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UID:20251121T152639EST-9820pbU4dc@132.216.98.100
DTSTAMP:20251121T202639Z
DESCRIPTION:From the geometry of numbers to Arakelov geometry\n\nArakelov g
 eometry is a modern formalism that extends in various directions the geome
 try of numbers founded by Minkowski in the nineteenth century. The objects
  of study are arithmetic varieties\, namely complex varieties that can be 
 defined by polynomial equations with integer coefficients. The theory expl
 oits the interplay between algebraic geometry and number theory and comple
 x analysis and differential geometry. Recently\, the formalism found beaut
 iful and important applications to the so-called Kudla programme and the C
 olmez conjecture. In the talk\, I will first introduce elementary facts in
  Minkowski's geometry of numbers. This will provide a motivation for the s
 equel\, where I will give my own view of Arakelov geometry\, by focusing o
 n toy (but non-trivial) examples of one of the central theorems in the the
 ory\, the arithmetic Riemann-Roch theorem mainly due to Bismut\, Gillet an
 d Soulé\, and generalizations. I hope there will be ingredients to satisfy
  different tastes\, for instance modular forms (arithmetic aspect)\, analy
 tic torsion (analytic aspect) and Selberg zeta functions (arithmetic\, ana
 lytic and dynamic aspects).\n
DTSTART:20170505T200000Z
DTEND:20170505T210000Z
LOCATION:Room PK-5115\, CA\, Pavillon Président-Kennedy\, 201\, ave du Prés
 ident-Kennedy
SUMMARY:Gerard Freixas\, Institut de Mathématiques de Jussieu
URL:/mathstat/channels/event/gerard-freixas-institut-d
 e-mathematiques-de-jussieu-267924
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