# Mathematics Colloquia and Seminars

A typical bacterial chromosome, for example the chromosome of the \emph{Escherichia coli} organism, occurs as a circular DNA molecule. During replication, two interlinked daughter chromosomes are produced. The cell employs a host of enzymes which correct topological linking via strand-passage or site-specific recombination, ensuring the survival of the cell. Circular DNA is modeled as a topological knot or link, and the most relevant links in this context are the $T(2, n)$ torus links, the most common of which is the right-handed trefoil $T(2, 3)$. Local reconnection events on circular DNA, in particular, site-specific recombination at sites in direct repeat or inverted repeat, are modeled topologically by band surgery operations on knots and links. Within this knot theoretic framework, we classify all band surgery operations from the trefoil knot to the $T(2, n)$ knots and links. This is accomplished by classifying certain Dehn surgeries on knots in the lens space $L(3, 1)$, a result which is proved by studying the behavior of the Heegaard Floer d-invariants under integral surgery along knots in $L(3,1)$. This project is joint work with Lidman and Vazquez.