Homological Day 2011
May 5-6, 2011
Department of Mathematics, University of Kansas,
Hailong Dao and Olgur Celikbas
This mini-conference, partially sponsored by
NSF and the University of Kansas,
will focus on several homological aspects of (non)commutative algebra. UPDATE: the conference has concluded. Some pictures can be found here .
Location: Department of Mathematics, University of Kansas.
The talks will be held at 306 or 408 Snow Hall.
Speakers and schedule:
Jorgensen (University of Texas, Arlington) 2:30-3:20pm May 5, 306 Snow Title: Pinched homological algebra and Tate (co)homology.
Abstract: We give a new construction called pinched tensor and pinched Hom of complexes over an associative ring, which resemble the ordinary tensor and Hom
of complexes. The new construction has the benefits of returning smaller complexes, and the homology gives the Tate Tor and Tate Ext when the complexes are complete resolutions of totally reflexive modules. As an application we prove that the Tate Tor and Ext functors are balanced, a question which has been open until now. This is joint work with Lars W. Christensen.
Coffee and snacks: 3:30-4:00 pm, Common Room
Takahashi (Shinshu University, Japan)
4:00h - 4:50pm, May 5, 306 SnowTitle: Dimensions of derived categories of commutative rings.
Abstract: Several years ago Rouquier introduced the notion of the dimension of a triangulated category, and proved that the bounded derived category of
coherent sheaves on a separated scheme of finite type over a perfect
field has finite dimension. In this talk, we study the dimension of
the bounded derived category of finitely generated modules over a
commutative noetherian ring. We show that it is finite when the base
ring is a complete local ring.
Petter Andreas Bergh (NTNU, Norway)
11h - 11:50h, May 6, 408 Snow
Title: Cohomological symmetry over exterior algebras.
Abstract: When is vanishing of Ext(M,N) equivalent to vanishing of Ext(N,M)? In the commutative local world, such symmetry holds for complete intersections (Avramov and Buchweitz), and, more generally, for AB rings (Huneke and Jorgensen). In the noncommutative world, the group algebras of finite groups have this property. We show that it holds for exterior algebras.
Liana Sega (University of Missouri, Kansas City)
12h - 12h50h, May 6, 408 Snow
Self-tests for freeness over commutative artinian rings.
Abstract: The main result presented in this talk will be that the commutative version of the Auslander-Reiten conjecture holds for Gorenstein local rings (R,m) with m^4=0 which admit an exact zero-divisor.