Aaron Luttman Assistant Professor Division of Science and Mathematics Bethany Lutheran College Meyer Hall 312 (507) 344 - 7397 luttman@blc.edu

Courses - Spring 2008

• MATH 110 - Math Problem Solving (Syllabus)
• MATH 111 - College Algebra (Syllabus)
• MATH 351 - Linear Algebra (Syllabus)
• MATH 450 - Abstract Algebra (Syllabus)

Stomatal Dynamics Movies:

• Original Data
  • Original Leaf Video (52MB) (from the "Complexity and Stomatal Behavior" group at Utah State University)
  • Preprocessed Leaf Video (24MB)
  
  

• Leaf Video Segmentation
  • Leaf Video with Contour-based Segmentation Overlayed (22MB)
  • Resulting Binary Segmentation (4MB)

Publications:

• Weakly Peripherally Multiplicative Surjections of Pointed Lipschitz Algebras, A. Jiménez-Vargas, Aaron Luttman, and Moisés Villegas-Vallecillos, Rocky Mountain J. Math., to appear, (PDF).
• Total Variation-Penalized Poisson Likelihood Estimation for Ill-posed Problems, Johnathan Bardsley and Aaron Luttman, Adv. Comput. Math., Special Volume on Mathematical Methods for Image Processing, to appear, (PDF).
• Norm Conditions and Uniform Algebra Isomorphisms, Aaron Luttman and Scott Lambert, Cent. Eur. J. Math., 6 (2008), no. 2, 272-280. (PDF).
• Analysis of Pattern Formation on the Surface of Transpiring Leaves, Aaron Luttman, Emily Stone, and Johnathan Bardsley, Physica D, 232 (2007), no. 2, 142-155. (PDF).
• Weakly Peripherally-Multiplicative Operators Between Uniform Algebras, Scott Lambert, Aaron Luttman, Thomas Tonev, Contemp. Math., 435 (2007), 265-281. (PDF).
• A Variational Approach to Video Segmentation for Botanical Data, Aaron Luttman and Johnathan Bardsley, SIAM J. Sci. Comput., 29 (2007), no. 4, 1550-1566. (PDF).
• Uniform Algebra Isomorphisms and Peripheral Multiplicativity, Aaron Luttman and Thomas Tonev, Proc. Amer. Math. Soc., 135 (2007), no. 11, 3589-3598. (PDF).

Ph.D. Thesis:

• A Three-dimensional Variational Approach to Video Segmentation, Aaron Luttman, University of Montana, 2006 (PDF).

  Advisors: Professors Johnathan Bardsley and Emily Stone

Current CV:

• Curriculum Vitae

Research Interests:

1. Image/Video Segmentation Methods
2. Bio-dynamical Systems
3. Uniform Algebras
4. Image Processing/Computer Vision
5. Functional Analysis
6. Inverse Problems
7. Partial Differential Equations
8. Level-Set Methods
9. Numerical Analysis

Education:

• Ph.D. Mathematics, University of Montana (2006)
• M.S. Mathematics, University of Minnesota (2000)
• B.S. Mathematics, Purdue University (1998)
• A.A. Liberal Arts, Bethany Lutheran College (1996)

Invited Talks:

• Extreme Values and Isomorphisms of Algebras of Lipschitz Functions, Colloquium, University of Montana, May 1, 2008.
• The Peripheral Spectrum and Function Algebra Isomorphisms, Analysis Seminar, Iowa State University, March 13, 2008.
• Using Video to Understand Leaf Transpiration, Colloquia, Augsburg College, January 24, Gustavus Adolphus College, February 7, College of St. Benedict and St. John's University, March 13, Macalester College, November 13, 2007, Winona State University, February 18, St. Olaf College, April 15, 2008.
• Video Segmentation and Analysis of Stomatal Patch Dynamics, Colloquium, Minnesota State University-Mankato, October 24, 2006.
• Video Segmentation and Analysis of Botanical Fluorescence Patterns, Annual Meeting, Montana Academy of Sciences, April 8, 2006.
• Complex Systems from Leaf Segmentation, Science of Complex Systems Seminar, sponsored by the Center for Computational Science & Engineering at University of California, Davis, March 15, 2006.
• A Variational Approach to Biological Video Segmentation Montana State University Applied Mathematics Seminar, Montana State University, January 26, 2006.

Conference Talks:

• Polynomial Preservation of the Spectrum and Uniform Algebra Isomorphisms, Classical Analysis 2007, University of North Carolina - Chapel Hill, September 8, 2007.
• Video Segmentation and Analysis of Botanical Fluorescence Patterns, MAA North Central Section Meeting, October 2006.
• Algebra Isomorphisms and Peripheral Ranges of Functions, The Fifth Conference on Function Spaces at SIUE, May 17, 2006.
• Active Contours Without Edges for Botanical Video Segmentation, SIAM Conference on Imaging Science 2006, May 16, 2006.
• Reconstruction and Tracking: An Industrial - Academic Collaboration, SIAM Conference on Mathematics for Industry: Challenges and Frontiers, October 24, 2005.
• Using Video to Understand Leaf Breathing, 2005 University of Montana Graduate Student and Faculty Research Conference, University of Montana, April 9, 2005.

Other Academic Work:

• IPAM 2005 Graduate Summer School: Intelligent Extraction of Information from Graphs and High-dimensional Data

  IPAM Summer School Homepage

• ESAT/PSI/VISICS Computer Vision Research Lab, Katholieke Universiteit Leuven (I worked at VISICS in 2001 and again in the summer of 2003.)

  VISICS Homepage

Personal Interests:

1. Hiking in the mountains
2. Hiking anywhere else
3. See Research Interests

Picture Links:

• Banach Algebras 2007 Pictures (including pics from Maine)
• Everglades National Park Pictures
• Pictures from our Fourth of July trip to Olympic National Park in Washington, USA
• Our Recent Trip to China
• Some of my wife's and my pictures.
• Yellowstone National Park Pictures
• Grand Teton National Park Pictures
• Animal Pictures
• Recent Trip to Glacier National Park with Some Other Tangential Pics

Other Links:

• The Young Mathematicians' Network
• Bethany Lutheran College Homepage
• University of Montana, Department of Mathematical Sciences
• John Bardsley's Homepage (My doctoral advisor)
• Scott Lambert's Homepage, (Scott and I collaborate on work in Functional Analysis.)
• The Plzen brewery (Pilsner Urquell, my favorite beer)
• The Purdue Water Ski Team (of which I am a former member)

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Thanks for stopping by. Come and visit again anytime! (Page updated May 5, 2008)