Archiv aktualit
 Seminář z diferenciální geometrie - 2.12.2019

Seminář z diferenciální geometrie pokračuje 2.12.2019 od 10:00 v učebně M5

#### Vincent Pecastaing (University of Luxembourg):

Actions of higher-rank lattices on conformal and projective structures

Abstrakt:
The main idea of Zimmer's program is that in real-rank at least 2, the rigidity of lattices of semi-simple Lie groups makes that their actions on closed manifolds are understandable. After a short survey giving a more precise idea of Zimmer's conjectures and their context, I will give recent results about conformal and projective actions of cocompact lattices. The fact that these geometric structures do not carry a natural invariant volume is one of the main motivations. We will see that the real-rank is bounded above like when the ambient Lie group is acting, and that at the critical value, the manifold is globally isomorphic to a model homogeneous space. The proofs rely in part on an "invariance principle" recently introduced by Brown, Rodriguez-Hertz and Wang, which guarantees the existence of finite invariant measures in some dynamical context.

Aktualizováno Pátek, 29 Listopad 2019 14:35

 Seminář z algebry - 28.11.2019

Další seminář z algebry se koná 28.11.2019 od 13.00 v posluchárně M5.

#### J. R. Gonzales

Grothendieck categories and their tensor product as filtered colimits

Abstrakt:
Grothendieck categories are the Ab-enriched Grothendieck topoi. In this talk, we will first show two different ways to obtain a Grothendieck category as a filtered colimit of its representing linear sites: one given by all possible representing linear sites, the other, coarser, given by the representing linear sites induced by the full subcategories of alpha-presentable objects, with varying regular cardinal alpha. Making use of the latter, we show that the tensor product of Grothendieck categories, introduced in previous joint work with Lowen and Shoikhet, is compatible via this construction with Kelly's alpha-cocomplete tensor product. This allows us to translate the functoriality, simmetry and commutativity of Kelly's tensor product to the tensor product of Grothendieck categories.

Aktualizováno Pondělí, 25 Listopad 2019 16:14

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