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UID:7790cff18b11a4ffd6b048d572d56761
CATEGORIES:Discrete Math
CREATED:20251015T153434
SUMMARY:Boris Bukh - The Oddtown problem modulo a composite number
LOCATION:Hill 705
DESCRIPTION:Speaker: Boris Bukh (https://www.cmu.edu/math/people/faculty/bukh.html) (Ca
 rnegie Mellon University) \nTitle: The Oddtown problem modulo a composite n
 umber \nAbstract: The Oddtown problem is the perhaps the simplest applicati
 on of the linear algebra method to extremal combinatorics. Motivated by the
  desire to better understand the method, we examine the generalization to c
 omposite moduli.\n\nA family of subsets of $[n]$ is $ell$-Oddtown if the si
 ze of each set is divisible by $ell$, but no intersection 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 our improvement to it.\n
 \nJoint work with Ting-Wei Chao and Zeyu Zheng\n
X-ALT-DESC;FMTTYPE=text/html:<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:20260826T234232
DTSTART;TZID=America/New_York:20251020T140000
DTEND;TZID=America/New_York:20251020T150000
SEQUENCE:0
TRANSP:OPAQUE
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