A space of phylogenetic networks
Abstract
This will be a discussion of the paper https://arxiv.org/abs/1607.06978.
Forthcoming events in this series
This will be a discussion of the paper https://arxiv.org/abs/1607.06978.
This will be a discussion of the paper https://arxiv.org/abs/1604.02618
This will be a quick introduction to tropical algebra and the main results from the paper https://arxiv.org/pdf/1604.00113.pdf
Finding implementable descriptions of the possible configurations of a knotted DNA molecule has remarkable importance from a biological point of view, and it is a hard and well studied problem in mathematics.
Here we present two newly developed mathematical tools that describe the configuration space of knots and model the action of Type I and II Topoisomerases on a covalently closed circular DNA molecule: the Reidemeister graphs.
We determine some local and global properties of these graphs and prove that in one case the graph-isomorphism type is a complete knot invariant up to mirroring.
Finally, we indicate how the Reidemeister graphs can be used to infer information about the proteins' action.
In this talk I will first briefly introduce 1-parameter persistent homology, and discuss some applications and the theoretical challenges in the multiparameter case. If time remains I will explain how tools from commutative algebra give invariants suitable for the study of data. This last part is based on the preprint https://arxiv.org/abs/1708.07390.
I will give an overview of the complexes used in algebraic topology using the language of abstract complexes.
This is a lunch seminar, so feel free to bring your lunch along!
We will discuss the Chapter "Cohomology" from the book "Elementary applied topology" by Robert Ghrist (available at https://www.math.upenn.edu/~ghrist/notes.html).
This is a lunch seminar, so feel free to bring your lunch along!
In this meeting we will talk about the first two chapters of Robert Ghrist's book "Elementary Applied Topology". The book is freely available at the following link: https://www.math.upenn.edu/~ghrist/notes.html
In the first meeting of the seminar we, and all participants who wish to do so, will each briefly introduce ourselves and our research interests. We will decide future talks and papers to read during this meeting.