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X-WR-CALNAME:Joseph Johns: \"Lefchetz fibrations on cotangent bundles an
 d Lagrangian submanifolds\"
PRODID:-//Apple Computer\, Inc//iCal 2.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
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TZID:America/New_York
LAST-MODIFIED:20090417T145312Z
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DTSTART:20090308T070000
TZOFFSETTO:-0400
TZOFFSETFROM:+0000
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DURATION:PT1H
LOCATION:Math 520\, Columbia University
DTSTAMP:20090417T145306Z
UID:BDC61D45-DF2A-49F9-B4E9-4DEB59A21F29
SEQUENCE:6
DTSTART;TZID=America/New_York:20090417T131000
SUMMARY:Joseph Johns: \"Lefchetz fibrations on cotangent bundles and Lag
 rangian submanifolds\"
DESCRIPTION:Abstract: Given a Morse function f: N --> R I will describe 
 a Lefschetz fibration pi: E --> C which models the complexification of f
  on the disk cotangent bundle D(T*N). I will then describe a program in 
 progress for studying closed exact Lagrangian submanifolds of T*N using 
 pi. The idea is to translate questions about Lagrangian submanifolds int
 o questions about representations of certain quivers\, following Seidel'
 s work on T*S^n.\n\nIf time permits I will discuss the following offshoo
 ts of this program: 1. The program yields a conjectural bridge between T
 he analysis of Fuk(T*N) by Nadler-Zaslow\, using constructible sheaves\,
  and that of Seidel\, using Picard-Lefschetz theory. 2. In a more geomet
 ric vein the construction of pi: E ---> C suggests a way to generalize m
 atching paths from spheres to more general manifolds.
ORGANIZER;CN="Robert Lipshitz":mailto:lipshitz@math.stanford.edu
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