Workshop on Topology

Topological and combinatorial methods in Theoretical Distributed Computing

Dmitry Feichtner-Kozlov
Institute for Algebra, Geometry, Topology, and their Applications, University of Bremen
November 7, 2015
In the first half of the talk I will give a very compressed introduction into parts of Theoretical Distributed Computing from the point of view of mathematician. I will describe how to construct simplicial models whose combinatorics contains important information about computability and complexity of standard distributed tasks. In the second part, I will outline our recent progress on estimating the complexity of the so-called Weak Symmetry Breaking task, where we are able to derive some quite surprising results.

Topological similarity of random cell complexes, and applications

Benjamin Schweinhart
Princeton University
December 10, 2014
Although random cell complexes occur throughout the physical sciences, there does not appear to be a standard way to quantify their statistical similarities and differences. I'll introduce the notions of a 'swatch' and a 'cloth', which provide a description of the local topology of cell complexes which is both general (any physical system that may be represented as a regular cell complex is admissible) and complete (any statistical question about the local topology may be answered from the cloth).

Loops and Self Reference in Language and Life

Tsvi Tlusty
Weizmann Institute of Science; Member, Simons Center for Systems Biology, IAS
March 6, 2013

We will discuss the notion of loops in linguistic structures, mainly in dictionaries. In a simplified view, a dictionary is a graph that links every word (vertex) to a set of alternative words (the definition) which in turn point to further descendants. Iterating through definitions, one may loop back to the original word. We will examine possible links between such definitional loops and the emergence of new concepts during the evolution of languages. Potential relation to living systems will be briefly discussed.