Related papers: Asymptotic dimension in Bedlewo
These are notes to accompany my lectures at the $2024$ "Current Developments in Mathematics" conference hosted by Harvard/MIT. The lectures were about some recent progress in our understanding of two and three dimensional dynamical systems,…
This paper presents the asymptotic analysis of random lattices in high dimensions to clarify the distance properties of the considered lattices. These properties not only indicate the asymptotic value for the distance between any pair of…
The aim of these notes (which were partially covered in lectures given at the Peyresq Summer School on 17--22 June, 2002) is to give an introduction to some mathematical aspects of supersymmetry. Some (hopefully) original point of view are…
We discuss some mistakes and curiosities concerned with the celebrated First International Topological Conference in Moscow, 1935.
In May 2015, a conference entitled "Groups, Geometry, and 3-manifolds" was held at the University of California, Berkeley. The organizers asked participants to suggest problems and open questions, related in some way to the subject of the…
A nonnegative number d_infinity, called asymptotic dimension, is associated with any metric space. Such number detects the asymptotic properties of the space (being zero on bounded metric spaces), fulfills the properties of a dimension, and…
These notes partly touch the topic of the talk given by the author at the XXXVIII Workshop on Geometric Methods in Physics, hold in June-July 2019 in Bia\l{}owie\.{z}a, Poland. They consist of a short and self-contained introduction to the…
Survey written for the Proceedings of the AMS Meeting on Algebraic Geometry, Seattle, 2005. Based on the talk delivered at this occasion, but a few comments on recent developments are added.
These notes are an expanded version of an introductory lecture on contact geometry given at the 2001 Georgia Topology Conference. They are intended to present some of the "topological" aspects of three dimensional contact geometry.
A trace on the C^*-algebra A of quasi-local operators on an open manifold is described, based on the results in \cite{RoeOpen}. It allows a description `a la Novikov-Shubin \cite{NS2} of the low frequency behavior of the Laplace-Beltrami…
We consider the isometry group of the infinite dimensional separable hyperbolic space with its Polish topology. This topology is given by the pointwise convergence. For non-locally compact Polish groups, some striking phenomena like…
We introduce a geometric property complementary-finite asymptotic dimension (coas- dim). Similar with asymptotic dimension, we prove the corresponding coarse invariant theorem, union theorem and Hurewicz-type theorem.
We study asymptotics of various Euclidean geometric phenomena as the dimension tend to infinity.
Talk given at NATO ARW in Kiev (September 2000) "Non-commutative Structures in Mathematics and Physics".
This is an extended abstract of lectures delivered at the 4th Warsaw Summer School on Statistical Physics in Kazimierz Dolny, June 25-July 2, 2011.
In this paper, we derive variational formulas for the asymptotic exponents (i.e., convergence rates) of the concentration and isoperimetric functions in the product Polish probability space under certain mild assumptions. These formulas are…
The asymptotic dimension theory was founded by Gromov in the early 90s. In this paper we give a survey of its recent history where we emphasize two of its features: an analogy with the dimension theory of compact metric spaces and…
Extended abstract of "Algebraic approach to position-dependent mass systems in both classical and quantum pictures", a series of three lectures delivered by the author in the VIII School on Geometry and Physics, 24 June-8 June 2019,…
Lecture given at BW2003 Workshop "Mathematical, Theoretical and Phenomenological Challenges Beyond Standard Model" 29 August-02 September, 2003 Vrnjacka Banja, Serbia
These are expanded notes from a four lecture mini-course given by the author at the Spring School on Non-archimedean geometry and Eigenvarieties, held at the University of Heidelberg in March 2023. The course discusses coherent sheaves,…