## Research Interests:

Matrix Manifolds, Geometric Data Analysis, Hyperspectral Imagery, Frame Theory, Linear Algebra

## Research Publications and Conference Experience

**Publications:**

1.

*Geodesic Paths for Time Dependent Covariance Matrices in a Riemannian Manifold*: IEEE Geoscience and Remote Sensing Letters, 2014, with Avishai Ben-David

2.

*A Flexible Flag Representation for Finite Collections of Subspaces of Mixed Dimensions*:

*Linear Algebra and its Applications, 2014, with Bruce Draper, Michael Kirby, Tim Marrinan, and Chris Peterson*

3.

*The Max-Length-Vector Line of Best Fit to a Set of Vector Subspaces and an Optimization Problem Over a Set of Hyperellipsoids*:

*Numerical Linear Algebra with Applications, 2015, with Daniel Bates, Brent Davis, Michael Kirby, and Chris Peterson*

4. A Generalized Schur-Horn Theorem for Frame Completions: Applied and Computational Harmonic Analysis, 2015, with Matthew Fickus and Miriam J. Poteet

5.

*Two Tangent Bundle Algorithms for Averaging Point Clouds on Grassmann and Stiefel Manifolds*: in preparation, with Michael Kirby and Chris Peterson

**Conference Presentations:**

1. Joint Math Meeting (JMM) Seattle January 2016

Title:

*Comparative Analysis of Matrix Manifold Means*

2. DTRA/NSF/NGA Algorithm Workshop July 2015 (poster)

Title:

*Improved Time-Dependent Background Covariance Matrix Estimation Using Geodesic Paths*

3. MAA Rocky Mountain Section Meeting April 2015

Title:

*When Matrix Manifold Means Need a Numerical Linear Algebra Lifeline*

4. Joint Math Meeting (JMM) Baltimore January 2014

Title:

*Constructing Optimal Finite Frames with a Given Set of Lengths*

5. Joint Math Meeting (JMM) San Diego January 2013

Title:

*Flag Mean of Generalized Grassmann Manifold Points*

6. DTRA/NSF/NGA Algorithm Workshop November 2012

Title:

*Manifold Analysis for Hyperspectral Imagery: A Collaboration with MIT Lincoln Lab*

7. International Council for Industrial and Applied Mathematics (ICIAM) July 2011

Title:

*Mean Variants on Special Manifolds*

8. DTRA/NSF Algorithm Workshop June 2011 (poster also)

Title:

*Means on Grassmann and Stiefel Manifolds for Characterization of Hyper-Spectral Chem-Bio Data*

9. Association of Christians in the Mathematical Sciences (ACMS) Conference May 2011

Title:

*Pattern Recognition in Large Data Sets*

10. CSU/PSI Workshop August 2010

Title:

*Modeling Data Cubes on Grassmann and Stiefel Manifolds*

11. DTRA/NSF Algorithm Workshop June 2010

Title:

*Manifold Comparison and Karcher Mean on Fabry-Perot Interferometer Sensor Data Set*

12. MAA Section Meeting April 2009

Title:

*Discriminative Canonical Correlations: An Offspring of Linear Discriminant Analysis*

**Other Conference Attendance:**

1. Joint Math Meeting (JMM) San Antonio January 2015

2. DTRA/NSF/NGA Algorithms for Threat Detection Program Review Boulder, CO March 2014

3. Quantitative Methods in Defense and National Security (QMDNS) April 2012

4. Joint Math Meeting (JMM) Boston January 2012

5. SIAM International Conference on Data Mining (SDM) April 2011

6. Western Algebraic Geometry Seminar (WAGS) April 2011

7. Western Algebraic Geometry Seminar (WAGS) November 2010

8. Received Scholarship for and Attended Gene Golub SIAM Summer School in Italy June 2010

**Seminars:**

1. Attended and presented at Mathematics Department Seminar at Bowdoin College

2. Attended and presented at Math Lunch at Bowdoin College

3. Active participant in Teaching Seminar at Bowdoin College

4. Lectured as an invited speaker for mathematics seminar at Kenyon College October 2012

5. Attended and presented at Pattern Analysis Laboratory seminar at Colorado State University

6. Attended and presented at Greenslopes graduate student seminar at Colorado State University