BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Common linear patterns are rare - N. Kamcev (Zagreb)
DTSTART:20211021T133000Z
DTEND:20211021T143000Z
UID:TALK164506@talks.cam.ac.uk
CONTACT:Professor Imre Leader
DESCRIPTION:Several classical results in Ramsey theory (including famous t
 heorems of Schur\, van der Waerden\, Rado) deal with finding monochromatic
  linear patterns in\ntwo-colourings of the integers. Our topic will be qua
 ntitative extensions of such results.\nA linear system L over F_q is commo
 n if the number of monochromatic solutions to L=0 in any two-colouring of 
 F_q^n^  is asymptotically at least the expected\nnumber of monochromatic s
 olutions in a random two-colouring of F_q^n^. Motivated by existing result
 s for specific systems (such as Schur triples and arithmetic\nprogressions
 )\, as well as extensive research on common and Sidorenko graphs\, the sys
 tematic study of common systems of linear equations was recently initiated
  by\nSaad and Wolf. Fox\, Pham and Zhao characterised common linear equati
 ons. I will talk about recent progress towards a classification of common 
 systems of\ntwo or more linear equations. In particular\, the uncommonness
  of an arbitrarily large system L can be reduced to studying single equati
 ons implied by L.\nJoint work with Anita Liebenau and Natasha Morrison.\n
LOCATION:MR12
END:VEVENT
END:VCALENDAR