A Criterion for Detecting m-regularity

Date: 
Thursday, April 5, 2018 - 2:00pm
Location: 
110 Math Science Building
Speaker: 
Will Allbritain
(MU Math)

In homological algebra, one technique we have for understanding a module is to compute its (first) syzygies. Even in a very nice setting, for example a homogeneous ideal in a polynomial ring over a field, this can be difficult, or at least computationally intensive. In their paper "A Criterion for Detecting $m$-regularity", Bayer and Stillman find a means of limiting the highest degree one must check to find minimal syzygies of such an ideal. They also discuss how passing to the initial ideal to find these syzygies, an idea advanced by earlier researchers, can be made to work out especially nicely when a particular monomial ordering, the graded reverse lex ordering, is used.