Special Session

Computational Topology and Geometry

in  Applications of Computer Algebra (ACA'2006)

June 26 - 29, 2006
Varna, Bulgaria

Session Organizers:

Dmytro Chibisov

Victor Ganzha

Ernst W. Mayr

Lehrstuhl für Effiziente Algorithmen
Institut für Informatik
Technische Universität München
Boltzmannstr. 3
D-85748 Garching

Session Abstract and Motivation:

The session is devoted to the algorithmic aspects and applications of computer algebra in topological and geometric modeling and computing. Industrial applications of computer graphics and computer vision, robotics,  computer aided geometric design (CAGD), computer aided manufacturing (CAM), nanotechnology, molecular biology, computer assisted surgery and some others require efficient and robust geometric algorithms. Many computational problems in these areas can be formulated using algebraic constraints, which have to be solved efficiently both in time and space. However, research in this field is very much in progress, and many problems remain open.

The goal of this forum is to bring together pure and applied mathematicians as well as computer scientists and engineers who develop or use symbolic computational methods and systems,  to exchange ideas and views and present research results concerning theoretical foundations of symbolic algorithms as well as recent geometric applications of computer algebra in science and industry.

Possible topics for this session include (but are not limited to):
  • Algorithms for algebraic and semi-algebraic sets
  • Quantifier elimination in geometry
  • Computational homology
  • Morse theory
  • Algorithms in differential geometry
  • Symbolic-numerical methods for curves/surfaces parameterization,implicitization and resolution of singularities
  • Geometric constraint solving
  • Motion planning 
  • Clifford Algebras
  • Dynamic geometry
  • Grid generation
  • Complexity considerations
  • Applications in 
    •  Computer graphics 
    •  Computer vision 
    •  CAGD   
    •  CAM    
    •  Robotics    
    •  Medical applications 
    •  Molecular biology
    •  Nanotechnology
    •  ...







Wed., June 28

Tetsuo Fukui (1), Jiro Sekiguchi (2)
(1) Department of Informatics and Mediology, Mukogawa Women's University, Nishinomiya, Japan
(2) Department of Mathematics, Tokyo University of Agriculture and Technology, Koganei, Japan

A Relation between the Weyl Group $W(E_8)$ and Eight-line Arrangements on a Real Projective Plane [PDF]

Wed., June 28

Grosio Stanilov, Slavka Slavova
Pedagogical College  Dobrich at University of Shumen, Bulgaria

A Realization of the Real Projective Plane onto a Triangle [PDF]

Wed., June 28

Erol Yilmaz
Department of Mathematics, Abant Izzet Baysal University Bolu, Turkey

Computing Radicals of Submodules of Free Modules over Polynomial Rings

Coffee Break

Wed., June 28


Dmytro Chibisov, Victor Ganzha, Ernst W. Mayr
(1), Evgenii V. Vorozhtsov (2)
(1) Technische Universität München, Institut für Informatik
(2) Institute of Theoretical and Applied Mechanics,
Russian Academy of Sciences, Novosibirsk, Russia

On the Provable Tight Approximation of Optimal Meshing for Non-Convex Regions [PDF]

Wed., June 28
Dmytro Chibisov
Technische Universität München, Institut für Informatik
Computing of Optimal Motion for 321 Kinematic Chains with Geometric Constraints [PDF]

For the complete ACA 2006 Program please see:


Further accepted presentations:

Robert H. Lewis
Fordham University, USA
Algorithmic Search for Flexibility using Resultants of Polynomial Systems  [PDF]

Hongbo Li,  Ning Zhang
Key Laboratory of Mathematics Mechanization
Academy of Mathematics and Systems Science
Chinese Academy of Sciences
Affine Bracket Algebra for Automated Theorem Proving in Affine Geometry [PDF]

Important Dates:  

Deadline for submission of abstract: May 30, 2006 (extended)

Conference Proceedings:

The proceedings containing abstracts of all the talks presented at the ACA'06 will be published before the Conference.The Local Arrangements Committee of ACA 2006 suggests the possibility full papers of some sessions to be published in special issues of Bulgarian journal Serdica Journal of Computing.These special issues will be published after the conference. For more information please see:


Applications of Computer Algebra in Geomety (related web-sites):

Special Session on Computational Topology and Geometry in ACA'05

Maple Application Center (Engineering, Mathematics->Geometry)
Mathematica in Engineering

Dmytro Chibisov, Victor Ganzha and Ernst W. Mayr, 01.04.2006