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SUMMARY:Ramsey theory: searching for order in chaos - Rob Morris (IMPA Rio
 )
DTSTART:20240502T150000Z
DTEND:20240502T160000Z
UID:TALK211375@talks.cam.ac.uk
CONTACT:HoD Secretary\, DPMMS
DESCRIPTION:In many different areas of mathematics (such as number theory\
 , discrete geometry and combinatorics)\, one is often presented with a lar
 ge "unstructured" object\, and asked to find a smaller "structured" object
  inside it. One of the earliest and most influential examples of this phen
 omenon was the theorem of Ramsey\, proved in 1930\, which states that if n
  = n(k) is large enough\, then in any red-blue colouring of the edges of t
 he complete graph on n vertices\, there exists a monochromatic clique on k
  vertices. In this talk I will discuss some of the questions\, ideas\, and
  new techniques that were inspired by this theorem\, and mention some rece
 nt progress on one of the central problems in the area: bounding the so-ca
 lled "diagonal" Ramsey numbers.\n\nBased on joint work with Marcelo Campos
 \, Simon Griffiths and Julian Sahasrabudhe.\n\nA wine reception in the Cen
 tral Core will follow the lecture\n
LOCATION:MR2\, CMS
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