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BEGIN:VEVENT
UID:4d07da9c4907928da90857d8ae7fd5bf
CATEGORIES:Discrete Math
CREATED:20251105T140934
SUMMARY:Sammy Luo - Mutually touching infinite cylinders and Ramsey theory 
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://math.mit.edu/directory/
 profile.html?pid=2561" style="text-decoration: none;"><span style="font-siz
 e: 11pt; font-family: Lato; color: #cc0000; background-color: transparent; 
 font-weight: 400; font-style: normal; font-variant: normal; text-decoration
 : underline; vertical-align: baseline; white-space: pre-wrap;">Sammy Luo</s
 pan></a><span style="font-size: 11pt; font-family: Lato; color: #000000; ba
 ckground-color: transparent; font-weight: 400; font-style: normal; font-var
 iant: normal; text-decoration: none; vertical-align: baseline; white-space:
  pre-wrap;"> (MIT)</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-color: transparent; font-weight: bold; fon
 t-style: normal; font-variant: normal; text-decoration: none; vertical-alig
 n: baseline; white-space: pre-wrap;">Title</span><span style="font-size: 11
 pt; font-family: Lato; color: #000000; background-color: transparent; font-
 weight: 400; font-style: normal; font-variant: normal; text-decoration: non
 e; vertical-align: baseline; white-space: pre-wrap;">: Mutually touching in
 finite cylinders and Ramsey theory&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; background-color: transparent; f
 ont-weight: bold; font-style: normal; font-variant: normal; text-decoration
 : none; vertical-align: baseline; white-space: pre-wrap;">Abstract</span><s
 pan style="font-size: 11pt; font-family: Lato; color: #000000; background-c
 olor: transparent; font-weight: 400; font-style: normal; font-variant: norm
 al; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;
 ">: Littlewood asked for the maximum number $N$ of congruent infinite cylin
 ders that can be arranged in $mathbb{R}^3$ so that every pair touches. In t
 his talk, we discuss the techniques behind some recent improvements on the 
 upper bounds for this problem, culminating in our recent result showing tha
 t $N leq 10$. Paired with a lower bound by Bozóki, Lee, and Rónyai, this es
 tablishes that $N in {7,8,9,10}$. Our method is based on linear algebra and
  Ramsey theory, and makes partial use of computer verification.</span></p><
 p dir="ltr" style="line-height: 1.38; margin-top: 9pt; margin-bottom: 0pt;"
 >&nbsp;</p><p dir="ltr" style="line-height: 1.38; margin-top: 0pt; margin-b
 ottom: 0pt;"><span style="font-size: 11pt; font-family: Lato; color: #00000
 0; background-color: transparent; font-weight: 400; font-style: normal; fon
 t-variant: normal; text-decoration: none; vertical-align: baseline; white-s
 pace: pre-wrap;">Based on joint work with Travis Dillon and Junnosuke Koizu
 mi.</span></p>
DTSTAMP:20260921T135846
DTSTART;TZID=America/New_York:20251110T140000
DTEND;TZID=America/New_York:20251110T150000
SEQUENCE:0
TRANSP:OPAQUE
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