We study distributed linearization or topological sorting in peer-to-peer networks. We define strict and eventual versions of the problem and consider these problems with and without input identifiers that do not exist in the system. None of these problems are solvable in the asynchronous messagepassing systems. We define a collection of oracles and prove which oracle combination is necessary t...

How to look at a dynamical system f at a small scale You should take a small piece of the phase space consider the rst return map to this piece and then rescale it to the original size The new dynamical system is called the renormalization Rf of the original one It may happen that Rf looks similar to f and then you can try to repeat this procedure and construct the second renormalization R f et...

[1] Estimates for the number of automorphisms of a Riemann surface, Sib. Math. J. 38 (1997), no. 5, 860–867. [2] On Wiman bound for arithmetic Riemann surfaces, with Grzegorz Gromadzki, Glasgow Math. J. 45 (2003), 173–177. [3] Cells and representations of right-angled Coxeter groups, Selecta Math., N. S. 10 (2004), 325–339. [4] On volumes of arithmetic quotients of SO(1,n), Ann. Scuola Norm. Su...