PositiveCharacteristic - Macaulay2/Workshop-2015-Boise GitHub Wiki

This group will focus on implementing various algorithms involving the Frobenius endomorphism.

As far as I am aware, Emily and Daniel have proposed to work on project that involves developing and implementing algorithms for computing so-called F-jumping numbers of polynomials (and consequently, roots of the associated Bernstein-Sato polynomials), and Zhibek mentioned perhaps implementing some algorithms that test whether a given ring is strongly F-regular (e.g., Glassbrenner's criteria).

Here are some references:

• http://arxiv.org/abs/math/0312486 (in which F-pure thresholds are defined.)
• http://arxiv.org/abs/math/0411170 (discusses F-thresholds of polynomials, and their connection with Bernstein-Sato polynomials.)
• http://arxiv.org/abs/math/0607660 (a good introduction to test ideals and jumping numbers in regular rings.)
• http://arxiv.org/abs/1104.2000 (a survey of test ideals. This is a good place to find other references.)
• D. Glassbrenner, Strong F-regularity in images of regular rings, Proceedings of the American Mathematical Society, 124 (1996) no. 2, 245-253.

The project proposed by Emily and Daniel requires a bit of background, and has no real references. So, it may be tricky for the entire group to work on this. That being said, there may be some other projects for people with less background, and we should definitely discuss this at the start of the workshop!