Research

1  Funded Research

1. Source: National Science Foundation.

Program: Research Experiences for Undergraduates (REU).
Title: Symbolic Software for Lax Pairs and Conservation Laws of Nonlinear Partial Differential Equations.
Award Number: CCF-0830783 (supplement).
Amount: $12,000.
Period: 09/01/2008-09/01/2011.
Students involved: Jacob Rezac, John-Bosco Tran, Travis ``Alan" Volz, undergraduate students.
2. Source: National Science Foundation.

Directorate: Computer and Information Science and Engineering (CISE).
Division: Computing and Communications Foundations (CCF).
Program: Numeric, Symbolic and Geometric Computing.
Title: Symbolic Software for Conservation Laws of Multi-Dimensional Continuous and Discrete Nonlinear Equations.
Award Number: CCF-0830783
Amount: $250,000.
Period: 09/01/2008-09/01/2001.
Person-Months or % of Effort: Summ.: 1 month in Summers 2009, 2010, and 2011.
3. Source: National Research Foundation South Africa.

Division: Information and Communication Technology.
Program: Unlocking the Future.
Title: Radial Basis Functions, Subdivision, and Nonlinear Systems.
Award Number: FA2007032500003.
Co-PI: B. Herbst.
Amount: R744,000 ($106,350), including R20,000 ($2,860) to support Hereman's research visit.
Period: 01/01/2008-01/01/2011.
Person-Months or % of Effort: 1 month in Spring 2008.
4. Source: National Science Foundation.

Program: Research Experiences for Undergraduates (REU).
Title: Design and Implementation of Symbolic Algorithms for Exact Solutions of Systems of Nonlinear Partial Differential Equations and Differential-Difference Equations.
Award Number: CCR-9901929 (supplement).
Amount: $12,000.
Period: 07/01/2003-07/31/2004.
Students involved: Adam Ringler and Ryan Sayers, undergraduate students.
5. Source: National Science Foundation.

Program: Research Experiences for Undergraduates (REU).
Title: Design and Implementation of Symbolic Algorithms for Exact Solutions of Systems of Nonlinear Partial Differential Equations and Differential-Difference Equations.
Award Number: CCR-9901929 (supplement).
Amount: $10,000.
Period: 03/22/2002-07/31/2003.
Students involved: Douglas Baldwin and Jack Sayers, undergraduate students.
6. Source: National Science Foundation.

Program: DMS-Infrastructure Program: Scientific Computing Research Environments for the Mathematical Sciences (SCREMS).
Title: Scientific Computing Research Environments for the Mathematical Sciences.
PI: G. Fairweather.
Co-PIs: B. Bialecki, W. Hereman, A. Rockwood, and J. Wang.
Award Number: DMS-0215491.
Amount: $25,000 (excluding cost sharing by CSM with $25,092).
Period: 07/30/2002-07/30/2004.
7. Source: National Science Foundation.

Program: Research Experiences for Undergraduates (REU).
Title: Design and Implementation of Symbolic Algorithms for Exact Solutions of Systems of Nonlinear Partial Differential Equations and Differential-Difference Equations.
Award Number: CCR-9901929 (supplement).
Amount: $10,000.
Period: 02/02/2001-07/31/2002.
Students involved: Douglas Baldwin and Benjamin Kowalski, undergraduate students.
8. Source: National Science Foundation.

Directorate: Computer and Information Science and Engineering (CISE).
Program: Numeric, Symbolic and Geometric Computation Program.
Title: Symbolic Software for the Study of Integrability of Nonlinear Partial Differential and Differential-Difference Equations.
Award Number: CCR-9901929.
Amount: $233,645.
Period: 08/15/1999-07/31/2002.
Students involved: Douglas Baldwin, Paul Blanchard, John "Jack" Milwid, Matthew Porter-Peden, Jack Sayers, Ryan Sayers, and Adam Rangler, undergraduate students; Paul Adams and Holly Eklund, graduate students.
9. Source: Wolfram Research, Inc.

Program: Visiting Scholar Grants 2000.
Title: Exact Solutions of Nonlinear Partial Differential Equations.
Amount: airfare, lodging, lifetime free Mathematica software.
Period: 06/00/2000-03/01/2001.
10. Source: National Science Foundation.

Program: Research Experiences for Undergraduates (REU).
Title: Research in the Department of Mathematical and Computer Sciences at the Colorado School of Mines.
Co-PI: G. Fairweather and B. Bath.
Senior Participants: W. Hereman et al.
Award Number: 9912293.
Amount: $49,673.
Period: 06/15/2000-06/14/2003.
Students involved: several undergraduate students.
11. Source: Colorado School of Mines.

Program: Technology Fee Committee.
Title: Upgrading the Student PC Laboratory in Mathematical and Computer Sciences.
Co-PI: X. Wu.
Amount: $7,854.
Period: Academic Year 1999-2000.
Students involved: undergraduate students in MACS courses, all MACS majors.
12. Source: National Science Foundation.

Program: DMS-Infrastructure Awards. Scientific Computing Research Environments for the Mathematical Sciences (SCREMS).
Title: Computing Environments for Mathematical Sciences Research.
Co-PIs: W. Navidi, B. Bialecki, L. Tenorio, and E. S. Van Vleck.
Award Number: DMS-9872005.
Amount: $37,595 (excluding cost sharing by CSM with $37,110).
Period: 07/15/1998-06/30/2000.
13. Source: National Science Foundation.

Program: Research Experiences for Undergraduates (REU).
Title: Research in the Department of Mathematical and Computer Sciences at the Colorado School of Mines.
PIs: E. Van Vleck and B. Bath.
Co-PIs: B. Bialecki, N. Bleistein, G. Fairweather, W. Hereman, R. Krishnapurum, M. Misra, W. Navidi, S. Pruess, J. Scales, and L. Tenorio.
Award Number: DMS-9732069.
Amount: $55,000.
Period: 08/01/1998-10/31/1999.
Students involved: several undergraduate students.
14. Source: National Science Foundation.

Program: Research Experiences for Undergraduates (REU).
Title: Design and Implementation of Integrability Tests in Mathematica for Systems of Nonlinear Differential Equations.
Award Number: CCR-9625421 (supplement).
Amount: $5,000.
Period: 05/01/1998-08/31/1999.
Student involved: Michael Colagrosso, undergraduate student.
15. Source: Colorado School of Mines.

Program: Curriculum Reform Committee and NSF Programs, Pedagogy and Process.
Title: Differential Equations: Creating an Applications Driven Course.
Co-PI: B. Bath.
Amount: $4,996.
Period: Summer and Fall 1997.
Students involved: Nadine Filosi, graduate student.
16. Source: Colorado Advanced Software Institute (CASI).

Program: CASI Undergraduate Research Grant Program.
Title: Computational Analysis of Electromagnetic Scattering.
Co-PIs: J. DeSanto and M. Misra.
Amount: $3,000.
Period: Academic Year 1997-1998.
Student involved: Grant Erdmann, undergraduate student.
17. Source: Colorado School of Mines.

Program: Technology Fee Committee.
Title: A Student Computing Laboratory in Mathematical and Computer Sciences.
Co-PI: B. Bath.
Amount: $57,500 (excluding cost sharing of $15,000 by MCS Department).
Period: Fall 1996.
Students involved: undergraduate and graduate students in MCS courses, all MCS majors.
18. Source: National Science Foundation.

Directorate: Computer and Information Science and Engineering (CISE).
Division: Computer-Communications Research.
Program: Numeric, Symbolic and Geometric Computation Program.
Title: Symbolic Software for the Investigation of Nonlinear Partial Differential Equations.
Award Number: CCR-9625421.
Amount: $87,000 (excluding cost sharing $14,908 from CSM).
Period: 09/15/1996-08/31/1999.
Student involved: Unal Goktas, graduate student.
19. Source: National Science Foundation.

Program: Research Experiences for Undergraduates (REU).
Title: Development of a Mathematica Program for the Painlevé Integrability Test of Nonlinear Differential Equations.
Award Number: CCR-9300978 (supplement).
Amount: $5,000.
Period: 05/01/1996-08/31/1996.
Student involved: Antonio Miller, undergraduate student.
20. Source: Department of Defense.

Program: Multi-disciplinary University Research Initiative (MURI).
Air Force Office of Scientific Research (AFOSR) Computational Electromagnetics Initiative.
Title: Electromagnetic Scattering from Rough Surfaces.
Co-PIs: J. DeSanto and M. Misra.
Award number: AFOSR Grant F49620-96-1-0039.
Amount: $290,000.
Period: 01/01/1995-12/31/2000.
Students involved: Grant Erdmann, undergraduate student; Jeffrey Boleng, graduate student.
21. Source: National Science Foundation.

Program: DMS-Infrastructure Awards. Scientific Computing Research Environments for the Mathematical Sciences (SCREMS).
Title: Mathematical Sciences Computing Research Environment.
Co-PIs: E. Van Vleck, M. Misra, G. Fairweather, and J. Scales.
Award number: DMS-9506603.
Amount: $50,000, matched by CSM with $80,655.
Period: Academic Year 1994-1995.
Students involved: Chris Elmer and Unal Goktas, graduate students.
22. Source: National Science Foundation.

Directorate: Computer and Information Science and Engineering (CISE).
Division: Computer-Communications Research.
Program: Numeric, Symbolic and Geometric Computation Program.
Title: Development of Symbolic Software for Nonlinear Partial Differential Equations.
Award Number: CCR-9300978.
Amount: $69,923 (excluding cost sharing by CSM with $4,000).
Period: 09/01/1993-08/31/1996.
Students involved: Chris Elmer and Unal Goktas, graduate students.
23. Source: National Science Foundation.

Program: Instrumentation and Laboratory Improvement (ILI).
Title: Toward making Mathematics a Laboratory Science.
Co-PIs: F. Hagin, B. Bath, R. Underwood, and J. Cohen.
Amount: $43,000 (excluding cosh sharing by CSM with $43,000).
Period: Academic Year 1990-1992.
24. Source: Thunder Basin Coal Company, Wright WY.

Program: Advanced Computing.
Title: The Bulldozer Project.
Amount: $12,000 ($5,000 in student support).
Period: 12/01/1990-07/31/1991.
Student involved: William Murphy, graduate student.

At Other Institutions

1. Source: North Atlantic Treaty Organization (NATO).

Title: Research Fellowship.
Amount: $7,000 (travel and living expenses) plus salary and benefits for 10 months.
Location: Department of Electrical and Computer Engineering, University of Iowa, Iowa City, Iowa.
Period: Academic Year 1985-1986.

2. Source: North Atlantic Treaty Organization (NATO).

Title: Research Fellowship.
Amount: $6,000 + salary and benefits for 10 months.
Location: Department of Electrical and Computer Engineering, University of Iowa, Iowa City, Iowa.
Period: Academic Year 1983-1984.

2  Undergraduate Research and Other Research Projects

• Field Sessions and Research for Undergraduate (REU) Projects



1. Title: Symbolic Software for Lax Pairs and Conservation Laws of Nonlinear Partial Differential Equations.
   Program: Research Experiences for Undergraduates (REU).
   Location and date: MACS, Colorado School of Mines, Summer 2009.
   Sponsor: Supplemental Award, National Science Foundation.
   Supervisors: Willy Hereman assisted by Douglas Poole and Terry Bridgman.
   Students involved: Jacob Rezac, John-Bosco Tran, Travis ``Alan" Volz, undergraduate students.
2. Title: Development of Algorithms and Mathematica Software for the Symbolic Computation of Conservation Laws of System of PDEs in Multi-dimensions.
   Program: Research Experiences for Undergraduates (REU).
   Location and date: MACS, Colorado School of Mines, Summer 2004.
   Sponsor: Field Session 2004 and Supplemental Award, National Science Foundation.
   Supervisors: Willy Hereman and Michael Colagrosso.
   Students involved: Lindsay Auble, Robert `Scott' Danford, Forrest Lundstrom, Maxine von Eye, undergraduate students.
3. Title: Development of Algorithms and Mathematica Software for Higher Euler and Homotopy Operators of Nonlinear Partial Differential Equations and Differential-Difference Equations.
   Program: Research Experiences for Undergraduates (REU).
   Location and date: MACS, Colorado School of Mines, Summer 2003.
   Sponsor: Field Session 2003 and Supplemental Award, National Science Foundation.
   Clients: W. Hereman and M. Colagrosso.
   Students involved: Ingo Kabirschke, Frances Martin, Kara Namanny, Adam Ringler, and Ryan Sayers, undergraduate students.
4. Title: Design and Implementation of Symbolic Algorithms for Recursion Operators of Systems of Nonlinear Partial Differential Equations and Differential-Difference Equations.
   Program: Research Experiences for Undergraduates (REU).
   Location and date: MACS, Colorado School of Mines, Summer 2002.
   Sponsor: Supplemental Award, National Science Foundation.
   Supervisor: Willy Hereman.
   Students involved: Douglas Baldwin and Jack Sayers, undergraduate students.
5. Title: Design and Implementation of Symbolic Algorithms for Testing Exact Solutions of Nonlinear Partial Differential Equations.
   Program: Research in the Department of Mathematical and Computer Sciences at the Colorado School of Mines.
   Location and date: MACS, Colorado School of Mines, Summer 2002.
   Sponsor: Research Experiences for Undergraduates (REU site), National Science Foundation.
   Supervisor: Willy Hereman.
   Students involved: Jason Blevins and Jeffrey Heath, undergraduate students.
6. Title: Implementation of Symbolic Algorithms for Exact Solutions of Systems of Nonlinear Partial Differential Equations.
   Program: Research Experiences for Undergraduates (REU).
   Location and date: MACS, Colorado School of Mines, Summer 2002.
   Sponsor: Supplemental Award, National Science Foundation.
   Supervisor: Willy Hereman.
   Students involved: Paul Blanchard, John Milwid, and Matthew Porter-Peden, undergraduate students.
7. Title: Design and Implementation of Symbolic Algorithms for Exact Solutions of Systems of Nonlinear Partial Differential Equations and Differential-Difference Equations.
   Program: Research Experiences for Undergraduates (REU).
   Location and date: MACS, Colorado School of Mines, Summer 2001.
   Sponsor: Supplemental Award, National Science Foundation.
   Supervisor: Willy Hereman.
   Students involved: Douglas Baldwin and Benjamin Kowalski, undergraduate students.
8. Title: Symbolic computation of tanh solutions of nonlinear partial differential equations.
   Program: Research in the Department of Mathematical and Computer Sciences at the Colorado School of Mines.
   Location and date: MACS, Colorado School of Mines, Summer 2000.
   Sponsor: Research Experiences for Undergraduates (REU site), National Science Foundation.
   Supervisor: Willy Hereman.
   Students involved: Steve Formenac, Andrew Menz, and Douglas Baldwin, undergraduate students.
9. Title: Mathematica implementation of the computation of solitons via Hirota's bilinear method.
   Program: Undergraduate Research.
   Location and date: MACS, Colorado School of Mines, Summer 1999.
   Sponsor: National Science Foundation.
   Supervisor: Willy Hereman.
   Student involved: Jeffrey Hanel, undergraduate students.
10. Title: Mathematica implementation of a technique for solving PDEs through homogenization.
    Program: Undergraduate Research.
    Location and date: MACS, Colorado School of Mines, Summer 1999.
    Sponsor: National Science Foundation.
    Supervisor: Willy Hereman.
    Student involved: Guy Somberg, undergraduate students.
11. Title: Symbolic computation of tanh and sech solutions of nonlinear partial differential and differential-difference equations.
    Program: Research in the Department of Mathematical and Computer Sciences at the Colorado School of Mines.
    Location and date: MACS, Colorado School of Mines, Summer 1999.
    Sponsor: Research Experiences for Undergraduates (REU site), National Science Foundation.
    Supervisor: Willy Hereman.
    Students involved: Linda Hong, Ryan Martino and Joel Miller, undergraduate students.
12. Title: Development of a Mathematica Program for the Painlevé Integrability Test for Systems of Nonlinear Differential Equations.
    Program: Research Experiences for Undergraduates (REU).
    Location and date: MACS, Colorado School of Mines, Summer 1998.
    Sponsor: Supplemental Award, National Science Foundation.
    Supervisor: Willy Hereman.
    Student involved: Michael Colagrosso.
13. Title: Development of a Mathematica Program for the Painlevé Integrability Test for Systems of Nonlinear Differential Equations.
    Program: Field Session.
    Location and date: MACS, Colorado School of Mines, Summer 1997.
    Client: Willy Hereman.
    Student involved: Michael Colagrosso.
14. Title: Computational Modeling of Rough Surface Scattering.
    Program: MURI Project and Field Session.
    Location and date: MACS, Colorado School of Mines, Summer 1996.
    Clients: John DeSanto, Willy Hereman, and Manavendra Misra.
    Students involved: Grant Erdmann, Amy Sinex, and Colleen Craig, undergraduate students.
    Additional team members: Jeff Boleng and Morrakot Khebchareon, graduate students.
15. Title: Design of a Mathematica Program for the Painlevé Test. .
    Program: Research Experiences for Undergraduates (REU).
    Location and date: MACS, Colorado School of Mines, Summer 1996.
    Supervisor: Willy Hereman.
    Student involved: Antonio Miller, undergraduate students.
16. Title: Development of a Mathematica Program for the Painlevé Integrability Test for Nonlinear Differential Equations.
    Program: Field Session.
    Location and date: MACS, Colorado School of Mines, Summer 1995.
    Client: Willy Hereman.
    Students involved: Tracy Otto and Antonio Miller, undergraduate students.
     
• Collaborative Research Projects on Wavelets and Diffusion Maps (including software design)



1. Barend Herbst, Department of Mathematics, Division of Applied Mathematics, University of Stellenbosch, Matieland, South Africa.
2. Lucas Monzon and Gregory Beylkin, Department of Applied Mathematics, University of Colorado, Boulder, Colorado.

 
• Collaborative Research Projects on Integrability of PDEs, DDEs, and lattice equations: Symmetries, Conservation Laws, Lax Pairs, Special Solutions (including software design).



1. Peter Hydon, Department of Mathematics, University of Surrey, Guildford, U.K.
2. Reinout Quispel and Peter Van der Kamp, Department of Mathematics, La Trobe University, Melbourne, Australia.
3. Michel Grundland, Centre de Recherches Mathématiques, Université de Montréal, Montréal, Québec, Canada.
4. Bernard Deconinck, Department of Applied Mathematics, University of Washington, Seattle.
5. Ünal Göktas, Wolfram Research, Inc., Champaign, Illinois.
6. Mark Hickman (sabbatical visitor, February 4-June 10, 2002), Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand.
7. Jan Sanders (and Jing Ping Wang), Department of Mathematics and Computer Science, Free University, Amsterdam, The Netherlands.
8. Willy Malfliet, Department of Physics, University of Antwerp, Antwerp, Belgium.
9. Thomas Wolf, Department of Mathematics, Brock University, St. Catharines, Ontario, Canada.
10. Frank Verheest, Department of Mathematical Physics and Astronomy Research, University of Ghent, Gent, Belgium.