Speaker: Yuriy Mileyko (UH)

Title: Internet and its Dimensions

Abstract

The large-scale structure of the Internet (or, rather of the graph of
the Autonomous System Nodes) has been attracting a lot of attention by
the researchers for decades. One family of attractive models for this
graph stipulates that it “looks like” is if sampled from a hyperbolic
plane. We shall discuss possible tests for the dimension of samples from
manifolds, and apply them to the ANS graph.

Speaker: Nicolas Monod (Ecole Poly Fed. de Lausanne)

Title: Cutting and pasting: Frankenstein’s method in group theory

Abstract:
We have known for a century that a ball can be decomposed into five pieces and these pieces rearranged so as to produce two balls of the same size as the original.
This apparent paradox has led von Neumann to the notion of amenability which is now much studied in many areas of mathematics.
However, the initial paradox has remained tied down to an elementary property of free groups of rotations for most of the 20th century. I will describe recent progress leading to new paradoxical groups.