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Mercredi 13 juin 14:00-17:00 Werner Müller  (Bonn)
Analytic torsion of locally symmetric spaces and growth of torsion in the cohomology of arithmetic groups

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Lieu : Salle 3L8

Résumé : Analytic torsion is a spectral invariant of a compact
Riemannian manifold defined in terms of regularized determinants of Laplace
operators on forms twisted by a flat bundle. Recently, the analytic
torsion has found interesting applications in the study of the growth of
torsion
in the cohomology of cocompact arithmetic groups, i.e., of compact
locally symmetric spaces defined by arithmetic groups. Since many
arithmetic groups are not cocompact, it is interesting to extend these
results to the non-cocompact case. In this talk I will report on recent
progress concerning this problem and discuss some open questions.

Analytic torsion of locally symmetric spaces and growth of torsion in the cohomology of arithmetic groups  Version PDF

Mercredi 6 juin 14:00-17:00 Yi-Jun Yao  (Fudan et IHES)
Some results about foliations

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Lieu : Salle 3L8

Résumé : In this talk, we will discuss some results that we obtained in the past years about (regular) foliations. The tools involved include some cyclic Hopf cohomology computations that we did with Xiang Tang and Weiping Zhang,
and also the notion of Roe algebras for groupoids that we defined with Xiang Tang and Rufus Willett.

Some results about foliations  Version PDF

Mercredi 23 mai 14:00-17:00 Eckhard Meinrenken  (Toronto)
Deformation spaces and normal forms

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Lieu : Salle 3L8

Résumé : We will use the deformation to the normal cone’ construction to
prove old and new normal form theorems, ranging from the Morse Lemma and
the Weinstein splitting theorem to local normal forms for Lie algebroids
and related structures. A central ingredient of these proofs is a
linearization lemma for Euler-like vector fields.

Deformation spaces and normal forms  Version PDF

Mercredi 16 mai 14:00-17:00 Farhad Babaee  (Fribourg (Suisse))
Complex tropical currents, and approximability problems

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Lieu : IMO Salle 3L8

Résumé : Demailly (2012) showed that the Hodge conjecture is equivalent to the statement that any (p,p)-dimensional closed current with rational cohomology class can be approximated by linear combinations of integration currents ; Moreover, the statement that all positive currents with rational cohomology class can be approximated by positive linear combinations of integration currents implies the Hodge conjecture (1982). In this talk, I will explain how basic ideas from tropical and toric geometry can lead to construction of a family of currents which does not satisfy the latter statement in any dimension and codimension higher than 1. The talk is based on collaborations with June Huh and Karim Adiprasito.

Complex tropical currents, and approximability problems  Version PDF