In this section, O×hol(Z) stands for the multiplicative group of the algebra Ohol(Z) of all holomorphic functions on a complex space Z, and Ohol,+(Z) for its additive group.

The configuration space $\mathcal{C}^n(X)$ of an algebraic curve $X$ is the algebraic variety consisting of all $n$-point subsets $Q\subset X$. We de…

The following proposition is Assertion (1) of Theorem 0.3:

Let M be a closed, orientable, irreducible, non-simply connected 3-manifold. We prove that if M admits a sequence of Riemannian metrics whose section…

In this section we explain the precise complexity problem studied by the GCT program, namely ¯¯¯¯¯¯¯¯¯¯¯¯VPws≠VNP, and place it in the context of Valiant’s algebraic model of NP-completeness [63, 64]. In particular, we compare this to the conjecture…

We discuss the geometry of orbit closures and the asymptotic behavior of Kronecker coefficients in the context of the Geometric Complexity Theory pro…

The authors are indebted to Pierre Liardet for valuable comments, and to the developpers of the PARI/GP system on which numerical experiments were performed.

The spectrum of a weighted Dirac comb on the Thue-Morse quasicrystal is investigated, and characterized up to a measure zero set, by means of the Bom…

Solutions of a diophantine equation $f(a,b) = g(c,d)$, with $a,b,c,d$ in some finite range, can be efficiently enumerated by sorting the values of $f…

Precession driven flows are found in any rotating container filled with liquid, when the rotation axis itself rotates about a secondary axis that is …

Let W=Mn(C), the space of complex matrices of size n. Its dimension is N=n2. The hypersurface in PW defined by the determinant is dual to the variety of rank one matrices, the Segre product Pn−1×Pn−1⊂PN−1.

We determine set-theoretic defining equations for the variety of hypersurfaces of degree d in an N-dimensional complex vector space that have dual va…

In this paper we study the maximal stable domains on minimal catenoids in Euclidean and hyperbolic spaces and in $H^2 \times R$. We in particular inv…

We give a necessary complex geometric condition for a bounded smooth convex domain in Cn, endowed with the Kobayashi distance, to be Gromov hyperboli…

A new framework for two-fluids flow using a Finite Element/Level Set method is presented and verified through the simulation of the rising of a bubbl…

Many processes in eukaryotic cells, including cell motility, rely on the growth of branched actin networks from surfaces. Despite its central role th…

In the first part of this paper we prove that the mapping class subgroups generated by the $D$-th powers of Dehn twists (with $D\geq 2$) along a spar…

When they first appear in the HR diagram, young stars rotate at a mere 10\% of their break-up velocity. They must have lost most of the angular momen…

We present a numerical study of electromagnetic reflection and cavity modes of 1D-sub-wavelength rectangular metallic gratings exposed to TM-polarize…

We construct Hadamard states for Klein-Gordon fields in a spacetime $M_{0}$ equal to the interior of the future lightcone $C$ from a base point $p$ i…

We study the tangential case in 2-dimensional almost-Riemannian geometry. We analyse the connection with the Martinet case in sub-Riemannian geometry…

We explore the influence of geometry variations on the structure and the time-dependence of the magnetic field that is induced by kinematic $\alpha^{…

We give formulas expressing Milnor invariants of an n-component link L in the 3-sphere in terms of the HOMFLYPT polynomial as follows. If the Milnor …

On montre facilement qu’un diviseur E sur une variété (lisse) X est exceptionnel si par un point général de E passe une courbe C⊂E avec E⋅C<0. On sait démontrer que cette propriété caractérise les diviseurs exceptionnels si dim(X)=2. On démontre ici…

We study the divisorial Zariski decomposition on varieties whose first Chern class is zero. We first prove that any exceptional divisor is contractib…

From 59Co and 23Na NMR, we demonstrate the impact of the Na+ vacancy ordering on the cobalt electronic states in Na0.75CoO2: at long time scales, the…

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