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UID:3cadd04443c3cc6617474fbedc297ae3
CATEGORIES:Discrete Math
CREATED:20250411T100433
SUMMARY:James Leng -  Szemerédi’s theorem, primes, and nilsequences
LOCATION:Hill 705
DESCRIPTION:<p dir="ltr" style="line-height: 1.38; margin-top: 9pt; margin-bottom: 0pt;
 "><span style="font-size: 11pt; font-family: Lato; color: #000000; backgrou
 nd-color: transparent; font-weight: bold; font-style: normal; font-variant:
  normal; text-decoration: none; vertical-align: baseline; white-space: pre-
 wrap;">Speaker:</span><span style="font-size: 10pt; font-family: Lato; colo
 r: #000000; background-color: transparent; font-weight: bold; font-style: n
 ormal; font-variant: normal; text-decoration: none; vertical-align: baselin
 e; white-space: pre-wrap;"> </span><a href="https://sites.google.com/view/j
 amesleng/home" style="text-decoration: none;"><span style="font-size: 11pt;
  font-family: Lato; color: #cc0000; background-color: transparent; font-wei
 ght: 400; font-style: normal; font-variant: normal; text-decoration: underl
 ine; vertical-align: baseline; white-space: pre-wrap;">James Leng </span></
 a><span style="font-size: 11pt; font-family: Lato; color: #000000; backgrou
 nd-color: transparent; font-weight: 400; font-style: normal; font-variant: 
 normal; text-decoration: none; vertical-align: baseline; white-space: pre-w
 rap;">(UCLA)</span></p><p dir="ltr" style="line-height: 1.38; margin-top: 9
 pt; margin-bottom: 10pt;"><span style="font-size: 11pt; font-family: Lato; 
 color: #000000; background-color: transparent; font-weight: bold; font-styl
 e: normal; font-variant: normal; text-decoration: none; vertical-align: bas
 eline; white-space: pre-wrap;">Title</span><span style="font-size: 11pt; fo
 nt-family: Lato; color: #000000; background-color: transparent; font-weight
 : 400; font-style: normal; font-variant: normal; text-decoration: none; ver
 tical-align: baseline; white-space: pre-wrap;">:&nbsp; Szemerédi’s theorem,
  primes, and nilsequences</span></p><p dir="ltr" style="line-height: 1.38; 
 margin-top: 9pt; margin-bottom: 0pt;"><span style="font-size: 11pt; font-fa
 mily: Lato; color: #000000; background-color: transparent; font-weight: bol
 d; font-style: normal; font-variant: normal; text-decoration: none; vertica
 l-align: baseline; white-space: pre-wrap;"><span style="font-size: 11pt; fo
 nt-family: Lato; color: #000000; background-color: transparent; font-weight
 : bold; font-style: normal; font-variant: normal; text-decoration: none; ve
 rtical-align: baseline; white-space: pre-wrap;">Abstract</span><span style=
 "font-size: 11pt; font-family: Lato; color: #000000; background-color: tran
 sparent; font-weight: 400; font-style: normal; font-variant: normal; text-d
 ecoration: none; vertical-align: baseline; white-space: pre-wrap;">: Let $r
 _k(N)$ be the largest subset of $[N] = {1, dots, N}$ with no k-term arithme
 tic progression. Szemerédi’s theorem states that $r_k(N) = o_k(N)$. We will
  go over the proof that achieves the best known upper bounds for $r_k(N)$ f
 or general $k$. We will discuss how the mathematics behind the proof relate
 s to counting primes along linear forms and the distribution of orbits on $
 G/Gamma$ with $G$ nilpotent and $Gamma$ discrete and cocompact. This is (pa
 rtly) based on joint work with Ashwin Sah and Mehtaab Sawhney.</span></span
 ></p>
DTSTAMP:20260829T023908
DTSTART;TZID=America/New_York:20250414T140000
DTEND;TZID=America/New_York:20250414T150000
SEQUENCE:0
TRANSP:OPAQUE
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