Topology Seminar- Topological methods for measuring entanglement in polymers

Speaker:Eleni Panagiotou (University of Tennessee at Chattanooga)
Date and time: Thursday, March 5, 5--6:00pm
Place: 1776 G street,  C-119
Title:  Topological methods for measuring entanglement in polymers

Abstract: .In this talk we will see how measures of entanglement complexity stemming from knot theory can be used to extract information related to material properties.In particular, we use Molecular Dynamics  simulations of polymers in different topologies and use the linking number to demonstrate that the topology relates to their mechanics. Physical filaments like polymers rarely satisfy the conditions needed to apply tools from knot theory directly and the only rigorous mathematical measures that we had so far where based on the Gauss linking integral. In this talk we will introduce a new definition of the Jones polynomial which reduces to the classical definition in the case of closed curves and is a continuous measure of entanglement complexity in the case of open curves in 3-space.