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DTSTART:20260308T070000
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DTSTART;TZID=America/Toronto:20260407T100000
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URL:https://uwaterloo.ca/pure-mathematics/events/phd-thesis-defense-15
SUMMARY:PhD Thesis Defense
CLASS:PUBLIC
DESCRIPTION:XIAO ZHONG\, UNIVERSITY OF WATERLOO\n\n_Topics in Arithmetic Dy
 namics_\n\nThis thesis studies several problems in arithmetic dynamics\, f
 ocusing\non preimages of invariant subvarieties\,common zeros of iterates 
 of\nrational functions\, and periodic curves for polynomial endomorphisms.
 \nWeinvestigate stabilization phenomena for rational points in backward\no
 rbits and develop dynamical cancellationresults for semigroups of\npolynom
 ials. We also prove a finiteness theorem for common zeros of\niterates ofc
 ompositionally independent rational functions\, answering a\nquestion of H
 sia and Tucker. Finally\, we studypolynomial endomorphisms\nof the project
 ive plane with many periodic curves\, showing that\nfamilies containinga Z
 ariski dense set of periodic curves must be\ninvariant under an iterate\, 
 and we classify maps admittinginfinitely\nmany periodic curves of bounded 
 degree.\n\nMC 5479
DTSTAMP:20260406T192939Z
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