Computational Topology Reading Group

Time: Tuesdays, 5:30 - 6:30pm. Location: D344.

Areas:

  1. Morse Theory
  2. Curves and Surfaces
  3. Homology
  4. Vector fields
  5. Singularity theory
  6. Knot theory/3-manifolds

Topics:

  1. alpha-Complexes
  2. Medial axis
  3. Contour trees/Reeb graphs
  4. Morse Complexes
  5. (Discrete) Morse Theory
  6. Manifold learning/reconstruction
  7. Persistent homology
  8. Flattening
  9. Simplification
  10. Vector fields
Meetings:
Date:April 26, May 03
Topic:Computing Persistent Homology
Papers:[ZC05]
We will look into the relationship between the persistence algorithm given in [ELZ02] and computing Smith normal form. We will read and discuss [ZC05]. Conference version of this paper is [ZC04].
Date:April 19, 2005
Topic:Decision tree complexity and Betti numbers
Papers:[Y94], [Y95]
And now for something completely different... To switch gears we will try reading and discussing [Y94] (and perhaps [Y95] depending on how people feel about these papers).
Date:April 12, 2005
Topic:Jacobi sets of mutliple Morse functions
Papers:[EH02]
To follow up on the discussion that came up during the last meeting, we will read and discuss [EH02].
Date:April 5, 2005
Topic:Time-varying Reeb graphs
Papers:[EHMP04], [CMEH+03]
We will continue the discussion of Reeb graphs. We will finish the last couple sections of [CMEH+03], and start [EHMP04].
Date:March 29, 2005
Topic:Reeb graphs
Papers:[CMEH+03]
We will continue the discussion of contour trees, or rather now Reeb graphs of 2-manifolds [CMEH+03]. If time permits we will talk about section 5 of [CSA03].
Date:March 22, 2005
Topic:Contour trees
Papers:[CSA03], [vKvOB+97]
We will discuss [CSA03]. For background reading and discussion of motivational applications see [vKvOB+97].
References:
DOI is the preferred way to get a paper if it is available.
[CMEH+03]
Kree Cole-McLaughlin, Herbert Edelsbrunner, John Harer, Vijay Natarajan, and Valerio Pascucci. Loops in reeb graphs of 2-manifolds. In SCG '03: Proceedings of the nineteenth annual symposium on Computational geometry, pages 344-350. ACM Press, 2003.
[ doi ]
[CSA03]
Hamish Carr, Jack Snoeyink, and Ulrike Axen. Computing contour trees in all dimensions. Comput. Geom. Theory Appl., 24(2):75-94, 2003.
[ doi | .pdf ]
[DE95]
Cecil Jose A. Delfinado and Herbert Edelsbrunner. An incremental algorithm for betti numbers of simplicial complexes on the 3-spheres. Comput. Aided Geom. Des., 12(7):771-784, 1995.
[ doi | .pdf ]
[EH02]
Herbert Edelsbrunner and John Harer. Jacobi sets of multiple Morse functions. In F. Cucker, R. DeVore, P. Olver, and E. Sueli, editors, Foundations of Computational Mathematics, pages 37-57, England, 2002. Cambridge University Press.
[ .pdf ]
[EHMP04]
Herbert Edelsbrunner, John Harer, Ajith Mascarenhas, and Valerio Pascucci. Time-varying reeb graphs for continuous space-time data. In SCG '04: Proceedings of the twentieth annual symposium on Computational geometry, pages 366-372. ACM Press, 2004.
[ doi | .pdf ]
[ELZ02]
Herbert Edelsbrunner, David Letscher, and Afra Zomorodian. Topological persistence and simplification. Discrete Comput. Geom., 28:511-533, 2002.
[ .pdf ]
[vKvOB+97]
Marc van Kreveld, René; van Oostrum, Chandrajit Bajaj, Valerio Pascucci, and Dan Schikore. Contour trees and small seed sets for isosurface traversal. In SCG '97: Proceedings of the thirteenth annual symposium on Computational geometry, pages 212-220. ACM Press, 1997.
[ doi | .pdf ]
[Yao94]
Andrew Chi-Chih Yao. Decision tree complexity and Betti numbers. In STOC '94: Proceedings of the twenty-sixth annual ACM symposium on Theory of computing, pages 615-624. ACM Press, 1994.
[ doi ]
[Yao95]
Andrew Chi-Chih Yao. Algebraic decision trees and Euler characteristics. Theor. Comput. Sci., 141(1-2):133-150, 1995.
[ doi ]
[ZC04]
Afra Zomorodian and Gunnar Carlsson. Computing persistent homology. In Proc. 20th Ann. ACM Sympos. Comput. Geom., pages 347-356, 2004.
[ doi | .pdf ]
[ZC05]
Afra Zomorodian and Gunnar Carlsson. Computing persistent homology. Discrete Comput. Geom., 33(2):249-274, 2005.
[ doi | .pdf ]
Last Modified: Thursday, 20-Apr-2006 17:48:46 EDT