BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Drupal iCal API//EN
X-WR-CALNAME:Events items teaser
X-WR-TIMEZONE:America/Toronto
BEGIN:VTIMEZONE
TZID:America/Toronto
X-LIC-LOCATION:America/Toronto
BEGIN:DAYLIGHT
TZNAME:EDT
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
DTSTART:20260308T070000
END:DAYLIGHT
BEGIN:STANDARD
TZNAME:EST
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
DTSTART:20251102T060000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
UID:69f5776898b2c
DTSTART;TZID=America/Toronto:20260408T090000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20260408T120000
URL:https://uwaterloo.ca/pure-mathematics/events/phd-thesis-defense-13
SUMMARY:PhD Thesis Defense
CLASS:PUBLIC
DESCRIPTION:LIAM OROVEC\, UNIVERSITY OF WATERLOO\n\n_Greedy and Lazy expans
 ions for Pisot and Salem Numbers_\n\nWe call a sequence (a_i) a beta-repre
 sentation for x provided that the\nsum over all positive integers ofa_i*be
 ta^{-i} is equal to x. We call\nthe lexicographically largest of of these 
 sequences the greedy\nexpansion for xunder base beta and the smallest we c
 all the lazy\nexpansion. A real number is called a Parry number if its\ngr
 eedyexpansion for 1 is eventually periodic or finite. Similarly we\nlabel 
 those real numbers whose lazy expansion for 1is eventually\nperiodic as la
 zy Parry numbers. Given a PV number with minimal\npolynomial M(x)\, we kno
 w thatfor sufficiently large value of m that\nthe polynomial T_m^{\\pm}(x)
  has a Salem root. We give criteria that\nrelatesthe greedy and lazy expan
 sions for 1 under these Salem numbers\nto the greedy and lazy expansions f
 or 1 underthe PV number. We\nconsider Salem numbers of degree 4\, the mini
 mal such degree. We will\nprove these arealways lazy Parry numbers and giv
 e explicit\nconstructions for their lazy expansions for 1. We compare\nthe
 seexpansions to the results of Boyd\, that proved that they are also\nParr
 y numbers.\n\nMC 5501
DTSTAMP:20260502T040248Z
END:VEVENT
END:VCALENDAR