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SUMMARY:Motivic distribution of rational curves
DTSTART:20230516T151500
DTEND:20230516T170000
DTSTAMP:20260429T161816Z
UID:3adb8eda0f5a6ceab86d13d1ecdb70974cd5b30d61c0b9cdb172fd0b
CATEGORIES:Conferences - Seminars
DESCRIPTION:Loïs Faisant (Université Grenoble Alpes)\n\nIn diophantine g
 eometry\, the Batyrev-Manin-Peyre conjecture originally concerns rational 
 points on Fano varieties. It describes the asymptotic behaviour of the nu
 mber of rational points of bounded height\, when the bound becomes arbitra
 ry large. \n\nA geometric analogue of this conjecture deals with the asym
 ptotic behaviour of the moduli space of rational curves on a complex Fano 
 variety\, when the « degree » of the curves « goes to infinity ». Var
 ious examples support the claim that\, after renormalisation in a relevant
  ring of motivic integration\, the class of this moduli space may converg
 e to a constant which has an interpretation as a motivic Euler product. \
 n\nIn this talk\, we will state this motivic version of the Batyrev-Manin-
 Peyre conjecture and give some examples for which it is known to hold : pr
 ojective space\, more generally toric varieties\, and equivariant compact
 ifications of vector spaces. \nIn a second part we will introduce the not
 ion of equidistribution of curves and show that it opens a path to new t
 ypes of results. \n 
LOCATION:MA A3 30 https://plan.epfl.ch/?room==MA%20A3%2030
STATUS:CONFIRMED
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