Concept

Coherent sheaf

Publications associées (55)

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Ultrafast tristable spin memory of a coherent polariton gas

Benoît Marie Joseph Deveaud, François Morier-Genoud, Marcia Portella Oberli, Taofiq Paraïso, Roland Cerna

Non-linear interactions in coherent gases are not only at the origin of bright and dark solitons and superfluids; they also give rise to phenomena such as multistability, which hold great promise for the development of advanced photonic and spintronic devi ...

Nature Publishing Group2013

Unified mechanistic multiscale mapping of two-phase flow patterns in microchannels

John Richard Thome, Rémi Revellin, Iztok Zun

To better understand the underlying two-phase phenomena and thus better predict transitions between the various two-phase flow patterns, it is necessary to update our way of thinking from one-of-a-kind flow pattern maps of limited applicability to a genera ...

Elsevier2013

On the second successive minimum of the Jacobian of a Riemann surface

To a compact Riemann surface of genus g can be assigned a principally polarized abelian variety (PPAV) of dimension g, the Jacobian of the Riemann surface. The Schottky problem is to discern the Jacobians among the PPAVs. Buser and Sarnak showed that the s ...

Springer Netherlands2012

Invariant frames for vector bundles and applications

Tudor Ratiu, Madeleine Jotz

This paper completes a proof of the Dirac reduction theorem by involutive tangent subbundles. As a consequence, Dirac reduction by a proper Lie group action having one isotropy type is carried out. The main technical tool in the proof is the notion of part ...

Springer Verlag2012

The norm of the Euler class

Nicolas Monod

We prove that the norm of the Euler class

\mathcal{E}

for flat vector bundles is

2^{-n}

(in even dimension

n

, since it vanishes in odd dimension). This shows that the Sullivan-Smillie bound considered by Gromov and Ivanov-Turaev is sharp. We construc ...

Springer Verlag2012

Generalized tensor idempotents and the telescope conjecture

Giordano Favi

We transpose Rickard's construction of idempotent representations to the general context of tensor triangulated categories. We connect our construction to the telescope conjecture and prove that the latter is of local nature. As an illustration, we extend ...

2011

Capacities, Systoles and Jacobians of Riemann Surfaces

Björn Mützel

To any compact Riemann surface of genus g one may assign a principally polarized abelian variety (PPAV) of dimension g, the Jacobian of the Riemann surface. The Jacobian is a complex torus and we call a Gram matrix of the lattice of a Jacobian a period Gra ...

EPFL2011

Categorical Foundations for K-theory

Nicolas Mathieu Michel

K-Theory was originally defined by Grothendieck as a contravariant functor from a subcategory of schemes to abelian groups, known today as K0. The same kind of construction was then applied to other fields of mathematics, like spaces and (not necessarily c ...

EPFL2010

Sub-Rayleigh resolution by phase imaging

Christian Depeursinge, Nicolas Pavillon, Etienne Shaffer, Muhammed Fatih Toy, Yann Jérôme Michel Pascal Cotte

We report the experimental observation of systematically occurring phase singularities in coherent imaging of sub-Rayleigh distanced objects. A theory that relates the observation to the sub-Rayleigh distance is presented and compared with experimental mea ...

Optical Society of America2010

Singularities of generic characteristic polynomials and smooth finite splittings of Azumaya algebras over surfaces

Manuel Ojanguren

Let k be an algebraically closed field. Let P(X-11,...,X-nn, T) be the characteristic polynomial of the generic matrix (X-ij) over k. We determine its singular locus as well as the singular locus of its Galois splitting. If X is a smooth quasi-projective s ...

Springer-Verlag2009

The norm of the Euler class

Nicolas Monod

We prove that the norm of the Euler class

\mathcal{E}

for flat vector bundles is

2^{-n}

(in even dimension

n

, since it vanishes in odd dimension). This shows that the Sullivan-Smillie bound considered by Gromov and Ivanov-Turaev is sharp. We construc ...

Springer Verlag2012