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SUMMARY:Vector bundles on metric graphs - Dmitry Zakharov\, Central Michig
 an University
DTSTART:20231018T131500Z
DTEND:20231018T141500Z
UID:TALK207121@talks.cam.ac.uk
CONTACT:Dhruv Ranganathan
DESCRIPTION:Metric graphs are piecewise-linear objects that arise as tropi
 calizations of algebraic curves. For a metric graph\, we can define notion
 s such as line bundles\, divisors\, linear equivalence\, and the Picard gr
 oup\, in complete analogy with the algebraic setting. Furthermore\, all of
  these notions behave well with respect to tropicalization. \n\nI will giv
 e a naive definition of vector bundles on metric graphs as torsors over th
 e tropical general linear group. A simple dimension count shows that our c
 onstruction is incomplete and does not fully capture tropicalization of al
 gebraic vector bundles. Nevertheless\, tropical vector bundles satisfy a n
 umber of results that are analogous to the algebraic setting\, such as the
  Birkhoff--Grothendieck theorem\, the Weil--Riemann--Roch theorem\, a Nara
 simhan--Seshadri correspondence\, and a version of Atiyah's classification
  of vector bundles on an elliptic curve.\n\nJoint work with Andreas Gross 
 and Martin Ulirsch.
LOCATION:CMS MR13
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