Jeudi 9 Janvier

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Jeudi 9 Janvier
Heure: 09:30 - 10:30
Lieu: IHP, Salle 201
Résumé: Topologie algébrique - Topological and geometric consequences of the almost Kähler identities -
Description: Joana CiriciI will explain a generalization of the so-called "Kähler package" to the
non-integrable setting. This package includes identities of various
Laplacians, dualities à la Hodge, Serre and hard Lefschetz, as well as a
Lefschetz-type decomposition theorem on certain spaces of harmonic
forms. I will then explain some topological implications of these
identities involving Betti numbers and the fundamental group of a
compact almost Kähler manifold. In particular, I will present new
combined geometric/topological obstructions for a manifold to admit a
symplectic form compatible with a given almost complex structure.
Heure: 10:50 - 11:30
Lieu: IHP, Salle 201
Résumé: Topologie algébrique - Operads, motives and logarithmic geometry -
Description: Dmitry VaintrobThe category of (differential graded) Gerstenhaber algebras is
known to have a rich and mysterious group of so-called "motivic"
symmetries. These symmetries, discovered by Dmitry Tamarkin, follow from a connection between Drinfeld associators and the operad Gerst classifying
operations in the Gerstenhaber algebra, and imply several important
formality and rigidity results including Kontsevich's deformation
quantization theorem, that any Poisson manifold admits a quantization. I will talk about a new point of view on these symmetries, using a geometric model expressing the operad Gerst in
terms of an operad in logarithmic algebraic geometry, with Betti
realization the operad of little disks. This point of view implies an
"integral-less" proof of several algebraic results previously proven
using analytic inputs, including deformation-quantization. I will
explain a generalization of this point of view to the operad BV responsible for BV algebras, as well as higher-genus analogues.