Hi Luiz,

Yes, Kingman coalescent followed by multispecies coalescent would allow you to talk about the cool (and mathematical work) done by Degnan, Rosenberg on the gene tree/species tree problem (e.g. for n>4 any species tree can have branch lengths where the most likely gene tree has a different topology) and o and the later (very elegant) folllow-up work by others incl Elizabeth Allman/Rhodes/Ane/Kubatko/Mossel/Roch on identifiability issues, and methods for consistently inferring species trees from (conflicting) gene trees.

Yes the Vogtmann-Billera-Holmes tree space could be another option - especially the CAT(0) strucuture and recent work to compute distances, find geodesics etc (perhaps the different space of ‘phylogenetic orgages’ could also be discussed - this has an interesting topological story involving CW complexes, toic cubes, etc. The latter space is arguably more relevant in some ways, but less studied.

Other topics that could form the basis of a talk to mathematicians could be (i) algebraic properties of Markov substitution model (eg. the work of the Tasmanian group in introducing Lie algebras into phylognetics) and/or (ii) the extensive work of the Berkeley crowd and Allman/Rhodes on the algebraic geometry of models. Also a maths talk on phylogenetic networks could be a further option.

Last year I had a popular-style survey paper on maths of phylogenetics in American Mathematical Monthly
and also gave 10 lectures in the US at a regional maths meeting on phylogenetics at Winthrop U- though this was more in the style of a tutorial for math grad students than a serious maths talk at a conference! Both the paper and the Winthrop lectures (as two .pdfs) are available on my webpage (one under publications, the other under talks - “winthrop”) if that’s useful. Hope these brief comments help.