| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
|
| Initial Amendment Date: | September 2, 2015 |
| Latest Amendment Date: | September 2, 2015 |
| Award Number: | 1547743 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Leland Jameson
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | September 1, 2015 |
| End Date: | August 31, 2017 (Estimated) |
| Total Intended Award Amount: | $19,020.00 |
| Total Awarded Amount to Date: | $19,020.00 |
| Funds Obligated to Date: |
|
| History of Investigator: |
|
| Recipient Sponsored Research Office: |
940 GRACE HALL NOTRE DAME IN US 46556-5708 (574)631-7432 |
| Sponsor Congressional District: |
|
| Primary Place of Performance: |
940 Grace Hall Notre Dame IN US 46556-5708 |
| Primary Place of
Performance Congressional District: |
|
| Unique Entity Identifier (UEI): |
|
| Parent UEI: |
|
| NSF Program(s): | COMPUTATIONAL MATHEMATICS |
| Primary Program Source: |
|
| Program Reference Code(s): |
|
| Program Element Code(s): |
|
| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
Recent developments in software for solving nonlinear polynomial systems may provide many scientists and engineers the tools needed to solve key problems in their research. To facilitate the training necessary to make best use of these powerful tools, the PIs will run a workshop May 23-25, 2016 at the University of Notre Dame. In addition to training, the workshop will also provide cross-fertilization between the mathematical sciences and other areas of science and engineering by bringing together a diverse group of researchers and software developers to exchange both knowledge and challenges. These interactions will spur practical research in applications while highlighting needs for future algorithm development.
Since they arise in many areas of science and engineering, several approaches have been developed for solving polynomial systems. The software package Bertini, which is being redeveloped in C++ and Python for modularity and scriptability, implements key numerical algebraic geometric algorithms for solving and manipulating polynomial systems. This workshop will bring together a wide range of computational scientists and practitioners to discuss recent progress and current challenges in software, algorithms, and applications of numerical algebraic geometry. This interdisciplinary workshop will include small group discussions, hands-on demonstrations of Bertini, and sessions focused on developing Bertini modules related to participants' particular interests.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
Note:
When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external
site maintained by the publisher. Some full text articles may not yet be available without a
charge during the embargo (administrative interval).
Some links on this page may take you to non-federal websites. Their policies may differ from
this site.
PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
This award was used to partially support many early career researchers (graduate students, postdocs, and researchers without federal funding) to attend two meetings held at the University of Notre Dame: "Workshop on Software and Applications of Numerical Algebraic Geometry" (May 23-25, 2016) and "Polynomials, Kinematics, and Robotics" (June 507, 2017).
The 2016 workshop taught the attendees about the basics of numerical algebraic geometry so that they can use these tools in their own research. This workshop also described using numerical algebraic geometry to solve several applications from robotics, kinematics, and chemical engineering. This workshop included software demonstrations so that the attendees can understand some of the tools available in numerical algebraic geometry as well as an open problem session. One of the open problems presented was the robotics synthesis problem for three-revolute spatial chains for body guidance, which has since been solved as a result of this workshop.
The 2017 conference included speakers who discussed the history of the development of numerical algebraic geometry, current successes in robotics and kinematics, and future research challenges. A poster presentation allowed many early career researchers to share their research with the participants of the conference. All participants received a 3D printed algebraic surface for their participation, with the top two posters receiving larger 3D printed algebraic surfaces for their accomplishments.
The intellectual merits lie in the expanded knowledge of addressing the fundamental topic of solving nonlinear polynomial systems of equations. By bringing together a diverse group of participants to exchange both knowledge and challenges, these events spurred practical research in applications while also highlighting immediate needs for research in algorithm development.
The broader impacts of this project include the broad use of algorithms and software tools in numerical algebraic geometry that provide new avenues for inquiry by the participants. This will help develop the next generation of strong ethical researchers by learning about techniques and challenges of solving nonlinear equations, as well as applying these tools to solve problems in science and engineering. These events encouraged diversity among the participants, both in terms of under-represented groups and in areas of research.
Last Modified: 09/16/2017
Modified by: Jonathan D Hauenstein
Please report errors in award information by writing to: awardsearch@nsf.gov.
