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Welcome to the Topological Molecular Biology Lab at UC Davis!

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Our group is interested in applications of topological methods to understand the three dimensional organization of the genome in different organisms, to study genome rearrangements and copy number changes in cancer, and to model the action of enzymes such as recombinases and topoisomerases. We use a combination of mathematical and computational methods including tools from low-dimensional topology, computational knot theory, random knotting, algebraic topology, persistence homology, combinatorics, statistics, Monte Carlo methods and computer visualization.

Our random knotting research involves studying topological and geometrical properties of link diagrams and of linked polygons. For example, the modeling of DNA and of enzymatic reactions has led us to generate very large ensembles of polygons in the simple cubic lattice. This has led to inquiring about their behavior when restricted to confined environments, as well as their minimal step number. We are also very interested in chirality, and need reliable nomenclature to distinguish between chiral pairs of knots, as well as between different symmetry types of two component links.
Find here the Symmetry motivated knot table and link table

We are deeply committed to promoting diversity in mathematics and the sciences. Our goal is to lead a truly interdisciplinary and vertically integrated group at the interface of mathematics and molecular biology. Find description of some of our research projects, our publications, and some of our dissemination and outreach efforts.