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 socalled "Kähler package" to the nonintegrable setting. This package includes identities of various Laplacians, dualities à la Hodge, Serre and hard Lefschetz, as well as a Lefschetztype 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 socalled "motivic" symmetries. These symmetries, discovered by Dmitry&nbsp;Tamarkin, follow from a connection between Drinfeld associators and the operad&nbsp;Gerst&nbsp;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.&nbsp;I will talk about a new point of view on these symmetries, using a geometric model expressing the operad&nbsp;Gerst&nbsp;in terms of an operad in logarithmic algebraic geometry, with Betti realization the operad of little disks. This point of view implies an "integralless" proof of several algebraic results previously proven using analytic inputs, including deformationquantization. I will explain a generalization of this point of view to the operad&nbsp;BV&nbsp;responsible for BV algebras, as well as highergenus analogues. 

