Topology Professor Professor De Witt L. Sumners
Cellular DNA is a long, thread-like molecule with
remarkably complex topology. Enzymes which manipulate the geometry
and topology of cellular DNA perform many important cellular
processes (including segregation of daughter chromosomes, gene
regulation, DNA repair, and generation of antibody diversity).
enzymes pass DNA through itself via enzyme-bridged transient breaks
in the DNA; other enzymes break the DNA apart and reconnect it
different ends. In the topological approach to enzymology, circular
DNA is incubated with an enzyme, producing an enzyme signature
form of DNA knots and links. By observing the changes in DNA geometry
(supercoiling) and topology (knotting and linking) due to enzyme
action, the enzyme binding and mechanism can often be characterized.
This lecture will discuss topological models for DNA strand passage
and exchange, and using the spectrum of DNA knots to infer
bacteriophage DNA packing in viral capsids.
Calculating the Secrets
of Life: Mathematics in Biology and Medicine Professor De Witt L. Sumners
Abstract: The human body is an extremely complicated
system. Spurred by spectacular recent progress, biology and medicine
are experiencing an explosion of data. In order to convert this
firehose of data into knowledge, mathematics and computation (both
old and new) are needed to build models and navigational tools.
talk will briefly discuss a few applications to show the impact
mathematics can have in biology and medicine: in the cell
(understanding how enzymes operate on DNA); in the heart (controlling
fibrillation); and in the brain (understanding brain function).
Demonic Graphs and Undergraduate
Research Professor Aparna Higgins
My work with undergraduates on mathematical research has been
one of the most satisfying aspects of my teaching career. This
will highlight some of the beauty and depth of the research done
former undergraduate students on line graphs and pebbling on graphs.
will consider iterated line graphs, some pioneering results in
graphs, and pebbling numbers of line graphs. The results of some
later students built on work done by the earlier ones, and have
some of my own recent research.