**Seminario de Álgebra**

**Lunes 18 de diciembre de 2017 a las 11:00 en el aula 420 del módulo 17 **

**Conferenciante: Eleonore Faber (University of Leeds)**

**Title: Endomorphism rings and rings of differential operators of finite global dimension
Abstract: In this talk we consider a normal toric algebra R over a field k of arbitrary characteristic. The module M of p^e-th roots of R, where p and e are positive integers, is then the direct sum of so-called conic modules. With a combinatorial method we construct certain complexes of conic modules over R and explain how these yield projective resolutions of simple modules over the endomorphism ring End_R(M). Thus we obtain a bound on the global dimension of End_R(M), which shows that this endomorphism ring is a so-called noncommutative resolution of singularities (NCR) of R (or Spec(R)). If the characteristic of k is p>0, then this fact allows us to bound the global dimension of the ring of differential operators D(R). This is joint work with Greg Muller and Karen E. Smith.**