Speaker: Rajiv Kumar
Title: Herzog-Kuhl Equations and its Applications - I
Abstract: In these talks, we will see relations between Hilbert series of a module and its graded Betti numbers. This gives relations between the
graded Betti numbers of a modules which are known as Herzog-Kuhl equations. As an application, we show that the property of R being Cohen-Macaulay is characterized by the existence of a pure Cohen-Macaulay R-module of finite projective dimension.
Speaker: Jai Laxmi
Title: Tate Resolutions - I
Abstract: Let S be a Noetherian ring, and R = S/I. It is always possible to construct a differential graded algebra (DG-algebra) resolution of R over S due to a result of Tate. If R is the residue field of S, then
Gulliksen proved that such a DG-algebra resolution is minimal. We shall discuss the construction of the Tate resolution in our talk.
10:00am
11:00am
12:00pm
1:00pm
2:00pm
3:00pm
4:00pm
5:00pm
6:00pm
Time:
9:30am-10:30am
Location:
Room 215, Department of Mathematics
Description:
Speaker: Rajiv Kumar
Title: Herzog-Kuhl Equations and its Applications - I
Abstract: In these talks, we will see relations between Hilbert series of a module and its graded Betti numbers. This gives relations between the
graded Betti numbers of a modules which are known as Herzog-Kuhl equations. As an application, we show that the property of R being Cohen-Macaulay is characterized by the existence of a pure Cohen-Macaulay R-module of finite projective dimension.
Time:
10:30am-11:30am
Location:
Room 215, Department of Mathematics
Description:
Speaker: Jai Laxmi
Title: Tate Resolutions - I
Abstract: Let S be a Noetherian ring, and R = S/I. It is always possible to construct a differential graded algebra (DG-algebra) resolution of R over S due to a result of Tate. If R is the residue field of S, then
Gulliksen proved that such a DG-algebra resolution is minimal. We shall discuss the construction of the Tate resolution in our talk.