Erica Uehara (Junior Associate Professor)

I’m the junior associate professor of the laboratory of physical statistics of the department of applied mathematics and physics from April 1st, 2023. My research focuses on the statistical properties of random walks with topological constraints: I’ve studied on a circular random walk (random polygon), which has the topological constraint that the end of the random walk should be equal to its origin. The statistical properties of knotted random polygons are very interesting. What is the probability of a polygon having the trivial knot or the trefoil knot? How large is the mean-square radius of knotted polygons? Recently, my research has been extended to a network of random walks, a set of random walks whose ends are topologically constrained each other. For example, a theta-shaped network is a triplet of random walks whose origins are identical and destinations are also identical. We invented a new method generating a network of random walks with any topological constraints by using the graph theory and linear algebra.
A random walk is one of coarse-grained models of a polymer chain. We’re trying to describe how topology changes polymer properties in general.

Tools for my research: Monte-Carlo method, Fortran 90/95, Wolfram Mathematica, linear algebra, graph theory, knots and links, etc.