Abstract: Abstract: Phylogenetic trees are important in the study of the evolution of diseases: the human microbiome, HIV and Covid-19 being just a few examples. The mathematical construction of a space of all trees enables the computation of "average" trees in the sense of Frechet. This space has the property of being negatively curved (CAT0) and some of its mathematical properties have consequences for the algorithms we use for combining trees and data, my talk will provide an overview of how the mathematical results can help statistical inference on biological problems that use phylogenies and some pointers to results and open problems in the area. Bio: Professor of Statistics, Stanford University. Trained in the French School of Data Analysis (Analyse des Données) in the 1980’s, Professor Holmes is a Data Scientists specialized in exploring and visualizing complex biological data. She is interested in integrating the information provided by phylogenetic trees, community interaction graphs and metabolic networks with sequencing data and clinical covariates in biological contexts such as immune system and cancer, resilience and biomarker detection in the human microbiome and drug resistance in HIV. The methods she develops use computational statistics, nonparametric computer intensive methods such as the bootstrap and MCMC to draw inferences about many complex biological phenomena and are made available as open source projects in Bioconductor and R. She teaches many courses in Statistics and Bioinformatics to biologists and mathematicians and has written a book with Wolfgang Huber that is freely available online: at http://bios221.stanford.edu/book/ . More information: http://statweb.stanford.edu/~susan/