Date/Time
Date(s) - 28/03/2025
3:30 pm - 4:30 pm

Speaker: Dr. Neal Madras (York University)
Research area: Probability theory and applications

Location: Hamilton Hall, Room 305

Title: A Discrete Mathematician’s Introduction to Polymer Topology

Abstract: A polymer is a large molecule made of many smaller units called monomers, perhaps thousands of monomers per molecule. In a branched polymer, some monomers are joined to three or more other monomers; a polymer that is not branched is linear polymer, which has the form of either a chain or a ring. Typically, a polymer has many flexible bonds, giving it a large number of possible spatial arrangements; chemists and physicists want to understand “typical” properties of these arrangements. We can rephrase such problems in terms of (asymptotic) combinatorics by treating space as a discrete periodic lattice consisting of sites and bonds, with each site being occupied by either a monomer or a solvent molecule.

This talk will focus on asymptotic enumeration questions of a topological nature, such as:  For a large ring polymer, how common are different knot types? In a large branched polymer, what branching structure is the most likely? How can topological properties be incorporated into models of adsorption (adhesion to a surface), an important kind of phase transition?  The answers are only partly known.

 

Coffee will be served in the same room, HH 305 at 3:00pm. All are welcome.