Department of

# Mathematics

Seminar Calendar
for events the day of Friday, October 10, 2014.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, October 10, 2014

4:00 pm in 243 Altgeld Hall,Friday, October 10, 2014

#### A Survey of Jet Bundles

###### Dan Hockensmith (UIUC Math)

Abstract: Jet bundles are a convenient framework for studying PDE's from a geometric perspective. We will introduce the notion of a jet bundle, incorporating examples along the way, and explicitly see how sections of a jet bundle can give rise to PDE's. We'll then survey some of the applications of jet theory. In particular, we'll explore the relationship between sections of the first jet bundle and connections on a fiber bundle, introduce the notion of an h-principle, and, time permitting, discuss some singularity theory. For the sake of time, there will be no proofs. Our discussion will center around some intriguing examples that will motivate why the theory of jet bundles is useful.

4:00 pm in 343 Altgeld Hall,Friday, October 10, 2014

#### Euclidean Geometry of Distance-Based Phylogenetic Methods

###### Ruth Davidson   [email] (UIUC)

Abstract: A phylogenetic tree models the common evolutionary history of a group of species or genes. A tree metric is a distance function on a set of species realized by a tree graph with edge weights. The set of all dissimilarity maps is a Euclidean space properly containing the space of all tree metrics as a polyhedral fan. Distance-based phylogenetic methods map arbitrary dissimilarity maps representing biological data to a tree metric, dividing the space of all dissimilarity maps into regions based upon which combinatorial tree is reconstructed by the method. Studying the geometry and statistical properties of the input and output spaces of these methods can give insight their observed behavior on biological data. We study the combinatorial geometry of the subdivision of Euclidean space induced by the distance-based methods UPGMA and Least-Squares Phylogeny and the statistical properties of inputs computed from aligned sequences using a model of sequence evolution. This talk includes results from joint work with Joe Rusinko, Seth Sullivant, and Jing Xi.

4:00 pm in 345 Altgeld Hall,Friday, October 10, 2014