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.
• main program and sub routines are written with MPI and C.
• 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. Computers and Mathematics with Applications 62(10): 3706-2721, 2011.
• 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.