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UID:ef70df317ed9db45fa9943e3f35560b5
CATEGORIES:Graduate Student Combinatorics Seminar Sponsored by DIMACS
CREATED:20230306T123135
SUMMARY:Reconstructing Random Pictures
LOCATION:Graduate Student Lounge\, 7th Floor\, Hill Center (and Zoom)
DESCRIPTION:Abstract:  Reconstruction problems ask whether or not it is possible to uni
 quely build a discrete structure from the collection of its substructures o
 f a fixed size. This question has been explored in a wide range of settings
 , most famously with graphs and the resulting Graph Reconstruction Conjectu
 re due to Kelly and Ulam, but also including geometric sets, jigsaws, and a
 belian groups. In this talk, we'll consider the reconstruction of random pi
 ctures (n-by-n grids with binary entries) from the collection of its k-by-k
  subgrids and prove a nearly-sharp threshold for k = k(n). Our main proof t
 echnique is an adaptation of the Peierls contour method from statistical ph
 ysics. Joint work with Bhargav Narayanan.\n \n
X-ALT-DESC;FMTTYPE=text/html:<p>Abstract:&nbsp;&nbsp;Reconstruction problems ask whether or not it is po
 ssible to uniquely build a discrete structure from the collection of its su
 bstructures of a fixed size. This question has been explored in a wide rang
 e of settings, most famously with graphs and the resulting Graph Reconstruc
 tion Conjecture due to Kelly and Ulam, but also including geometric sets, j
 igsaws, and abelian groups.&nbsp;In this talk, we'll consider the reconstru
 ction of random pictures (n-by-n grids with binary entries) from the collec
 tion of its&nbsp;k-by-k subgrids and prove a nearly-sharp threshold for k =
  k(n). Our main proof technique is an adaptation of the Peierls contour met
 hod from statistical physics. Joint work with Bhargav Narayanan.<br> </p>
CONTACT:Corrine Yap - Rutgers University
X-EXTRAINFO:Zoom link: https://rutgers.zoom.us/j/91649887793?pwd=MDB4aXdYUytERWUxZ0xhUk
 53bURUUT09 \nMeeting ID: 916 4988 7793\nPassword: gcs2023
DTSTAMP:20260828T085945
DTSTART;TZID=America/New_York:20230308T121500
DTEND;TZID=America/New_York:20230308T133000
SEQUENCE:0
TRANSP:OPAQUE
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