Justin Marks
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Justin Marks

Associate Professor of Mathematics

DepartmentDepartment of Math and Computer Science (MCS)
Biola AffiliationsFaculty
Websitehttps://justmarks.weebly.com/

Documents

CV Document (PDF)

Degrees

  • Ph.D., Mathematics, Colorado State University
  • M.S., Mathematics, Colorado State University
  • B.S., Mathematics, Westmont College

Biography

Justin Marks completed his B.S. in Mathematics at Westmont College, and earned his M.S. and doctorate in Mathematics at Colorado State University. His dissertation was in the area of geometric data analysis, with emphasis on developing algorithms for computing mean representatives for a collection of points on a Riemannian manifold. Marks held four postdoctoral positions, including appointments with MIT Lincoln Laboratory, Air Force Institute of Technology, Bowdoin College and Wesleyan University. He comes to Biola after serving three years as an assistant professor at Gonzaga University, during which he helped launch a bachelor of science degree in applied mathematics, and taught for a semester in Florence, Italy. Marks' current research interests center on designing matrix manifold algorithms to extract useful information from big data sets, such as images of human faces and hyperspectral imagery. A native of Palo Alto in the San Francisco Bay area, Marks is delighted to return to sunny California.

Awards

  • Spring 2019 NSF Conference Grant (to support Data Science and Image Analysis Conference) — Gonzaga University
  • Fall 2017 McDonald Work Award (to support undergraduate research) — Gonzaga University
  • 2014 - 2015 Project NExT Fellow
  • Spring 2014 Faculty Development Council Teaching Development Award — Bowdoin College
  • Fall 2013 Faculty Development Council Research Development Award — Bowdoin College
  • Fall 2010 -Spring 2011Selected as Graduate Teaching Assistant Mentor for new GTAs — Colorado State University
  • June 2010 Granted Scholarship to attend Gene Golub SIAM Summer School in Italy
  • May 2010 Inducted into Phi Kappa Phi
  • Summer 2009 Graduate Research Fellowship — Mathematics Department, Colorado State University
  • May 2006 Inducted into Omicron Delta Kappa Leadership Society

Publications

  • A Generalized Schur-Horn Theorem for Frame Completions. Applied and Computational Harmonic Analysis, Matthew Fickus, Justin Marks, Miriam J. Poteet. (2015).
  • 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, Daniel Bates, Brent Davis, Michael Kirby, Justin Marks, Chris Peterson., (2015).
  • Geodesic Paths for Time Dependent Covariance Matrices in a Riemannian Manifold. IEEE Geoscience and Remote Sensing Letters, Avishai Ben-David, Justin Marks, (Sept 2014).  
  • A Flag Representation for Finite Collections of Subspaces of Mixed Dimensions. Linear Algebra and its Applications, Bruce Draper, Michael Kirby, Justin Marks, Tim Marrinan, Chris Peterson, (June 2014). 
  • Two Tangent Bundle Algorithms for Averaging Point Clouds on Grassmann and Stiefel Manifolds, Michael Kirby, Justin Marks, Chris Peterson. In preparation for submission.

Presentations

Selected Presentations

  • Conference of the Pacific Northwest, Washington State University, Pullman, WA. Presented on “In Pursuit of the Grassmann Manifold Projection Mean Data Science and Image Analysis.” Feb 2020.
  • SIAM Conference on Applied Algebraic Geometry, University of Bern, Bern, Switzerland. Presented on “Matrix Manifold Means.” July 2019.
  • Mathematics Colloquium, University of Idaho, Moscow, ID. Presented on “Matrix Manifold Means.” March 2019.
  • Mathematics Seminar Course, Gonzaga University, Spokane, WA. Presented on “Image Analysis in MATLAB.” March 2019.
  • AMS Graduate Chapter Colloquium, Washington State University, Pullman, WA/ Presented on “Matrix Manifold Means.” Nov 2018.
  • Mathematics Colloquium, University of Montana, Missoula, MT. Presented on “Matrix Manifold Means.” Oct 2018.
  • SIAM Annual Meeting, Portland, OR.Presented on “How NAG Advances Our Capabilities of Computing Matrix Manifold Means.” July 2018.
  • Data Science Day, WSU, Pullman, WA. Presented on “Subspace Means.” April 2017. 
  • Mathematics Colloquium, CSU, Chico, Chico, CA. Presented on “Manifold Methods for Averaging Subspaces.” April 2017.
  • AMS Sectional Meeting, WSU, Pullman, WA. Presented on “Grassmann Manifold Means” (poster). April 2017.
  • AMS Sectional Meeting, WSU, Pullman, WA. Presented on “Subspace Video Fingerprinting” (poster, with Ethan Mahintorabi). April 2017.
  • Joint Math Meeting, Atlanta, GA. Presented on “Tangent Bundle Algorithms for Averaging Point Clouds on Grassmann and Stiefel Manifolds.” January 2017.
  • Joint Math Meeting, Seattle, WA. Presented on “Comparative Analysis of Matrix Manifold Means.” January 2016. 
  • Spokane Regional Mathematics Colloguium, Gonzaga University, Spokane, WA. Presented on “Tangent/Normal Bundle Manifold Mean Algorithms.” December 2016.
  • DTRA/NSF/NGA Algorithm Workshop, National Science Foundation, Arlington, VA. Presented on “Improved Time-Dependent Background Covariance Matrix Estimation Using Geodesic Paths” (Poster) July 2015.
  • MAA Rocky Mountain Section Meeting, Colorado College, Colorado Springs, CO. Presented on “When Matrix Manifold Means Need a Numerical Linear Algebra Lifeline.” April 2015. 
  • Joint Math Meeting, Baltimore, MD. Presented on “Constructing Optimal Finite Frames with a Given Set of Lengths.” January 2014. 
  • Joint Math Meeting, San Diego, CA. Presented on “Flag Mean of Generalized Grassmann Manifold Points.” January 2013.

Research Interests

  • Geometrics data analysis
  • Matrix analysis and applications
  • Computational linear algebra
  • Hyperspectral imagery
  • Frame theory
  • Compressed sensing

Courses

  • Quantitative Reasoning
  • Biostatistics
  • Number Theory/Math History

Areas of Expertise for Media Interviews

  • Mathematics
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