Free resolutions and computations, Berkeley 2017

Adelphi University, Garden City NY

Investigators

Abstract

This award supports participation in the conference and software development workshop entitled "Stillman's Conjecture and other Progress on Free Resolution" to be held on July 17-21, 2017, at the University of California, Berkeley. A core focus for this meeting is two important and timely areas of research. The conference will bring together leading experts with young researchers at a time of exciting developments and new breakthroughs. Many of these recent developments were inspired by computer experiments, which are becoming more common within the fields of algebraic geometry and commutative algebra. The workshop will focus on developing Macaulay2, a leading computer algebra system within these fields. By helping researchers develop their own packages, there will be immediate research impact as they and others compute new examples which push the mathematical frontier. Such examples can answer old questions and inspire new ideas, just like those that are to be presented at the scientific conference. Further information is available at the conference website: https://macaulay2.github.io/Workshop-2017-Berkeley/ The first two days of the meeting will be a conference on free resolutions and commutative algebra. The time is ripe for such a conference; in Summer 2016 Irena Peeva and Jason McCullough (both of whom will speak at the meeting) resolved a famous 38-year-old conjecture on free resolutions due to Eisenbud-Goto. There has also been recent progress on Stillman's question, which asks for a bound on projective dimension of an ideal, based solely on the number of generators and degrees (Mel Hochster and Craig Huneke will give talks on their work). The meeting will then switch gears, to a software development workshop for Macaulay2, one of the world's leading software systems for supporting research in commutative algebra and algebraic geometry. Macaulay2 is open source, and one of the key ways in which it extends its functionality is through packages, which allow researchers to write functions that utilize Macaulay2's core functions. The workshop will enhance research infrastructure by constructing packages which will be subsequently integrated into Macaulay2. It will also serve as a training ground for algebraists to use and write for Macaulay2. The workshop will build bridges and foster connections between workers on the theoretical and computational aspects of free resolutions. Macaulay2 workshops have a history of being inclusive both in terms of including underrepresented groups and for including participants from a wide variety of positions. The organizers are committed to continuing this tradition.