- Series
- Algebra Seminar
- Time
- Monday, April 8, 2013 - 5:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Seth Sullivant – North Carolina State University – http://www4.ncsu.edu/~smsulli2/
- Organizer
- Anton Leykin

I will discuss two problems in phylogenetics where a geometric
perspective provides substantial insight. The first is the
identifiability problem for phylogenetic mixture models, where the
main problem is to determine which circumstances make it possible to
recover the model parameters (e.g. the tree) from data. Here tools
from algebraic geometry prove useful for deriving the current best
results on the identifiability of these models.
The second problem concerns the performance of distance-based
phylogenetic algorithms, which take approximations to distances
between species and attempt to reconstruct a tree. A classical result
of Atteson gives guarantees on the reconstruction, if the data is not
too far from a tree metric, all of whose edge lengths are bounded away
from zero. But what happens when the true tree metric is very near a
polytomy? Polyhedral geometry provides tools for addressing this
question with some surprising answers.