# Mathematics Colloquia and Seminars

### Cherednik algebras and subspace arrangements

Algebra & Discrete Mathematics

 Speaker: José Simental Rodríguez, UC Davis Location: 2112 MSB Start time: Mon, Dec 10 2018, 11:00AM

For fixed e and n, we consider the set of points in C^n that have some e
coordinates equal. This is a subspace arrangement, whose defining ideal
has been studied from the point of view of combinatorial commutative
algebra. This ideal turns out to be a module over the type A rational
Cherednik algebra (with parameter 1/e). I will explain joint work with
C. Bowman and E. Norton, that confirms a conjecture of
Berkesch-Griffeth-Sam by constructing a resolution of the e-equals ideal
by standard modules. Forgetting the action of the Cherednik algebra,
this gives a minimal graded-free resolution of the ideal, thus providing
formulas (given in terms of abacus combinatorics) for interesting
homological invariants, such as the Hilbert series and the
Castelnuovo-Mumford regularity. Time permitting, I will explain how to
generalize this to slightly more general subspace arrangements. No prior
knowledge of Cherednik algebras will be assumed.