## Fall 2017

## Spring 2017

## April 26th, 14:15 in room 734

**Title:** Presentations of braid/spherical twist groups

**Speaker:** Yu Zhou

**Abstract:** Let S be a surface with non-empty boundary and with a finite set of decorating points. The braid twist group BT(S) of S is the subgroup of its mapping class group MCG(S) generated by the braid twists along simple arcs connecting distinct decorating points. When S arises from a triangulated marked surface, there is an associated quiver with potential (Q,P). It was shown by Yu Qiu that BT(S) is isomorphic to the subgroup ST(D) of Aut(D) generated by the spherical twists, where D is the finite dimensional derived category of the Ginzburg dg algebra of (Q,P). In this talk, I will give various presentations of these twist groups. This is joint work with Yu Qiu.

## February 15th, 14:15-15:15 in room 734

**Title:** Projective level and the Homological Conjectures

**Speaker:** William Sanders

**Abstract:** The projective level of a complex of R-modules F is roughly the number steps it takes to build F from direct sums of shifts of projective R-modules. In this talk, we will discuss lower bounds of this invariant. When R is a commutative Noetherian local ring, these lower bounds are related to collection of statements known as the Homological Conjectures. The homological conjectures were open for many years but many of them were resolved this summer by Yves André. The relation of these conjectures to projective level provides a new triangulate vantage to consider this interesting subject.