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UID:9c6330d6dbdf745d60f4fadb4ac2189f
CATEGORIES:Discrete Math
CREATED:20241030T164825
SUMMARY:Jinyoung Park - Lipschitz functions on expanders 
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><a href="https://sites.google.com/view/jinyoungpark"
  style="text-decoration: none;"><span style="font-size: 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;">Jinyoung Park</span></a><span styl
 e="font-size: 11pt; font-family: Lato; color: #000000; background-color: tr
 ansparent; font-weight: 400; font-style: normal; font-variant: normal; text
 -decoration: none; vertical-align: baseline; white-space: pre-wrap;"> (NYU)
 </span></p><p dir="ltr" style="line-height: 1.38; margin-top: 9pt; margin-b
 ottom: 10pt;"><span style="font-size: 11pt; font-family: Lato; color: #0000
 00; background-color: transparent; font-weight: bold; font-style: normal; f
 ont-variant: normal; text-decoration: none; vertical-align: baseline; white
 -space: pre-wrap;">Title</span><span style="font-size: 11pt; font-family: L
 ato; color: #000000; background-color: transparent; font-weight: 400; font-
 style: normal; font-variant: normal; text-decoration: none; vertical-align:
  baseline; white-space: pre-wrap;">: Lipschitz functions on expanders&nbsp;
 </span></p><p dir="ltr" style="line-height: 1.38; margin-top: 9pt; margin-b
 ottom: 0pt;"><span style="font-size: 11pt; font-family: Lato; color: #00000
 0; background-color: transparent; font-weight: bold; font-style: normal; fo
 nt-variant: 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; fon
 t-style: normal; font-variant: normal; text-decoration: none; vertical-alig
 n: baseline; white-space: pre-wrap;">:&nbsp; We will discuss the typical be
 havior of M-Lipschitz functions on d-regular expander graphs, where an M-Li
 pschitz function means any two adjacent vertices admit integer values diffe
 r by at most M. While it is easy to see that the maximum possible height of
  an M-Lipschitz function on an n-vertex expander graph is about C*M*log n, 
 where C depends (only) on d and the expansion of the given graph, it was sh
 own by Peled, Samotij, and Yehudayoff (2012) that a uniformly chosen random
  M-Lipschitz function has height at most C'*M*loglog n with high probabilit
 y, showing that the typical height of an M-Lipschitz function is much small
 er than the extreme case. Peled-Samotij-Yehudayoff's result holds under the
  condition that, roughly, any "not-so-large" vertex sets expand by about M*
 log(dM). We will show that the same result holds under a much weaker condit
 ion assuming that d is large enough. This is joint work with Robert Krueger
  and Lina Li. </span></p>
DTSTAMP:20260827T101355
DTSTART;TZID=America/New_York:20241104T140000
DTEND;TZID=America/New_York:20241104T150000
SEQUENCE:0
TRANSP:OPAQUE
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