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SUMMARY:A geometric version of the circle method
DTSTART:20180321T161500
DTEND:20180321T171500
DTSTAMP:20260407T113730Z
UID:afea4f5fb420d0f5dfaa4b5b6ae39bff2ba1bc94977cedc06a0ec772
CATEGORIES:Conferences - Seminars
DESCRIPTION:Will Savin (ETH\, Zurich)\nThe circle method can be used to es
 timate the number of rational points on a smooth hypersurface of low degre
 e in projective or affine space\, verifying cases of the Manin conjecture.
  A function field version of the circle method can be used in the same way
  to estimate the number of rational curves on such a hypersurface defined 
 over a finite field. Rational curves on a hypersurface are parameterized b
 y a moduli space\, so this raises the question of whether geometric inform
 ation about this space can be gleaned from the circle method. Indeed\, Bro
 wning and Vishe were able to calculate the dimension in this way\, and sho
 w it is irreducible. In this talk\, I will explain how Browning and myself
  were able to obtain further information\, calculating the high-degree coh
 omology of this space\, by developing a geometric analogue of the circle m
 ethod.
LOCATION:MA A3 30 https://plan.epfl.ch/?room=MAA330
STATUS:CONFIRMED
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