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DTSTART:20260308T070000
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DTSTART:20251102T060000
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DTSTART;TZID=America/Toronto:20260408T120000
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URL:https://uwaterloo.ca/pure-mathematics/events/phd-thesis-defense-14
SUMMARY:PhD Thesis Defense
CLASS:PUBLIC
DESCRIPTION:JÉRÉMY CHAMPAGNE\, UNIVERSITY OF WATERLOO\n\n_Weyl's Equidist
 ribution Theorem in function fields and multivariable\ngeneralizations_\n\
 nThis thesis is concerned with finding a suitable function field\nanalogue
  to the classical equidistribution theorem of Weyl. More\nspecifically\, w
 e are interested in the distribution of polynomial\nvalues f(x) as x runs 
 over the ring Fq[T]\, and where the coefficients\nof f(X) are taken from t
 he field of formal power series Fq((1/T)).\nClassically\, results of this 
 type were all subject to the constraint\ndeg f <p where in liu and wooley were able nbreak this characteristic barrier using modern developments>\nf^τ(X) which preserves th
 e size of Weyl sums\, and is such that\nf^τ(X) does not involve any power
 s divisible by p.\n\nThe second sets of results is concerned with a multiv
 ariate\ngeneralization of the method of Lê-Liu-Wooley. As such\, we use a
 \nmultivariate version of Vinogradov's Mean Value Theorem together with\nt
 he Large Sieve Inequality to obtain suitable minor arc estimates for\nWeyl
  sums in d variables. We then use these minor arc estimates to\nstudy the 
 distribution of polynomial values f(x_1\,...\,x_d)$ as\n(x_1\,...\,x_d) ru
 ns over Fq[T]^d\, and we also consider the case where\neach of x_1\,...\,x
 _d is required to be monic.\n\nMC 6029
DTSTAMP:20260406T212020Z
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