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There is a well developed theory (see [5, 9]) of analysis on certain types of fractal sets, of which the Sierpinski Gasket (SG) is the simplest non-trivial example. In this theory the fractals are vie...
We prove a Beurling-Helson type theorem on modulation spaces. More precisely, we show that the only C1 changes of variables that leave invariant themodulation spaces Mp,q(Rd) are affine functions on R...
We prove analogues for Cartan geometries of Gromov's major theorems on automorphisms of rigid geometric structures. The starting point is a Frobenius theorem, which says that in nitesimal automorphis...
The main motivation of this paper arises from classical questions about actions of Lie groups preserving a geometric structure: which Lie groups can act on a manifold preserving a given structure, a...
We prove that a recurrent random walk (RW) in i.i.d. random environment (RE) on a strip which does not obey the Sinai law exhibits the Central Limit asymptotic behaviour.
We consider excited random walk on a strip. We assume that the cookies are positive and that the total expected drift per site is less than 1/L where L is the width of the strip. We prove a quenched...
We prove a local limit the sums of independent random vectors satisfying appropriate tightness assumptions. In particular, the local limit theorem holds in dimension 1 if the summands are uniformly bo...
An Extension of Barbashin-Kraso vski-LaSalle Theorem to a Class of Nonautonomous Systems.
We consider the evolution of a connected set on the plane carried by a space periodic incompressible stochastic flow. While for almost every realization of the stochastic flow at time t ...
In 1912 Bieberbach proved that every compact flat Riemannian manifold M is finitely covered by a flat torus. More precisely, M has the form (F\G)/H where G is a group of translations of Euclidean ...
The ˉrst ingredient is quite deep, and we will not say anything much about its proof, using it simply as a \black box". The second ingredient is elementary, and we take this opportunity to present a...
We consider the evolution of a connected set on the plane carried by a space periodic incompressible stochastic flow. While for almost every realization of the stochastic flow at time t mo...
Consider an elliptic curve E without complex multiplication defined over the rationals.The absolute Galois group of Q acts on the group of torsion points of E, and this action can be expressed in term...
We describe an explicit version of Hilbert’s irreducibility theorem using a generalization of Gallagher’s larger sieve. We give applications to the Galois theory of random polynomials, and to the imag...
We present a simple constructive proof of the Uniformization Theorem which works for plane domains. The proof is a combination of covering space theory and Koebe's constructive proof of the Riemann ma...

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