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DTSTART:20230312T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20240115T143000
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URL:https://uwaterloo.ca/pure-mathematics/events/joint-pure-mathematics-col
 loquium-deans-distinguished-women
SUMMARY:Joint Pure Mathematics Colloquium & Dean's Distinguished Women in\n
 Mathematics\, Statistics\, and Computer Science Lecture
CLASS:PUBLIC
DESCRIPTION:SARAH PELUSE\, UNIVERSITY OF MICHIGAN\n\n\"ARITHMETIC PATTERNS 
 IN DENSE SETS\"\n\nSome of the most important problems in combinatorial nu
 mber theory ask\nfor the size of the largest subset of the integers in an 
 interval\nlacking points in a fixed arithmetically defined pattern. One ex
 ample\nof such a problem is to prove the best possible bounds in Szemeréd
 i's\ntheorem on arithmetic progressions\, i.e.\, to determine the size of 
 the\nlargest subset of {1\,...\,N} with no nontrivial k-term arithmetic\np
 rogression x\,x+y\,...\,x+(k-1)y. Gowers initiated the study of higher\nor
 der Fourier analysis while seeking to answer this question\, and used\nit 
 to give the first reasonable upper bounds for arbitrary k. In this\ntalk\,
  I'll discuss recent progress on quantitative polynomial\,\nmultidimension
 al\, and nonabelian variants of Szemerédi's theorem and\non related probl
 ems in harmonic analysis and ergodic theory.\n\nMC 5501
DTSTAMP:20260513T183111Z
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