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# Departmental Colloquia

Our department is proud to host weekly colloquium talks featuring research by leading mathematicians from around the world. Most colloquia are held on Fridays at 4pm in Parker Hall, Room 250 (unless otherwise advertised) with refreshments preceding at 3:30pm in Parker Hall, Room 244.

**Mathematics & Statistics Colloquium: Dr. Anuj Srivastava**

**Apr 21, 2017 04:00 PM**

Speaker: **Dr. Anuj Srivastava**, Florida State University (http://ani.stat.fsu.edu/~anuj/)

Title: Recent Advances in Elastic Functional Data Analysis

Abstract: Functional data analysis (FDA) is fast becoming an important research area, due to its broad applications in many branches of science. An essential component in FDA is the registration of points across functional objects. Without proper registration the results are often inferior and difficult to interpret. The current practice in FDA community is to treat registration as a pre-processing step, using off-the-shelf alignment procedures, and follow it up with statistical analysis of the resulting data. In contrast, Elastic FDA is a more comprehensive approach, where one solves for the registration and statistical inferences in a simultaneous fashion. The key idea here is to use Riemannian metrics with appropriate invariance properties, to form objective functions for alignment and to develop statistical models involving functional data. While these elastic metrics are complicated in general, we have developed a family of square-root transformations that map these metrics into simpler Euclidean metrics, thus enabling more standard statistical procedures. Specifically, we have developed techniques for elastic functional PCA and elastic regression models involving functional variables. I will demonstrate this ideas using imaging data in neuroscience where anatomical structures can often be represented as functions (curves or surfaces) on intervals or spheres. Examples of curves include DTI fiber tracts and sulcal folds while examples of surfaces include subcortical structures (hippocampus, thalamus, putamen, etc). Statistical goals here include shape analysis and modeling of these structures and to use their shapes in medical diagnosis.

Faculty host: Guanqun Cao

**Joint Math-Bio Colloquium**

**Apr 07, 2017 04:00 PM**

Speaker: **John Rhodes** (U. Alaska, Fairbanks)

Title: The Geometry and Algebra of Evolution: Developing a new tool for phylogenetic analysis of genomic data

Abstract: Using DNA sequences as a basis for inferring evolutionary relationships between organisms has become routine over the past 30 years. However, as sequence datasets grow from single genes to entire genomes, new tools are needed and novel mathematical approaches continue to be investigated.

After explaining the basic probabilistic models of sequence evolution on trees, this talk will present a non-standard way of viewing them, as high-dimensional geometric objects with algebraic descriptions (algebraic varieties). This perspective motivates the purely mathematical problem of finding an explicit algebraic description of the models, whose answer in turn leads to a new practical tool for biological data analysis, the Split Score. This score is a statistically consistent measure of support in a data set for a single edge

within a tree, without regard to the rest of the tree branching pattern. Pleasantly, it can be implemented using highly-developed scientific computation packages, and an analysis of a full chromosome typically requires only minutes. Several examples of its use on biological datasets will be shown.

The intended audience spans mathematics, statistics, and biology. Familiarity with any of the fields, and a willingness to take a journey passing through the others, is all that is required.

Faculty host: Luke Oeding

PLEASE NOTE LOCATION ABOVE

**Mathematics & Statistics Colloquium: Leslie Hogben**

**Mar 31, 2017 04:00 PM**

Speaker: **Leslie Hogben**, Iowa State University (https://math.iastate.edu/directory/leslie-hogben/)

Title: Enhanced principal rank characteristic sequences of symmetric and Hermitian matrices

Abstract: For an \(n\times n\) symmetric matrix over a field or a complex Hermitian matrix, the principal rank characteristic sequence is \(r_0]r_1 r_2 \cdots r_n\) where \(r_k\) equals 1 or 0 according as whether or not there is a nonzero principal minor of order \(k\) for \(k=1,\dots,n\) and \(r_0=1\) if and only if \(A\) has a diagonal entry equal to zero. In 2012 Brualdi, Deaett, Olesky, and van den Driessche introduced the principal rank characteristic sequence in part to assist with the principal minor assignment problem for real symmetric matrices. This problem, to determine which \(2^n\)-vectors of real numbers can occurs as the minors of an \(n\times n\) real symmetric matrix, was highlighted as a challenge problem by Holtz and Schneider in 2004 and studied by Holtz and Sturmfels in 2007 via hyperdeterminantal relations. The enhanced principal rank characteristic sequence (epr-sequence) of a symmetric or Hermitian \(n\times n\) matrix is the sequence \(\ell_1 \ell_2 \cdots \ell_n\) where \(\ell_k\) is \({\tt A}\), \({\tt S}\), or \({\tt N}\) according as all, some, or none of its principal minors of order \(k\) are nonzero. The study of epr-sequences provides additional information that may be helpful in work on the principal minor assignment, while remaining more tractable than the full problem. Enhanced principal rank characteristic sequences were also used to answer the following question asked in 2004 by Johnson, Kroschel, and Omladič: ``For a real symmetric matrix, which lists of sizes, for which there exists a singular principal submatrix, can occur?" This talk will survey recent results for epr-sequences and distinguish the behavior of such sequences for symmetric matrices from those for Hermitian matrices.

This talk is based on joint work with W. Barrett, S. Butler, M. Catral, S.M. Fallat, H. T. Hall, Xavier Martínez-Rivera, B.L. Shader, P. van den Driessche, and M. Young.

Faculty host: T-Y Tam

**Mathematics & Statistics Colloquium: Philippe Gaillard**

**Mar 10, 2017 04:00 PM**

**Philippe Gaillard**

1. Summary of the activity of the Statistical Consulting Center from Fall 2014 to Fall 2016

2. Overview of the research projects

3. Two statistical tools useful in statistical consulting:

3.1. Ballantines are Venn diagrams used for the visual representation of shared variance. This representation is approximate (not to scale), I propose an exact representation in two

dimensions, for the case of three variables.

3.2. There are several existing methods to assess the agreement between two continuous variables. For this same purpose, I propose a proportion test, which combines some of

the advantages of several of the existing methods.

**Mathematics & Statistics Colloquium: Alex Clark**

**Mar 03, 2017 04:00 PM**

PLEASE NOTE: CHANGE IN DATE

Speaker: **Alex Clark**, University of Leicester (http://www2.le.ac.uk/departments/mathematics/extranet/staff-material/staff-profiles/adc20)

Title: Tiling Spaces: Their Structure and Unexpected Examples

Abstract: In this talk we will explain how one can introduce a natural topological structure to certain spaces of tilings of the plane. These spaces admit a natural dynamical system that captures many of the important properties of the tilings, including the spectral properties of associated quasicrystals. After a review of some of the fundamental results about the structure of these tiling spaces, we shall explain some recent results of Clark and Sadun that have far reaching implications for higher dimensional dynamical systems.

In particular, we shall explore a counterexample to conjectures which has the consequence that higher dimensional dynamics are fundamentally different from those of dimension one.

Faculty host: Krystyna Kuperberg

**AU-AUM Mathematics & Statistics Colloquium: Yue Chen**

**Feb 24, 2017 04:00 PM**

Speaker: **Yue Chen**, AUM

Title: Double Negative Behavior in Metamaterials

Abstract: Metamaterials are a new form of structured materials designed to have electromagnetic properties not generally found in nature. In this talk, I will introduce a rigorous mathematical framework for controlling localized resonances and predicting exotic behavior inside optical metamaterials. The theory provides a rational basis for designing microstructure using multiphase nonmagnetic materials to create backward wave behavior across prescribed frequency ranges.

Last Updated: 09/11/2015