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I will present a dimension jump result of limit sets on RP^2 for representations of surface groups in SL(3,R). For Anosov representations, we prove the equality between the Hausdorff dimension and the...
I will present a dimension jump result of limit sets on RP^2 for representations of surface groups in SL(3,R). For Anosov representations, we prove the equality between the Hausdorff dimension and the...
In this talk, I will give a survey of results related to the problem of computing Hausdorff dimension of various dynamically defined sets, such as singular vectors. The aim is to try to describe the l...
简要介绍概率论中的耦合方法及其在基础数学中的应用。引入新的变测度耦合,以简单的随机微分方程为例,将其应用于建立无穷维Harnack不等式、Bisnut导数公式和分布积分公式。
The classical Allard regularity says, a rectifiable varifold in the unit ball of the Euclidean space passing through the original point with volume density close to 1 and generalized mean curvature sm...
The passage from discrete schemes for surface line defects (steps) to nonlinear macroscopic laws for crystals is studied via formal asymptotics in one space dimension. Our goal is to illustrate by exp...
We compute the Buhler-Reichstein essential dimension of a complex abelian variety using Kummer theory.
Essential dimension is a numerical invariant of an algebraic group G introduced by J. Buhler and the second author to study the complexity of G-torsors over a eld K. It has since been studied by se...
We prove that the essential dimension of the spinor group Spinn grows exponentially with n and use this result to show that quadratic forms with trivial discriminant and Hasse-Witt invariant are more...
In this paper we consider questions of the following type. Let k be a base eld and K=k be a eld extension. Given a geometric object X over a eld K (e.g. a smooth curve of genus g) what is the le...
We affirmatively answer a conjecture in the preprint “Essential dimension and algebraic stacks,” proving that the essential dimension of an abelian variety over a number field is inʂ...
A block code from an irreducible shift of finite type can be lifted canonically through resolving maps to a resolving map. There is an application to Markovian maps.
We consider the evolution of a connected set in Euclidean space carried by a periodic incompressible stochastic ow. While for almost every realization of the random ow at time t most of the part...
The famous ergodic hypothesis suggests that for a typical Hamiltonian on a typical energy surface nearly all trajectories are dense. KAM theory disproves it.Ehrenfest (The Conceptual Foundations of th...
We show that for the Sitnikov example and for the restricted planar circular 3–body problem the set of oscillatory motions often has maximal Hausdorff dimension. Also, we construct Newhouse domains fo...

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