## Calendar

**Departmental Events, Spring 2014:**

**Wednesday, 14 May 2014, 3pm Room TBA: Department Colloquium**

**Ruth Davidson**

**Department of Mathematics
North Carolina State University
**

Distance-based phylogenetic methods near a polytomy

* A phylogenetic tree models the common evolutionary history of a group of
species. A tree metric is a distance function on a set of species
realized by a tree with edge weights. Distance-based phylogenetic
algorithms attempt to solve the NP-hard least-squares phylogeny problem
by mapping an arbitrary dissimilarity map representing biological data
to a tree metric. The set of all dissimilarity maps is a Euclidean space
properly containing the space of all tree metricsÂ asÂ a polyhedral
fan. Outputs of distance-based tree reconstruction algorithms
suchÂ asÂ UPGMA and Neighbor-Joining are points in the maximal cones in
the fan. Tree metrics with polytomies, or internal vertices of degree
higher than three, lie at the intersections of maximal cones. A
phylogenetic algorithm divides the space of all dissimilarity maps into
regions based upon which combinatorial tree is reconstructed by the
algorithm. We use polyhedral geometry to compare the local nature of the
subdivisions induced by least-squares phylogeny, UPGMA, and
Neighbor-Joining. Our results suggest that in some circumstances, UPGMA
and Neighbor-Joining poorly match least-squares phylogeny when the true
tree has a polytomy. Â This is joint work with Seth Sullivant.Â *

**Monday, 24 February 2014, 11am, Gillet 311: Department Colloquium**

**Prof. Anthony Gamst**

**Department of Biostatistics and Bioinformatics
University of California, San Diego**

Some Problems in the Analysis of High-Dimensional Models

* Models with large numbers of nuisance parameters are common in modern
statistics, having applications in laboratory medicine, econometrics,
genomics, medical imaging, physics, epidemiology, and many other areas.
Classical techniques, including Maximum Likelihood and Bayesian
approaches, often produce sub-optimal or even inconsistent estimates of
the parameters of interest in these models, while asymptotically
unbiased estimating equations work rather generally. We study several
such models, identify the sources of bias and spurious correlation which
lead to inconsistency or sub-optimality, and compute the minimal
smoothness required for the existence of root-n consistent (and
efficient) parameter estimates. We also examine simultaneous estimation
of nuisance parameters and parameters of interest. These results are
related to every-day practice, particularly to the analysis of
regression models with many predictors, and some heuristics are given.*

**Monday, 10 February 2014, 11am, Gillet 311: Department Colloquium**

**Prof. Erik Guentner**

**Department of Mathematics
University of Hawai'i**

Geometry and noncommutative duals of groups

* Nonommutative geometry, in the sense of Alain Connes, proceeds from
the observation that properties of a topological space are reflected
by properties of the algebra of functions on it. Â Further, in cases
when the natural topological space is poorly behaved it may be
profitably be replaced by a noncommutative C*-algebra, the algebra
of 'functions on a noncommutative space'. Â In the talk I will survey
results relating geometric properties of a discrete group to its
harmonic analysis as manifested by the noncommutative dual space of
the group.*

**Thursday, 6 February 2014, 2pm, Gillet 311: Department Colloquium**

**Prof. Loredana Lanzani**

**Department of Mathematics
University of Arkansas**

Harmonic Analysis Techniques in Several Complex Variables

*abstract*

**Monday, 3 February 2014, 11am, Gillet 219: Department Colloquium**

**Prof. Michael Usher**

**Department of Mathematics
University of Georgia**

The geometry of the Hamiltonian diffeomorphism group

*An important object associated to any symplectic manifold is its
infinite-dimensional group of "Hamiltonian diffeomorphisms," consisting
of those diffeomorphisms which arise as time-evolution maps in a
generalization of Hamilton's formulation of classical mechanics. Rather
unusually for an infinite-dimensional Lie group, the Hamiltonian
diffeomorphism group admits a bi-invariant metric induced by a norm on
its Lie algebra, discovered by Hofer, which can be viewed as giving a
coordinate-independent measurement of the "energy" of any Hamiltonian
diffeomorphism. Â I will discuss some progress in understanding this
still-rather-mysterious metric, concerning for instance whether it is
always unbounded and how it interacts with submanifolds, and will also
touch on some open questions.*

**Monday, 27 January 2014, 11am, Gillet 219: Department Colloquium**

**Prof. David Savitt**

**Department of Mathematics
Brown University**

Galois representations

* The absolute Galois group of the field of rational numbers is a
fundamental object of study in number theory. I will begin by giving a
tour of the representation theory of this group, with an emphasis on
representations in characteristic p. In the second half of the talk I
will describe my recent work with Gee, Liu, and others on
generalizations of the weight part of Serre's conjecture.*

**Friday, 24 January 2014, 11am, Gillet 219: Department Colloquium**

**Prof. Bianca Viray**

**Department of Mathematics
Brown University
**

The local to global principle for rational points

* Let X be a connected smooth projective variety over Q. If X has a Q
point, then X must have local points, i.e. points over the reals and
over the p-adic completions Q_p. However, local solubility is often not
sufficient. Manin showed that quadratic reciprocity together with
higher reciprocity laws can obstruct the existence of a Q point (a
global point) even when there exist local points. We will give an
overview of this obstruction (in the case of quadratic reciprocity) and
then show that for certain surfaces, this reciprocity obstruction can be
viewed in a geometric manner. More precisely, we will show that for
degree 4 del Pezzo surfaces, Manin's obstruction to the existence of a
rational point is equivalent to the surface being fibered into genus 1
curves, each of which fail to be locally solvable. This talk will be
suitable for a general audience.*

**Friday, 24 January 2014, Carman Hall, 11am: CMACS Talk**

**Prof. Bud Mishra**

**Courant Institute of Mathematical Sciences
New York University**

Last modified: Mar 11, 2014