Search results for "Group action"
showing 5 items of 15 documents
Entropy, Lyapunov exponents, and rigidity of group actions
2018
This text is an expanded series of lecture notes based on a 5-hour course given at the workshop entitled "Workshop for young researchers: Groups acting on manifolds" held in Teres\'opolis, Brazil in June 2016. The course introduced a number of classical tools in smooth ergodic theory -- particularly Lyapunov exponents and metric entropy -- as tools to study rigidity properties of group actions on manifolds. We do not present comprehensive treatment of group actions or general rigidity programs. Rather, we focus on two rigidity results in higher-rank dynamics: the measure rigidity theorem for affine Anosov abelian actions on tori due to A. Katok and R. Spatzier [Ergodic Theory Dynam. Systems…
A construction of equivariant bundles on the space of symmetric forms
2021
We construct stable vector bundles on the space of symmetric forms of degree d in n+1 variables which are equivariant for the action of SL_{n+1}(C), and admit an equivariant free resolution of length 2. For n=1, we obtain new examples of stable vector bundles of rank d-1 on P^d, which are moreover equivariant for SL_2(C). The presentation matrix of these bundles attains Westwick's upper bound for the dimension of vector spaces of matrices of constant rank and fixed size.
On the nonarchimedean quadratic Lagrange spectra
2018
We study Diophantine approximation in completions of functions fields over finite fields, and in particular in fields of formal Laurent series over finite fields. We introduce a Lagrange spectrum for the approximation by orbits of quadratic irrationals under the modular group. We give nonarchimedean analogs of various well known results in the real case: the closedness and boundedness of the Lagrange spectrum, the existence of a Hall ray, as well as computations of various Hurwitz constants. We use geometric methods of group actions on Bruhat-Tits trees. peerReviewed
homogeneous embeddings of SL2(C) modulo a finite sub-group.
2000
L'objet de ce travail est l'étude des variétés algébriques normales complexes munies d'une action algébrique de $SL_{2}$ et qui contiennent $SL_{2}/H$ comme orbite ouverte, $H$ étant un sous-groupe fini de $SL_{2}$.Plus précisément on définit un plongement homogène de $SL_{2}/H$ comme la donnée d'une $SL_{2}$-variété irréductible $X$ (quasi-projective ou non) contenant $SL_{2}/H$ comme orbite ouverte et d'un morphisme $SL_{2}$-équivariant de $SL_{2}$ dans $X$.Les plongements homogènes lisses ainsi que les plongements minimaux (plongements lisses et complets qui ne sont pas des éclatements d'un autre plongement lisse complet) de $SL_{2}/\{Id\}$ et de $SL_{2}/\{\pm Id\}$ ont été déterminés pa…