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We consider two basic problems of algebraic topology: the extension problem and the computation of higher homotopy groups, from the point of view of computability and computational complexity. The extension problem is the following: Given topological space ...
Let u be a unipotent element of a simple algebraic group G over a field k of characteristic p. We develop a method for computing the connected component of Z(CG(u)) in the cases where p is positive and both it and the rank of G are small eno ...
Supramenability of groups is characterised in terms of invariant measures on locally compact spaces. This opens the door to constructing interesting crossed product C*-algebras for non-supramenable groups. In particular, stable Kirchberg algebras in the UC ...
n this extended abstract, we survey some of the recent results on approximating the traveling salesman problem on graphic metrics.We start by briefly explaining the algorithm of Oveis Gharan et al. [1] that has strong similarities to Christofides’ famo ...
An indoor localization method for estimating the location of nodes (n1, n2), at least one node (n1) being connected to at least another node (n2) by at least two different channels (ch1, ch1′), comprising the following steps: measuring a distance between t ...
We are developing a novel interconnection method to form reliable joints between truly stretchable electrode mounts and rigid substrates. This is needed as the electrodes must be connected to implanted electronics if they are to be used for long term impla ...
For several computational problems in homotopy theory, we obtain algorithms with running time polynomial in the input size. In particular, for every fixed k >= 2, there is a polynomial-time algorithm that, for a 1-connected topological space X given as a f ...
We define and study analogs of curve graphs for infinite type surfaces. Our definitions use the geometry of a fixed surface and vertices of our graphs are infinite multicurves which are bounded in both a geometric and a topological sense. We show that the ...
We study the steady-state probability distribution of diffusion and consensus strategies that employ constant step-sizes to enable continuous adaptation and learning. We show that, in the small step-size regime, the estimation error at each agent approache ...
We construct a distance on the moduli space of symplectic toric manifolds of dimension four. Then we study some basic topological properties of this space, in particular, path-connectedness, compactness, and completeness. The construction of the distance i ...
