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SUMMARY:On the dynamical Mordell-Lang conjecture - Par Kurlberg
DTSTART:20121114T160000Z
DTEND:20121114T170000Z
UID:TALK39459@talks.cam.ac.uk
CONTACT:Bob Hough
DESCRIPTION:Let $V$ be a variety\, and let $\\phi : V \\to V$ be a\nmorphi
 sm.  If an (infinite) forward orbit of a point intersects a\nsubvariaty $W
 $ infinitely many times\, what can be said about $W$?  The\ndynamical Mord
 ell-Lang conjecture asserts that this can only happen\nfor "the obvious re
 ason"\, namely that $W$ is $\\phi$-preperiodic.  We\nwill give a brief bac
 kground on the conjecture\, and using a $p$-adic\nanalytic approach\, prov
 e it for certain coordinatewise actions.\nAssuming certain "random map ass
 umptions"\, the approach should work\nfor more general maps if the mod $p$
  periodic part of orbit avoids the\nramification locus of $\\phi$.  Howeve
 r\, in sufficiently high\ndimensions the approach breaks down due to the p
 eriods being too long.\nWe will discuss this in more detail\, and present 
 numerical evidence\nfor the validity of the random map assumption in vario
 us dimensions.
LOCATION:MR11\, CMS
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