Research Activities

Interests:

·         Computational Algebraic Geometry

·         Scientific Computing

·         Mathematical Software development

·         High Performance Computing

Software:

·         PHClab: A MATLAB/Octave interface to PHCpack. 

• gives the user access to the functionality of PHCpack within a MATLAB/Octave session.
• provides automatic conversions of the formats for polynomial systems and solutions
• parallel computation on a set of origami equations are conducted by using the combination of PHClab, MPITB for Octave.

  This accomplishment + a nice comment can also be found at the website of MPITB for Octave.

·         Parallel Implementation of a Subsystem-by-Subsystem Solver in PHCpack.

o        main program and sub routines are written with MPI and C.

o        the divide-and-conquer algorithm is implemented.

Publications and Work In progress:

·         Yun Guan and Jan Verschelde: Sampling Algebra Sets using Local Intrinsic Coordinates. The abstract and manuscript. Submitted.

·         Yun Guan and Jan Verschelde: Parallel Implementation of a Subsystem-by-Subsystem Solver. The abstract and manuscript. In the proceedings of the 22th High Performance Computing Symposium, Quebec City, 9-11 June 2008. Pages 117-123. IEEE Computer Society, 2008.

·         Yun Guan and Jan Verschelde: PHClab: A MATLAB/Octave interface to PHCpack. The abstract and paper. Take a look at the Poster. In IMA Volume 148: Software for Algebraic Geometry, edited by Michael E. Stillman, Nobuki Takayama, and Jan Verschelde. Pages 15-32, Springer-Verlag, 2008.

Presentations:

·         Local Numerical Representation of Algebraic Sets. AMS Joint Mathematics Meeting, San Francisco, CA, Jan. 2010.

·         Conditioning Numerical Representations of Algebraic Sets. ACA 2009 Session on ``Symbolic and Numeric Computation'' ETS, Montreal, Canada, 25-28 June 2009.

·         Solving Polynomial Systems with PHCpack and PHClab. JMM Contributed Talk. Washington DC, 6 January 2009.

·         Parallel Implementation of a Subsystem-by-Subsystem Solver. AMS Special Session on ``Numerical and Symbolic Techniques in Algebraic Geometry and its Applications". 5-6 October 2007, DePaul University (Chicago, IL). slides of the talk

·         Poster and Software Demonstration: PHClab: A MATLAB/Octave interface to PHCpack. Workshop on ``Software for Algebraic Geometry". Institute for Mathematics and its Applications, Minnesota, 23-27 October 2006.