12 research outputs found
Topological defects in spinor condensates
We investigate the structure of topological defects in the ground states of
spinor Bose-Einstein condensates with spin F=1 or F=2. The type and number of
defects are determined by calculating the first and second homotopy groups of
the order-parameter space. The order-parameter space is identified with a set
of degenerate ground state spinors. Because the structure of the ground state
depends on whether or not there is an external magnetic field applied to the
system, defects are sensitive to the magnetic field. We study both cases and
find that the defects in zero and non-zero field are different.Comment: 10 pages, 1 figure. Published versio
A lattice in more than two Kac--Moody groups is arithmetic
Let be an irreducible lattice in a product of n infinite irreducible
complete Kac-Moody groups of simply laced type over finite fields. We show that
if n is at least 3, then each Kac-Moody groups is in fact a simple algebraic
group over a local field and is an arithmetic lattice. This relies on
the following alternative which is satisfied by any irreducible lattice
provided n is at least 2: either is an S-arithmetic (hence linear)
group, or it is not residually finite. In that case, it is even virtually
simple when the ground field is large enough.
More general CAT(0) groups are also considered throughout.Comment: Subsection 2.B was modified and an example was added ther
Property (T) and rigidity for actions on Banach spaces
We study property (T) and the fixed point property for actions on and
other Banach spaces. We show that property (T) holds when is replaced by
(and even a subspace/quotient of ), and that in fact it is
independent of . We show that the fixed point property for
follows from property (T) when 1
. For simple Lie groups and their lattices, we prove that the fixed point property for holds for any if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive Banach spaces.Comment: Many minor improvement
Anosov representations: Domains of discontinuity and applications
The notion of Anosov representations has been introduced by Labourie in his
study of the Hitchin component for SL(n,R). Subsequently, Anosov
representations have been studied mainly for surface groups, in particular in
the context of higher Teichmueller spaces, and for lattices in SO(1,n). In this
article we extend the notion of Anosov representations to representations of
arbitrary word hyperbolic groups and start the systematic study of their
geometric properties. In particular, given an Anosov representation of
into G we explicitly construct open subsets of compact G-spaces, on which
acts properly discontinuously and with compact quotient.
As a consequence we show that higher Teichmueller spaces parametrize locally
homogeneous geometric structures on compact manifolds. We also obtain
applications regarding (non-standard) compact Clifford-Klein forms and
compactifications of locally symmetric spaces of infinite volume.Comment: 63 pages, accepted for publication in Inventiones Mathematica
Concurrent shifts in wintering distribution and phenology in migratory swans: Individual and generational effects
Range shifts and phenological change are two processes by which organisms respond to environmental warming. Understanding the mechanisms that drive these changes is key for optimal conservation and management. Here we study both processes in the migratory Bewick's swan (Cygnus columbianus bewickii) using different methods, analysing nearly 50 years of resighting data (1970–2017). In this period the wintering area of the Bewick's swans shifted eastwards (‘short-stopping’) at a rate of ~13 km/year, thereby shortening individual migration distance on an average by 353 km. Concurrently, the time spent at the wintering grounds has reduced (‘short-staying’) by ~38 days since 1989. We show that individuals are consistent in their migratory timing in winter, indicating that the frequency of individuals with different migratory schedules has changed over time (a generational shift). In contrast, for short-stopping we found evidence for both individual plasticity (individuals decrease their migration distances over their lifetime) and generational shift. Additional analysis of swan resightings with temperature data showed that, throughout the winter, Bewick's swans frequent areas where air temperatures are c. 5.5°C. These areas have also shifted eastwards over time, hinting that climate warming is a contributing factor behind the observed changes in the swans' distribution. The occurrence of winter short-stopping and short-staying suggests that this species is to some extent able to adjust to climate warming, but benefits or repercussions at other times of the annual cycle need to be assessed. Furthermore, these phenomena could lead to changes in abundance in certain areas, with resulting monitoring and conservation implications. Understanding the processes and driving mechanisms behind population changes therefore is important for population management, both locally and across the species range
Year-round spatiotemporal distribution pattern of a threatened sea duck species breeding on Kolguev Island, south-eastern Barents Sea
Simplicity and superrigidity of twin building lattices
Kac-Moody groups over finite fields are finitely generated groups. Most of them can naturally be viewed as irreducible lattices in products of two closed automorphism groups of non-positively curved twinned buildings: those are the most important (but not the only) examples of twin building lattices. We prove that these lattices are simple if the corresponding buildings are irreducible and not of affine type (i.e. they are not Bruhat-Tits buildings). Many of them are finitely presented and enjoy property (T). Our arguments explain geometrically why simplicity fails to hold only for affine Kac-Moody groups. Moreover we prove that a nontrivial continuous homomorphism from a completed Kac-Moody group is always proper. We also show that Kac-Moody lattices fulfill conditions implying strong superrigidity properties for isometric actions on non-positively curved metric spaces. Most results apply to the general class of twin building lattices