4,014 research outputs found
Arithmeticity vs. non-linearity for irreducible lattices
We establish an arithmeticity vs. non-linearity alternative for irreducible
lattices in suitable product groups, such as for instance products of
topologically simple groups. This applies notably to a (large class of)
Kac-Moody groups. The alternative relies on a CAT(0) superrigidity theorem, as
we follow Margulis' reduction of arithmeticity to superrigidity.Comment: 11 page
On the cohomology of some exceptional symmetric spaces
This is a survey on the construction of a canonical or "octonionic K\"ahler"
8-form, representing one of the generators of the cohomology of the four
Cayley-Rosenfeld projective planes. The construction, in terms of the
associated even Clifford structures, draws a parallel with that of the
quaternion K\"ahler 4-form. We point out how these notions allow to describe
the primitive Betti numbers with respect to different even Clifford structures,
on most of the exceptional symmetric spaces of compact type.Comment: 12 pages. Proc. INdAM Workshop "New Perspectives in Differential
Geometry" held in Rome, Nov. 2015, to appear in Springer-INdAM Serie
Even Galois Representations and the Fontaine--Mazur conjecture II
We prove, under mild hypotheses, that there are no irreducible
two-dimensional_even_ Galois representations of \Gal(\Qbar/\Q) which are de
Rham with distinct Hodge--Tate weights. This removes the "ordinary" hypothesis
required in previous work of the author. We construct examples of irreducible
two-dimensional residual representations that have no characteristic zero
geometric (= de Rham) deformations.Comment: Updated to take into account suggestions of the referee; the main
theorems remain unchange
Noise characterization of transistors in a 1.2 m CMOS-SOI technology up to a total dose of 12 Mrad (SI)
Reduction and approximation in gyrokinetics
The gyrokinetics formulation of plasmas in strong magnetic fields aims at the
elimination of the angle associated with the Larmor rotation of charged
particles around the magnetic field lines. In a perturbative treatment or as a
time-averaging procedure, gyrokinetics is in general an approximation to the
true dynamics. Here we discuss the conditions under which gyrokinetics is
either an approximation or an exact operation in the framework of reduction of
dynamical systems with symmetryComment: 15 pages late
Chaos for Liouville probability densities
Using the method of symbolic dynamics, we show that a large class of
classical chaotic maps exhibit exponential hypersensitivity to perturbation,
i.e., a rapid increase with time of the information needed to describe the
perturbed time evolution of the Liouville density, the information attaining
values that are exponentially larger than the entropy increase that results
from averaging over the perturbation. The exponential rate of growth of the
ratio of information to entropy is given by the Kolmogorov-Sinai entropy of the
map. These findings generalize and extend results obtained for the baker's map
[R. Schack and C. M. Caves, Phys. Rev. Lett. 69, 3413 (1992)].Comment: 26 pages in REVTEX, no figures, submitted to Phys. Rev.
Is every toric variety an M-variety?
A complex algebraic variety X defined over the real numbers is called an
M-variety if the sum of its Betti numbers (for homology with closed supports
and coefficients in Z/2) coincides with the corresponding sum for the real part
of X. It has been known for a long time that any nonsingular complete toric
variety is an M-variety. In this paper we consider whether this remains true
for toric varieties that are singular or not complete, and we give a positive
answer when the dimension of X is less than or equal to 3.Comment: 13 page
Global Jacquet-Langlands correspondence, multiplicity one and classification of automorphic representations
In this paper we show a local Jacquet-Langlands correspondence for all
unitary irreducible representations. We prove the global Jacquet-Langlands
correspondence in characteristic zero. As consequences we obtain the
multiplicity one and strong multiplicity one theorems for inner forms of GL(n)
as well as a classification of the residual spectrum and automorphic
representations in analogy with results proved by Moeglin-Waldspurger and
Jacquet-Shalika for GL(n).Comment: 49 pages; Appendix by N. Grba
The word and Riemannian metrics on lattices of semisimple groups
Let G be a semisimple Lie group of rank ≥ 2 and Γ an irreducible lattice. Γ has two natural metrics: a metric inherited from a Riemannian metric on the ambient Lie group and a word metric defined with respect to some finite set of generators. Confirming a conjecture of D. Kazhdan (cf. Gromov [Gr2]) we show that these metrics are Lipschitz equivalent. It is shown that a cyclic subgroup of Γ is virtually unipotent if and only if it has exponential growth with respect to the generators of Γ
Tits-Satake projections of homogeneous special geometries
We organize the homogeneous special geometries, describing as well the
couplings of D=6, 5, 4 and 3 supergravities with 8 supercharges, in a small
number of universality classes. This relates manifolds on which similar types
of dynamical solutions can exist. The mathematical ingredient is the
Tits-Satake projection of real simple Lie algebras, which we extend to all
solvable Lie algebras occurring in these homogeneous special geometries. Apart
from some exotic cases all the other, 'very special', homogeneous manifolds can
be grouped in seven universality classes. The organization of these classes,
which capture the essential features of their basic dynamics, commutes with the
r- and c-map. Different members are distinguished by different choices of the
paint group, a notion discovered in the context of cosmic billiard dynamics of
non maximally supersymmetric supergravities. We comment on the usefulness of
this organization in universality classes both in relation with cosmic billiard
dynamics and with configurations of branes and orbifolds defining special
geometry backgrounds.Comment: 65 pages, LaTeX; v2: added reference; v3: small corrections, section
3.3 modifie
- …