Graduate Students

• Kylash Viswanathan
  • Jan Verschelde and Kylash Viswanathan: Locating the Closest Singularity in a Polynomial Homotopy. The abstract and manuscript. In the Proceedings of the 24th International Workshop on Computer Algebra in Scientific Computing (CASC 2022), edited by F. Boulier, M. England, T.M. Sadykov, and E.V Vorozhtsov, volume 13366 of Lecture Notes in Computer Science, pages 333-352, Springer-Verlag, 2022.
  • Jan Verschelde and Kylash Viswanathan: Extrapolating Solution Paths of Polynomial Homotopies towards Singularities with PHCpack and phcpy. The abstract and manuscript.

Alumni

• Nathan Bliss: Computing Series Expansions of Algebraic Space Curves. PhD thesis, UIC, Spring 2018.
  • Nathan Bliss, Jeff Sommars, Jan Verschelde, and Xiangcheng Yu: Solving Polynomial Systems in the Cloud with Polynomial Homotopy Continuation. The abstract and manuscript. In the Proceedings of the 17th International Workshop on Computer Algebra in Scientific Computing (CASC 2015), edited by V.P. Gerdt, W. Koepf, W.M. Seiler, and E.V. Vorozhtsov, volume 9301 of Lecture Notes in Computer Science, pages 87-100, Springer-Verlag, 2015.
  • Nathan Bliss and Jan Verschelde: Computing all Space Curve Solutions of Polynomial Systems by Polyhedral Methods. The abstract and manuscript. In the Proceedings of the 18th International Workshop on Computer Algebra in Scientific Computing (CASC 2016), edited by V.P. Gerdt, W. Koepf, W.M. Seiler, and E.V. Vorozhtsov, volume 9890 of Lecture Notes in Computer Science, pages 73-86, Springer-Verlag, 2016.
  • Nathan Bliss and Jan Verschelde: The Method of Gauss-Newton to Compute Power Series Solutions of Polynomial Homotopies. The abstract and manuscript. Linear Algebra and Its Applications 542:569-588, 2018.
• Jeff Sommars: Algorithms and Implementations in Computational Algebraic Geometry. PhD thesis, UIC, Spring 2018.
  • Nathan Bliss, Jeff Sommars, Jan Verschelde, and Xiangcheng Yu: Solving Polynomial Systems in the Cloud with Polynomial Homotopy Continuation. The abstract and manuscript. In the Proceedings of the 17th International Workshop on Computer Algebra in Scientific Computing (CASC 2015), edited by V.P. Gerdt, W. Koepf, W.M. Seiler, and E.V. Vorozhtsov, volume 9301 of Lecture Notes in Computer Science, pages 87-100, Springer-Verlag, 2015.
  • Jeff Sommars and Jan Verschelde: Computing Pretropisms for the Cyclic n-Roots Problem. In EuroCG 2016, 32nd European Workshop on Computational Geometry, EuroCG 2016, Lugano, Switzerland, March 30--April 1, 2016, pages 235-238. The abstract and manuscript.
  • Jeff Sommars and Jan Verschelde: Pruning Algorithms for Pretropisms of Newton Polytopes. The abstract and manuscript. In the Proceedings of the 18th International Workshop on Computer Algebra in Scientific Computing (CASC 2016), edited by V.P. Gerdt, W. Koepf, W.M. Seiler, and E.V. Vorozhtsov, volume 9890 of Lecture Notes in Computer Science, pages 489-503, Springer-Verlag, 2016.
  • Anders Jensen, Jeff Sommars, and Jan Verschelde: Computing Tropical Prevarieties in Parallel. The abstract and revised manuscript. In PASCO 2017: Proceedings of the International Workshop on Parallel Symbolic Computation, Kaiserslautern, Germany, July 23-24, 2017, edited by Hans-Wolfgang Loidl, Michael Monagan, Jean-Charles Faugere.
• Xiangcheng Yu: Accelerating Polynomial Homotopy Continuation on Graphics Processing Units. PhD thesis, UIC, Fall 2015. (first job: software engineer, Microsoft),
  • Jan Verschelde and Xiangcheng Yu: GPU acceleration of Newton's method for large systems of polynomial equations in double double and quad double arithmetic. The abstract and revised manuscript. In Proceedings of the 16th IEEE International Conference on High Performance Computing and Communication (HPCC 2014), pages 161-164, IEEE Computer Society, 2014.
  • Jan Verschelde and Xiangcheng Yu: Accelerating Polynomial Homotopy Continuation on a Graphics Processing Unit with Double Double and Quad Double Arithmetic. The abstract and manuscript. In PASCO 2015, Proceedings of the 7th International Workshop on Parallel Symbolic Computation, edited by Jean-Guillaume Dumas and Erich L. Kaltofen, pages 109-118, ACM 2015.
  • Jan Verschelde and Xiangcheng Yu: Tracking Many Solution Paths of a Polynomial Homotopy on a Graphics Processing Unit. The abstract and manuscript. In the Proceedings of the 17th IEEE International Conference on High Performance Computing and Communications (HPCC 2015), pages 371-376, IEEE Computer Society, 2015.
  • Nathan Bliss, Jeff Sommars, Jan Verschelde, and Xiangcheng Yu: Solving Polynomial Systems in the Cloud with Polynomial Homotopy Continuation. The abstract and manuscript. In the Proceedings of the 17th International Workshop on Computer Algebra in Scientific Computing (CASC 2015), edited by V.P. Gerdt, W. Koepf, W.M. Seiler, and E.V. Vorozhtsov, volume 9301 of Lecture Notes in Computer Science, pages 87-100, Springer-Verlag, 2015.
  • Jan Verschelde and Xiangcheng Yu: Polynomial Homotopy Continuation on GPUs. The abstract and manuscript. ACM Communications in Computer Algebra, volume 49, issue 4, pages 130-133, 2015.
• Danko Adrovic: Solving Polynomial Systems with Tropical Methods. PhD thesis, UIC, Fall 2012. (first job: visiting lecturer at UIC)
  • Danko Adrovic and Jan Verschelde: Tropical Algebraic Geometry in Maple, a preprocessing algorithm for finding common factors to multivariate polynomials with approximate coefficients. The abstract and manuscript. Journal of Symbolic Computation 46(7):755-772, 2011.
  • Danko Adrovic and Jan Verschelde: Computing Puiseux Series for Algebraic Surfaces. The abstract and manuscript. In the Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation (ISSAC 2012), Grenoble, France, July 22-25, 2012. Edited by Joris van der Hoeven and Mark van Hoeij, pages 20-27, ACM 2012.
  • Danko Adrovic and Jan Verschelde: Polyhedral Methods for Space Curves Exploiting Symmetry Applied to the Cyclic n-roots Problem. The abstract and (revised) manuscript. In Computer Algebra in Scientific Computing, 15th International Workshop, CASC 2013, Berlin, Germany, edited by Vladimir P. Gerdt, Wolfram Koepf, Ernst W. Mayr, and Evgenii V. Vorozhtsov. Lecture Notes in Computer Science, Volume 8136, pages 10-29, 2013.
  • Danko Adrovic and Jan Verschelde: a Polyhedral Method to Compute all Affine Solution Sets of Sparse Polynomial Systems. The abstract and manuscript.
• Genady Yoffe: Using Parallelism to compensate for Extended Precision in Path Tracking for Polynomial System Solving. PhD thesis, UIC, Spring 2012. (first job: postdoc at UIC)
  • Jan Verschelde and Genady Yoffe: Polynomial Homotopies on Multicore Workstations. The abstract and manuscript. In PASCO 2010, Proceedings of the 2010 International Workshop on Parallel Symbolic Computation, edited by Marc Moreno Maza and Jean-Louis Roch, pages 131-140, ACM 2010.
  • Jan Verschelde and Genady Yoffe: Quality Up in Polynomial Homotopy Continuation by Multithreaded Path Tracking. The abstract and manuscript.
  • Jan Verschelde and Genady Yoffe: Evaluating polynomials in several variables and their derivatives on a GPU computing processor. The abstract and manuscript. In the Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops (PDSEC 2012). 21-25 May 2012, Shanghai China. IEEE Computer Society, 2012. Pages 1391-1399.
  • Jan Verschelde and Genady Yoffe: Orthogonalization on a General Purpose Graphics Processing Unit with Double Double and Quad Double Arithmetic. The abstract and revised manuscript. In the Proceedings of the 2013 IEEE 27th International Parallel and Distributed Processing Symposium Workshops (PDSEC 2013). 20-20 May 2013, Boston, Massachusetts. IEEE Computer Society, 2013, pages 1373-1380.
• Yun Guan: Numerical Homotopies for Algebraic Sets on a Parallel Computer. PhD Thesis, UIC, Summer 2010. (first job: visiting lecturer at UIC)
  • Yun Guan and Jan Verschelde: PHClab: A MATLAB/Octave interface to PHCpack. The abstract, the poster, and paper . In IMA Volume 148: Software for Algebraic Geometry, edited by Michael E. Stillman, Nobuki Takayama, and Jan Verschelde. Pages 15-32, Springer-Verlag, 2008.
  • 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: Sampling Algebraic Sets in Local Intrinsic Coordinates. The abstract and manuscript. Computers and Mathematics with Applications 62(10): 3706-2721, 2011.
• Kathy Piret: Computing Critical Points of Polynomial Systems using PHCpack and Python. PhD Thesis, UIC, Summer 2008. (first job at Harold Washington College)
  • Kathy Piret and Jan Verschelde: Sweeping Algebraic Curves for Singular Solutions. The abstract and revised manuscript, Journal of Computational and Applied Mathematics 234(4): 1228-1237, 2010.
• Yan Zhuang: Parallel Implementation of Polyhedral Homotopy Methods. PhD thesis, UIC, Summer 2007. (first job at Wolfram Research)
  • Jan Verschelde and Yan Zhuang: Parallel Implementation of the Polyhedral Homotopy Method. The Abstract, revised manuscript in gzipped ps, and in pdf format. Proceedings of the 2006 International Conference on Parallel Processing Workshops. 14-18 Augustus 2006. Columbus, Ohio. High Performance Scientific and Engineering Computing. Edited by Timothy Mark Pinkston and Fusun Ozguner. Pages 481-488, IEEE Computer Society, 2006.
  • Anton Leykin, Jan Verschelde, and Yan Zhuang: Parallel Homotopy Algorithms to Solve Polynomial Systems. The Abstract, manuscript in gzipped ps, and in pdf format. Proceedings of ICMS 2006, LNCS 4151, edited by Andrew Iglesias and Nobuki Takayama. Pages 225-234, Springer-Verlag, 2006.
• Mina Khan: Certifying Approximate Solutions of Polynomial Systems, MS Thesis, UIC, Summer 2007.
• Ailing Zhao: Newton's Method with Deflation for Isolated Singularities of Polynomial Systems. PhD thesis, UIC, Summer 2007. (first job at Wolfram Research)
  • Anton Leykin, Jan Verschelde, and Ailing Zhao: Higher-Order Deflation for Polynomial Systems with Isolated Singular Solutions. The Abstract, manuscript in gzipped ps, and in pdf format.
  • Anton Leykin, Jan Verschelde, and Ailing Zhao: Evaluation of Jacobian Matrices for Newton's Method with Deflation to approximate Isolated Singular Solutions of Polynomial Systems. The Abstract, manuscript in gzipped ps, and in pdf format. In SNC 2005 Proceedings. International Workshop on Symbolic-Numeric Computation. Xi'an, China, July 19-21, 2005. Edited by Dongming Wang and Lihong Zhi. Pages 19-28, 2005. Revised manuscript in gzipped ps and pdf format.
  • Anton Leykin, Jan Verschelde, and Ailing Zhao: Newton's method with deflation for isolated singularities of polynomial systems. The Abstract, revised manuscript in gzipped ps, and in pdf format. Theoretical Computer Science 359(1-3): 111-122, 2006.
• Yusong Wang: Computing Dynamic Output Feedback Laws with Pieri Homotopies on a Parallel Computer. PhD thesis, UIC, Spring 2005. (first job: postdoc at Argonne National Laboratory)
  • Jan Verschelde and Yusong Wang: Computing Dynamic Output Feedback Laws. The Abstract and gzipped postscript file, of the revised manuscript in pdf format. Data consists of input and output. IEEE Transactions on Automatic Control 49(8):1393-1397, 2004.
  • Jan Verschelde and Yusong Wang: Computing Feedback Laws for Linear Systems with a Parallel Pieri Homotopy. The Abstract and manuscript in pdf format. Proceedings of the 2004 International Conference on Parallel Processing Workshops. 15-18 August 2004. Montreal, Quebec, Canada. High Performance Scientific and Engineering Computing. Edited by Yuanyuan Yang. Pages 222-229, IEEE Computer Society, 2004.
  • Jan Verschelde and Yusong Wang: Numerical Homotopy Algorithms for Satellite Trajectory Control by Pole Placement. The Abstract and Revised gzipped postscript file, manuscript in pdf format. Proceedings of MTNS 2002, Mathematical Theory of Networks and Systems (CDROM), Notre Dame, August 12-16, 2002.