3:00pm - 5:00pmComputations in algebraic geometry
Chair(s): Diane Maclagan (University of Warwick), Gregory G. Smith (Queen's University)
This minisymposium highlights the use of computation inside algebraic geometry. Computations enter algebraic geometry in several different ways including numerical strategies, symbolic calculations, experimentation, and simply as a fundamental conceptual tool. Our speakers will showcase many of these aspects together with some applications.
(25 minutes for each presentation, including questions, followed by a 5-minute break; in case of x<4 talks, the first x slots are used unless indicated otherwise)
Regularity of S_n-invariant monomial ideals
Claudiu Raicu
University of Notre Dame
Consider a polynomial ring R in n variables with the action of the symmetric group Sn by coordinate permutations. I will describe an explicit recipe for computing the graded components of the modules Ext(I,R), when I is an arbitrary Sn-invariant monomial ideal, as well as the maps induced by inclusions of such ideals. As a consequence, this gives explicit formulas for the the regularity of Sn-invariant monomial ideals.
On subring counting and simultaneous monomialization
Anne Frübhis-Krüger
University of Hanover
The task of determining the order zeta function for certain number rings (which is just a sophisticated form of counting subrings) gives rise to a particular kind of p-adic integrals. The domain of integration of these stubbornly withstands standard techniques, including even an out-of-the-box Hironaka-style resolution of singularities. However, choosing centers of blow-ups using the structural properties of the problem, a simultaneous monomialization of the conditions can be achieved, making the problem again accessible to usual methods. This talk is based on joint work with Josh Maglione, Bernd Schober, and Christopher Voll.
Asymptotic syzygies for products of projective space
Juliette Bruce
University of Wisconsin
We will discuss results describing the asymptotic syzygies of products of projective space, in the vein of the explicit methods of Ein, Erman, and Lazarsfeld’s non-vanishing results on projective space.
Where can toric syzygies live?
Milena Hering
University of Edinburgh
Syzygies of toric varieties admit a natural grading by the character lattice of the corresponding torus. I will give some results on the the regions in the character lattice in which toric syzygies can be supported. This is joint work with Castryck and Lemmens.
