Biological & Soft Matter Seminar: Tutorial Talk - Homotopy theory and classification of defects in ordered media

Zoom: https://tau-ac-il.zoom.us/j/88904888353?pwd=dDIwaXRxSjlsVElkR0dXdTNPTGhnZz09

Abstract: 

This tutorial will review the classification of topologically nontrivial structures in the order parameter fields in various ordered media, describing the common techniques and procedures for analyzing these topological field configurations. I will systematically overview examples of different singular defects and solitonic field configurations, their energetic stability and the topological classification based on the homotopy theory. The specific examples to be discussed will include topological defects and solitons in liquid crystals, magnets, ferroelectrics, superconductors and other ordered media. The large variety of symmetries accessible to these condensed matter systems will offer insights into how the symmetry of the ordered media and dimensionality of both physical and order parameter spaces determine the types of defects and solitons that can be found in a particular physical system. The tutorial will also include a discussion of how the studies of defects and solitons in media like liquid crystals and colloids can offer insights into topologically related structures in other branches of physics, with examples such as the use of nematic liquid crystal disclinations to model the behavior of elusive cosmic strings in the Early Universe cosmology.