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

  • Southern California Applied Math Symposium, UC San Diego, San Diego, CA. Presented on "Maximizing Stable Matches in the Stable Marriage Problem." April 2024.
  • MathFest, Tampa, FL. Presented on "Flag Mean Lab for Intermediate Linear Algebra." August 2023.
  • Southern California Applied Math Symposium, UC Irvine, Irvine, CA. Presented on "In Pursuit of the Grassmann Manifold Projection Mean." April 2023.
  • Association of Christians in the Mathematical Sciences Meeting, Azusa Pacific University, Azusa, CA. Presented on "Pursuing Discriminative Statistics for Buried Object Detection using Ground Penetrating Radar." June 2022.
  • Data Science and Image Analysis Conference of the Pacific Northwest, Washington State University, Pullman, WA. Presented on “In Pursuit of the Grassmann Manifold Projection Mean.” 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.
  • SIAM Annual Meeting, Portland, OR. Presented on "How NAG Advances Our Capabilities of Computing Matrix Manifold Means." July 2018.

Research Interests

  • Geometric Data Analysis
  • Matrix Manifolds
  • Frame Theory
  • Stable Marriage Problem

Courses

  • Linear Algebra
  • Linear Algebra II
  • Numerical Analysis
  • Complex Variables
  • Business Statistics

Areas of Expertise for Media Interviews

  • Mathematics
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