Project III (MATH 3382)
Jeffrey Giansiracusa - email: jeffrey.giansiracusa@durham.ac.uk
Darwin first introduced the idea of an evolutionary tree. Life forms evolve and differentiate into distinct species, and this process can be mapped and depicted with mathematical trees. Phylogenetics is the study of these trees, and working with these trees involves some fascinating mathematics. With modern gene sequencing technology, we can collect a large number of gene sequences, and the basic problem is to try to reconstruct the evolutionary relationships from the genetic data. Applications range from tracking the spread and evolution of viruses (think of the various strains of covid or flu), to digital humanities and analysis of the many different versions of Chaucer's Canterbury tales.
In this project we'll explore a variety of topics in the mathematics, algorithms, and statistics of working with phylogenetic trees.
Algebra II (MATH 2581)
Discerete Mathematics (MATH 1031)
Lecture Notes: The Mathematics of Phylogenetics
Elizabeth S. Allman, John A. Rhodes
http://www.dms.uaf.edu/~jrhodes/PhyloBook.pdf
The Mathematics of Phylogenetics
Lior Pachter, Bernd Sturmfels
https://arxiv.org/abs/math/0409132
Semple, Charles.; Steel, M. A.
Available in Bill Bryson library: https://discover.durham.ac.uk/permalink/44DUR_INST/k3s6qp/alma991004973859707366