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BEGIN:VEVENT
UID:7790cff18b11a4ffd6b048d572d56761
CATEGORIES:Discrete Math
CREATED:20251015T153434
SUMMARY:Boris Bukh - The Oddtown problem modulo a composite number
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><span style="font-size: 11pt; font-famil
 y: Lato; color: #000000; background-color: transparent; font-weight: 400; f
 ont-style: normal; font-variant: normal; text-decoration: none; vertical-al
 ign: baseline; white-space: pre-wrap;"></span><a href="https://www.cmu.edu/
 math/people/faculty/bukh.html" style="text-decoration: none;"><span style="
 font-size: 11pt; font-family: Lato; color: #cc0000; background-color: trans
 parent; font-weight: 400; font-style: normal; font-variant: normal; text-de
 coration: underline; vertical-align: baseline; white-space: pre-wrap;">Bori
 s Bukh</span></a><span style="font-size: 11pt; font-family: Lato; color: #0
 00000; background-color: transparent; font-weight: 400; font-style: normal;
  font-variant: normal; text-decoration: none; vertical-align: baseline; whi
 te-space: pre-wrap;"> (Carnegie Mellon University)&nbsp;</span></p><p dir="
 ltr" style="line-height: 1.38; margin-top: 9pt; margin-bottom: 10pt;"><span
  style="font-size: 11pt; font-family: Lato; color: #000000; background-colo
 r: transparent; font-weight: bold; font-style: normal; font-variant: normal
 ; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">
 Title</span><span style="font-size: 11pt; font-family: Lato; color: #000000
 ; background-color: transparent; font-weight: 400; font-style: normal; font
 -variant: normal; text-decoration: none; vertical-align: baseline; white-sp
 ace: pre-wrap;">: The Oddtown problem modulo a composite number&nbsp;</span
 ></p><p dir="ltr" style="line-height: 1.38; margin-top: 0pt; margin-bottom:
  0pt;"><span style="font-size: 11pt; font-family: Lato; color: #000000; bac
 kground-color: transparent; font-weight: bold; font-style: normal; font-var
 iant: normal; text-decoration: none; vertical-align: baseline; white-space:
  pre-wrap;">Abstract</span><span style="font-size: 11pt; font-family: Lato;
  color: #000000; background-color: transparent; font-weight: 400; font-styl
 e: normal; font-variant: normal; text-decoration: none; vertical-align: bas
 eline; white-space: pre-wrap;">: The Oddtown problem is the perhaps the sim
 plest application of the linear algebra method to extremal combinatorics. M
 otivated by the desire to better understand the method, we examine the gene
 ralization to composite moduli.</span></p><p dir="ltr" style="line-height: 
 1.38; margin-top: 9pt; margin-bottom: 0pt;"><span style="background-color: 
 transparent; font-family: Lato; font-size: 11pt; white-space-collapse: pres
 erve; caret-color: auto;"></span></p><p dir="ltr" style="line-height: 1.38;
  margin-top: 0pt; margin-bottom: 0pt;"><span style="font-size: 11pt; font-f
 amily: Lato; color: #000000; background-color: transparent; font-weight: 40
 0; font-style: normal; font-variant: normal; text-decoration: none; vertica
 l-align: baseline; white-space: pre-wrap;">A family of subsets of $[n]$ is 
 $ell$-Oddtown if the size of each set is divisible by $ell$, but no interse
 ction is divisible by $ell$. How large can $ell$-Oddtown be? We explain the
  history of the problem, present the best known bound due to Szegedy, and o
 ur improvement to it.</span></p><p dir="ltr" style="line-height: 1.38; marg
 in-top: 9pt; margin-bottom: 0pt;"><span style="background-color: transparen
 t; font-family: Lato; font-size: 11pt; white-space-collapse: preserve; care
 t-color: auto;"></span></p><p dir="ltr" style="line-height: 1.38; margin-to
 p: 0pt; margin-bottom: 0pt;"><span style="font-size: 11pt; font-family: Lat
 o; color: #000000; background-color: transparent; font-weight: 400; font-st
 yle: normal; font-variant: normal; text-decoration: none; vertical-align: b
 aseline; white-space: pre-wrap;">Joint work with Ting-Wei Chao and Zeyu Zhe
 ng</span></p>
DTSTAMP:20260826T214005
DTSTART;TZID=America/New_York:20251020T140000
DTEND;TZID=America/New_York:20251020T150000
SEQUENCE:0
TRANSP:OPAQUE
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