Computational Topology with Applications Prof. V. Pascucci

Class Information:

Term	Number (index)	Subject	Catalog #	Section	Days	Time	Location	Office Hours
Spring 2013	16980	CS	6170	001	Monday, Wednesday (makeup classes on Friday when needed)	MW, 10:45 AM-12:05 PM (F 11:50 AM-01:10PM Pizza Served)	WEB 2760	TBD

Course Overview. This course provides a gentle introduction to topology-based techniques for the analysis and visualization of geometric models. Students will learn about fundamental topological invariants (connectedness, Euler characteristic, orientability, etc…) and constructs (Reeb graphs, Morse-Smale complexes, etc…), as well as efficient algorithms for their computation. Special emphasis will be given to the analysis of the algorithms with respect to: (i) asymptotic complexity, (ii) robustness, and (iii) data structures and implementation issues. The practical use of the techniques presented in class will be demonstrated for the analysis of geometric models commonly used in Computer Graphics and Scientific Visualization. Successful completion of the course will enable the students to pursue new research directions in this field and/or apply the most recent topological techniques to related areas such as computer graphics, geometric modeling, meshing, data analysis, and scientific visualization.

Prerequisites. There are no formal prerequisites for this class. Students will be expected to have basic knowledge of geometric data structures and algorithmic techniques.

Tentative Syllabus (changes based on student feedback will be considered):

Graphs and Connected Components	Manifolds and Orientability	Simplicial Complexes	Homology Groups and Betti Numbers
January 7, 2013	January 9, 2013	January 14, 2013	January 16, 2013
No Class MLK Day holiday January 21, 2013	Matrix Reduction and Smith Normal Form January 23, 2013	(PL) Morse Functions and transversality January 28, 2013	Optimal Computation of Reeb Graphs in 2D January 30, 2013
Robust Computation of Reeb Graphs in nD February 4, 2013	Optimal Computation of Contour Trees in nD February 6, 2013	Persistence and Topological Simplification February 11, 2013	Augmented and Hierarchical Contour Trees February 13, 2013
No Class Presidents’ Day Holiday February 18, 2013	Jacobi Sets and Comparison of Morse Functions February 20, 2013	Jacobi Sets and Dynamic Morse Functions February 25, 2013	2D Morse-Smale Complex February 27, 2013
Hierarchical 2D Morse-Smale Complex March 4, 2013	3D Morse-Smale Complex March 6, 2013	No Class Spring Break March 11, 2013	No Class Spring Break March 13, 2013
Hierarchical 3D Morse-Smale Complex March 18, 2013	Robustness and Simulation of Simplicity March 20, 2013	Delaunay Triangulations and Voronoi Diagrams March 25, 2013	Alpha Complex and Alpha Shapes March 27, 2013
Foundations of Discrete Morse Theory April 1, 2013	Practical Computation of Morse-Smale Complexes April 3, 2013	Topology Based Data Exploration April 8, 2013	Topological Analysis of High Dimensional Data April 10, 2013
CaseStudy1: The Topology of Runtime Memory References April 15, 2013	CaseStudy2: Failure of Porous Materials Under Stress April 17, 2013	CaseStudy3: Understanding Demographics of Crime and Designing New Clean Fuels April 22, 2013	CaseStudy4: Active Sites In Molecular Surfaces April 24, 2013
	Final Project Presentation (all day) Refreshments will be served May 3, 2013

Reading and supplemental material

There is no formal book for class. The instructor will distribute printouts of notes or research papers related to each lecture.

The following links include various relevant materials such as book, research papers, and software:

· Main Book:

o Computational Topology by H. Edelsbrunner and J. Harer

· Other Books:

o Topology (2nd Edition) by J. Munkres

o Morse Theory by J. Milnor

o Combinatorial Topology by P. S. Alexandrov

o An Introduction to Morse Theory by Y. Matsumoto

· Information on the Web:

o BioGeometry

o Computational Geometry Pages by J. Erickson

o GemDir by E. Mücke

o CGAL

Assignments

The students will be given individual and group assignments. The main assignment will be a project. Although the students will be provided with a list of available projects, the students are encouraged to propose projects in areas of personal interest. For larger projects the students will be allowed to work in small groups.

Late Submission of Assignments

Assignments will not be accepted late. Students will be given a one-time two-day extension for an unexpected event.

Class Participation and Absences

Participation in class is an integral part of the course. Attendance is mandatory.
More than two unjustified absences will impact negatively the grade.

Grading

Each student will be evaluated based on:

· Attendance and participation in class (20%),

· Assignments (2 0%),

· Project (50%),

· Final project presentation (10%).

Students With Disabilities

The University of Utah seeks to provide equal access to its programs, services and activities for people with disabilities. If you will need accommodations in the class, reasonable prior notice needs to be given to the Center for Disability Services, 162 Olpin Union Building, 581-5020 (V/TDD). CDS will work with you and the instructor to make arrangements for accommodations.

All written information in this course can be made available in alternative format with prior notification to the Center for Disability Services.