This proposal will provide support for an Intensive Workshop for Macaulay2 Development, to be held on August 5th-9th, 2012 at Wake Forest University in Winston-Salem, NC. Approximately 30 researchers will attend the workshop. The main objective is to implement algorithms in the following three rapidly growing areas: enumerative geometry, numerical algebraic geometry, homological algebra, and algebraic statistics. These areas have significant applications in fields as diverse as computational biology, data analysis, statistics, and theoretical physics. It is the expectation, therefore, that the packages developed through this workshop will advance our knowledge and understanding across multiple disciplines. Some emphasis will also be placed on enhancing the multithreaded capabilities of Macaulay2.
Macaulay2 is one of the leading computer algebra systems for research and teaching in algebraic geometry and commutative algebra. The ability to perform increasingly complicated computations in more areas of these two fields continues to revolutionize both research in algebraic geometry and commutative algebra, and the breadth of the applications of these fields to other areas of research. Most of the other related computer algebra systems are based in foreign countries and continued competitiveness of Macaulay2, a leading United States--based program, depends on both a broad community contributing to its development and the funding to support this community through intensive workgroup meetings.
The participation of both experienced and novice researchers from a variety of institutions is crucial to the work of these workshops. These intensive workshops are also a great opportunity for graduate students and postdoctoral fellows to enhance their package-writing skills early in their careers, taking advantage of the experience and research expertise of the more senior researchers as well as sharing their own expertise with the group. A strong presence from young researchers also helps the base of mathematicians programming for Macaulay2 to grow over time. Travel and lodging support for these workshops are critical to both the intensive nature of the workshop and to the future development of Macaulay2.
Algebraic geometry is the study of solution sets to systems of polynomial equations. It has applications in a number of fields such as physics, robotics, operations research, and statistics. Its underpinnings are based in the field of commutative algebra. Of late, computational tools have provided each field with much-needed insight to both formulate new results and prove long-standing conjectures. Macaulay2 is a software package that is useful for performing computations and conducting research in commutative algebra, algebraic geometry, and its applications. From August 5-9, 2012, we held an intensive workshop consisting of 30 individuals at Wake Forest University to work on software written in the Macaulay2 language that extends this functionality. Our work at the workshops can be summarized as follows. 1. Find important topics of research and computational needs in the community and implement the code necessary to keep research in related fields moving forward. 2. Develop, grow and mentor the community of Macaulay2 users and more importantly, those comfortable with writing Macaulay2 packages. 3. Facilitate the development and stabilization of the infrastructure of the program and the community developing it. The workshop was quite successful, as we attracted a number of senior members in the field, as well as a healthy number of graduate students and novices to the Macaulay2 system. Among the participants were 8 women, and 10 graduate students. The training of underrepresented groups, as well as early-career mathematicians is an important part of the broader impacts of this conference. A complete list of the packages developed at this conference, as well as the topics discussed, can be found in the final report, or can also be found on the wiki for the conference: http://wiki.macaulay2.com/Macaulay2/index.php?title=WFU2012_-_Main_Page
