题   目：Phylogenetic lassos and the triple conjecture

报告人：Professor Stefan Gruenewald

时   间：2014年12月19日    下午4:00--5:00

地   点：东区管理科研楼  数学科学学院1518室

摘   要：
The most common structures to visualize evolutionary relationships between species or other taxonomic units are phylogenetic trees. Here we consider leaf-labelled unrooted trees, where the leaves are called taxa and represent the species living in the presence. Each interior vertex represents an ancestor of a subset of the taxa set. Generically, all interior vertices have degree 3, and we call a phylogenetic tree with that property binary. Every edge has a positive length associated with it, so aphylogenetic tree defines a metric on its taxa set where the distance between two taxa is the length of the unique path between them. It is a classical result in phylogenetics that a tree can be reconstructed efficiently from its induced metric.

More recently, Dress, Huber, and Steel studied the situation where some of the distance information is missing. Given a phylogenetic tree, they call a subset of the set of unordered pairs of taxa a strong phylogenetic lasso, if there is no other phylogenetic tree having identical distances on every pair in the subset. In my talk, I will give examples and some sufficient as well as some necessary conditions for a set of pairs to be a lasso, and I will solve the most prominent open question that the authors above asked: In a binary phylogenetic tree, every interior vertex defines a tripartition of the taxa set, as removing the vertex disconnects the tree into three components. The triple cover conjectures says that a collection L of unordered pairs is a strong phylogenetic lasso, if for every interior vertex, we can find one representative from every part of its tripartition such that all three pairs from those three taxa are in L.

主办单位: 中国科学技术大学数学科学学院
         中科院吴文俊数学重点实验室

欢迎广大师生参加！