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SUMMARY:Integral Points on affine diagonal cubic surfaces - H Uppal (Bath)
DTSTART:20240604T133000Z
DTEND:20240604T143000Z
UID:TALK215644@talks.cam.ac.uk
CONTACT:Jef Laga
DESCRIPTION:The sum of three cubes conjecture states that any integer not 
 congruent to 4 or 5 mod 9 can always be represented as the sum of three in
 teger cubes. Geometrically\, this means that the affine cubic surfaces cor
 responding to this family of equations always have an integral point. Coll
 iot-Thélène and Wittenberg showed that these surfaces have no “cohomol
 ogical obstruction” to the existence of integral points (more formally\,
  there is no integral Brauer-Manin obstruction to the integral Hasse princ
 iple). In this talk\, we study natural generalizations of these surfaces\,
  namely diagonal affine cubic surfaces\, and we will show that\, in this m
 ore general setting\, there are instances of the integral Hasse principle 
 failing. Moreover\, we will provide bounds for the frequency of these fail
 ures. Time permitting\, we will also discuss possible improvements on the 
 results presented in the talk. (Joint work with Julian Lyczak and Vlad Mit
 ankin).
LOCATION:MR13
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