18,898 research outputs found
Financing Europe's Fast Movers. Bruegel Policy Brief 2008/01, January 2008
Summary. Arguments about structural policies in Europe, including the EU’s Lisbon strategy, put a legitimate emphasis on labour and product market reforms, but often overlook the role of the financial system in fostering innovation and growth. Corporate finance is crucial for the emergence of new companies, well beyond the much-analysed technology sector. In a knowledge economy where companies rely less on physical investment, traditional bank loans are insufficient. While Europe has a world-class financial system for established companies, new instruments tailored to the needs of emerging firms remain underdeveloped in most EU countries
The mirror conjecture for minuscule flag varieties
We prove Rietsch's mirror conjecture that the Dubrovin quantum connection for
minuscule flag varieties is isomorphic to the character D-module of the
Berenstein-Kazhdan geometric crystal. The idea is to recognize the quantum
connection as Galois and the geometric crystal as automorphic. We reveal
surprising relations with the works of Frenkel-Gross, Heinloth-Ng\^o-Yun and
Zhu on Kloosterman sheaves. The isomorphism comes from global rigidity results
where Hecke eigensheaves are determined by their local ramification. As
corollaries we obtain combinatorial identities for counts of rational curves
and the Peterson variety presentation of the small quantum cohomology ring
Combinatorial substitutions and sofic tilings
A combinatorial substitution is a map over tilings which allows to define
sets of tilings with a strong hierarchical structure. In this paper, we show
that such sets of tilings are sofic, that is, can be enforced by finitely many
local constraints. This extends some similar previous results (Mozes'90,
Goodman-Strauss'98) in a much shorter presentation.Comment: 17 pages, 16 figures. In proceedings of JAC 201
Purification of single-photon entanglement with linear optics
We show that single-photon entangled states of the form |0>|1>+|1>|0> can be
purified with a simple linear-optics based protocol, which is eminently
feasible with current technology. Besides its conceptual interest, this result
is relevant for attractive quantum repeater protocols.Comment: 4 pages, 3 figure
Security of Quantum Key Distribution with Entangled Qutrits
The study of quantum cryptography and quantum non-locality have
traditionnally been based on two-level quantum systems (qubits). In this paper
we consider a generalisation of Ekert's cryptographic protocol [Ekert] where
qubits are replaced by qutrits. The security of this protocol is related to
non-locality, in analogy with Ekert's protocol. In order to study its
robustness against the optimal individual attacks, we derive the information
gained by a potential eavesdropper applying a cloning-based attack.Comment: 9 pages original version: july 2002, replaced in january 2003
(reason: minor changes
Rational curves on homogeneous cones
Let G/Q be an homogeneous variety embedded in a projective space P thanks to
an ample line bundle L. Take a projective space containing P and form the cone
X over G/Q, we call this a cone over an homogeneous variety.
Let a class of 1-cycle on X. In this article we describe the
irreducible components of the scheme of morphisms of class from a
rational curve to X.
The situation depends on the line bundle L : if the projectivised tangent
space to the vertex contains lines (i.e. if G/Q contains lines in P) then the
irreducible components are described as in our paper math.AG/0407123 by the
difference between Cartier and Weil divisors. On the contrary if there is no
line in the projectivised tangent space to the vertex then there are new
irreducible components corresponding to the multiplicity of the curve through
the vertex.
As in math.AG/0407123 we use a resolution Y of X (the blowing-up) and study
the curves on Y.Comment: In english, 13 page
- …