(C). How do these connecti
 ons extend when smooth curves degenerate to singular curves?\nIn this talk
 \, we extend this correspondence over the moduli space of stable curves. W
 e construct an algebra isomorphism between the cohomology of universal com
 pactified Jacobians and a quotient of the cohomology of moduli spaces stab
 le curves with additional symmetrized markings. Our construction is motiva
 ted by recent progress on the P=W conjecture and logarithmic Abel-Jacobi t
 heory. This isomorphism allows us to transfer structures between two sides
 \, leading to several applications. This is joint work in progress with Aa
 ron Pixton.\n\n\nhttps://math-events.uni-bonn.de/event/1704/
LOCATION:Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/1704/
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