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Research Interests
- Knot theory, computational geometry, combinatorial geometry and
algorithms, approximate algebraic computation, data
structures and algorithms, graph theory, algebraic geometry, topology, mathematical logic, basics of computer science.
Activities
Events
Talk: A Symbolic-Numeric Algorithm for Computing the Alexander Polynomial of a Plane Curve Singularity
Talk: GENOM3CK - A library for GENus cOMputation of plane Complex algebraiC Curves using Knot theory
Talk: Topology Analysis of Complex Curves Singularities using Knot Theory
Talk: The Genus Computation Problem: Symbolic-Numeric Solutions and Beyond
- Applications of Computer Algebra (ACA), Session Symbolic
Computation and Deduction in System Design and Verification, Research Institute for Symbolic Computation, Hagenberg-Austria, July 27-30, 2008.
Talk: Systematic Exploration of Mathematical Theories
Talk: Scheme-Based Systematic Exploration of Natural Numbers
Research Seminar meetings
Talk: Hybrid Symbolic-Numeric Methods in Polynomial Algebra.
Talk: Advanced Knot Theory.
Talk: Basic Knot Theory.
Talk: Symbolic Numeric Algorithms for Genus Computation Based on Knot Theory.
Talk: Why Knot? Alternative Solution to the Genus Computation Problem.
Talk: A Symbolic Numeric Algorithm for Genus Computation.
Research Seminar meetings of the Doctoral Program "Computational Mathematics"
Talk: Symbolic-Numeric Algorithms for Plane Algebraic Curves
Talk: Symbolic-Numeric Algorithms for Invariants of Plane Curve Singularities
Talk: The Genus Computation Problem and Approximate Algebraic Computation
Talk: The Genus Computation Problem: Symbolic-Numeric Solutions and Beyond
- Doctoral Program "Computational Mathematics" Workshop
of the Doctoral Program: Computational Mathematics from Linz, Doctoral
Program: Confluence of Vision and Graphics from Graz and Doctoral
Program: Numerical Simulation in Technical Sciences, Pichl
Schladming-Austria, July 7-10, 2009.
Talk: A Symbolic-Numeric Algorithm for Genus Computation
Talk: A Symbolic-Numeric Algorithm for Genus Computation
Talk: Singularities and Knots
Scientific visits
- Scientific visit to Dan Bates, Department of Mathematics, Colorado State University, Fort Collins, US. August 12, 2011 - September 3, 2011.
Main Purpose: Study methods from numerical algebraic geometry with practical applications to the Ph.D. topic.
Main Purpose: Extension and improvement of the joint work of the Ph.D. topic (i.e. implementation issues).
Main Purpose: Continuation and extension of the joint work of the Ph.D. topic (i.e. implementation issues).
Talk: A Symbolic-Numeric Algorithm for Genus Computation
Main Purpose: Research concerning the theoretical and practical aspects
of the Ph.D. topic (i.e. study on the topology of space algebraic
curves, implementation issues concerning Axel algebraic geometric
modeler)
Talk: Why Knot? Alternative Solution to the Genus Computation Problem
Software
GENOM3CK- A library for solving the genus computation problem
- GENOM3CK is a free library implemented in Axel and Mathemagix (i.e. in C++ using Qt Script for Applications, and Open Graphics Library).
- Shortly, GENOM3CK contains operations from algebraic geometry, topology and knot theory on a plane complex algebraic curve. GENOM3CK was developed for supporting completely the symbolic-numeric algorithms for plane complex algebraic curves (i.e. algebraic link, Alexander polynomial, delta-invariant, Milnor number of a singularity, genus of the curve, etc).
- GENOM3CK -Now available for Mac OS X and Linux.
- Dependencies: Qt4 (Shortly, Qt is a cross-platform application and UI framework) and Axel (Shortly, Axel is a free algebraic geometric modeler for manipulating algebraic curves and surfaces).
- Download and installation instructions available at GENOM3CK homepage.
- For detailed information on the library and the symbolic-numeric algorithms which are implemented in the library, please browse the online documentation of GENOM3CK. This online documentation was created with TeXmacs.
- For detailed information concerning the released versions of the library and its main functionalities, please browse the webpage on VERSIONS and FUNCTIONALITIES of GENOM3CK.
For any questions or suggestions on the library please feel free to contact: madalina.hodorog@oeaw.ac.at
Mathematica packages for computations in algebraic geometry
- A package for computing the stereographic projection of a plane complex
algebraic curve from the 4-dimensional space into the 3-dimenisional
space. Click here for Stereographic projection.
- A package for computing the domain for the stereographic projection of a
plane complex algebraic curve from the 4-dimensional space into the
3-dimensional space. Click here for Domain.
- A package for generating automatically XML files from Mathematica computations. Click here for Generate XML files.
- HELP ON USING THE PACKAGES: After downloading the packages one has to
put them in a directory where Mathematica can find them on its search
path. To find the default search path, start Mathematica and execute the
command $Path. Mathematica will list the directories that will be
searched. Thus if you place the downloaded packages into one of these
directories, you can use the command Needs["namepackage`"] to load the
package. You can read more about using Mathematica packages here.
- HELP ON USING THE PACKAGES: Here you can download a Mathematica sample file about using the packages.
- These Mathematica packages were created for supporting partly the symbolic-numeric algorithms for plane complex algebraic curves.
For any questions or suggestions on the packages please feel free to contact: madalina.hodorog@oeaw.ac.at
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