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SUMMARY:Motives\, quadratic forms and arithmetic
DTSTART;VALUE=DATE-TIME:20210607T060000Z
DTEND;VALUE=DATE-TIME:20210611T150000Z
DTSTAMP;VALUE=DATE-TIME:20210506T221800Z
UID:indico-event-6044@indico.math.cnrs.fr
DESCRIPTION:\n\n*** Postponed ***\n\n(April 4th\, 2021) Due to the ongoing
sanitary crisis and its latest developments in France\, we regretfully ha
ve to postpone the conference\, very likely to May or June 2022.\n\nTheme\
n\nMotives were originally introduced by Grothendieck in the sixties to pr
ovide a universal source to various cohomology theories of algebraic\, geo
metric and arithmetic nature.\n\nThe works of Hanamura\, Levine and Voevod
sky in the nineties\, followed by many others\, have shed a new light on t
he subject by introducing triangulated categories of motives and relating
them to a newly defined homotopy category of schemes. More recent avatars
of motives include the motives with modulus of Kahn\, Miyazaki\, Saito and
Yamazaki or the log-motives of Binda\, Park and Østvær\, both purposely
avoiding A1-invariance.\n\nMotivic methods have also pervaded arithmetic
geometry\, which is the use of methods of algebraic geometry over a base o
f arithmetic nature such as a number field\, in order to study number theo
retical problems such as Diophantine equations. Several famous unresolved
conjectures predict general patterns and guide mathematicians in the area\
, among which Grothendieck's standard conjectures\, the Hodge conjecture(s
)\, the Tate conjecture and the Beilinson conjecture.\n\nThe remaining the
me of this conference\, quadratic forms\, is a subject in its own right. T
he algebraic theory of quadratic forms over fields has bloomed in the last
fifty years\, with tremendous progress in the computations of their discr
ete invariants. The connexion with motives goes both ways: the understandi
ng of the motives of geometric objects related to quadratic forms\, such a
s quadrics\, has been the source of many beautiful results on quadratic fo
rms\, while in reverse\, invariants of quadratic nature\, such as Hermitia
n K-theory or Chow-Witt groups somewhat surprisingly appear in the endomor
phisms of the motivic stable homotopy category of schemes.\n\nSpeakers / O
rateurs\n\n\n \n Luca Barbieri-Viale (Milan)\n \n \n Olivier Benoist (Pari
s)\n \n \n Federico Binda (Milan)\n \n \n Jean-Louis Colliot-Thélène (O
rsay) \n \n \n Frédéric Déglise (Lyon)\n \n \n Hélène Esnault (Berli
n)\n \n \n Florian Ivorra (Rennes)\n \n \n Moritz Kerz (Regensburg) - to b
e confirmed\n \n \n Florence Lecomte (Strasbourg)\n \n \n Marc Levine (Ess
en)\n \n \n Hiroyasu Miyazaki (Takao)\n \n \n Alena Pirutka (New-York\, Pa
ris)\n \n \n Sujatha (Vancouver)\n \n \n Claire Voisin (Paris)\n \n \n Ol
ivier Wittenberg (Villetaneuse)\n \n \n Takao Yamazaki (Sendai)\n \n\n\nOr
ganizers / Organisateurs\n\nJérôme Burési\, Baptiste Calmès\, Ivo Dell
'Ambrogio\, Ahmed Laghribi\n\nScientific Committee / Comité scientifique\
n\nYves André\, Anna Cadoret\, Shuji Saito\n\n \nhttps://indico.math.cnr
s.fr/event/6044/
LOCATION:
URL:https://indico.math.cnrs.fr/event/6044/
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