Related papers: Asymptotic dimension in Bedlewo
We analytically compute asymptotic expansions of a 1-dimensional sub-manifold of stable and unstable manifolds in a 4-dimensional symplectic mapping by using the method called asymptotic expansions beyond all orders. This method enables us…
This is a brief review paper summarizing talks at the NATO school on Complexity and Large Deviations in Geilo, Norway, 2001.
This is a survey of open problems in different parts of combinatorial and additive number theory. The paper is based on lectures at the Centre de Recerca Matematica in Barcelona on January 23 and January 25, 2008.
This text is a set of lecture notes for a series of four talks given at I.P.A.M., Los Angeles, on March 18-20, 2003. The first lecture provides a quick overview of symplectic topology and its main tools: symplectic manifolds, almost-complex…
We study the complexity with respect to Borel reducibility of the relations of isometry and isometric embeddability between ultrametric Polish spaces for which a set $D$ of possible distances is fixed in advance. These are, respectively, an…
We propose a novel approach to dimensionality reduction combining techniques of metric geometry and distributed persistent homology, in the form of a gradient-descent based method called DIPOLE. DIPOLE is a dimensionality-reduction…
BMS symmetries have been attracting a great deal of interest in recent years. Originally discovered as being the symmetries of asymptotically flat spacetime geometries at null infinity in General Relativity, BMS symmetries have also been…
Based on comments made at the 23rd Solvay Conference, December 2005, Brussels.
These are notes for a summer course given at the PIMS Summer School on Geometric and Topological Aspects of the Representation Theory of Finite Groups in Vancouver, July 27-30 2016.
Lectures given at the CIMPA School "Geometrie sous-riemannienne", Beirut, Lebanon, 2012
In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve…
This is an expanded version of the lecture notes for a minicourse that I gave at a summer school called "Advanced Course on Geometry and Dynamics of Integrable Systems" at CRM Barcelona, 9--14/September/2013. In this text we study the…
Open problems of the conference "Automorphisms of Affine Spaces" held July 6-10 2009 at the Radboud University, Nijmegen, The Netherlands.
We survey some recent developments in the asymptotic geometry of the Hitchin moduli space, starting with an introduction to the Hitchin moduli space and hyperk\"ahler geometry.
Searches for extra dimensions have been made at the four LEP experiments, ALEPH, DELPHI, L3 and OPAL, where different processes have been searched for within both the ADD and Randall-Sundrum scenarios. Since no signs of any signal have been…
In three and two dimensions the asymptotic symmetry groups of $AdS$ spaces are infinite dimensional. This can be explained easily by noting the relations $AdS_3 \simeq SL(2)$ and $AdS_2 \simeq SL(2)/SO(2)$, i.e. that the asymptotic…
The article is an attempt to investigate the issues of asymptotic analysis for problems involving fractional Laplacian where the domains tend to become unbounded in one-direction. Motivated from the pioneering work on second order elliptic…
This text is based on lectures by the author in the Summer School `Algebraic Geometry and Hypergeometric Functions' in Istanbul in June 2005. It gives a review of some of the basic aspects of the theory of hypergeometric structures of…
Recently, chains of increasing symmetric ideals have attracted considerable attention. In this note, we summarize some results and open problems concerning the asymptotic behavior of several algebraic and homological invariants along such…
We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the…