Problem Session , Seattle 1996 Compiled by Dave Benson

The 1988 AAAI Workshop on Explanation

Expert system explanation is the study of how to give an expert system the ability to provide an explanation of its actions and conclusions to a variety of users (including the domain expert, knowledge engineer, and end user). The 1988 AAAI Workshop on Explanation brought together many of the world’s experts on expert system explanation in an attempt to highlight key research areas and question...

On the Castelnuovo-mumford Regularity of the Cohomology Ring of a Group

Dave Benson, in [2], conjectured that for any finite group G and any prime p the Castelnuovo-Mumford regularity of the cohomology ring, H(G,Fp), is zero. He showed that reg(H(G,Fp)) ≥ 0 and succeeded in proving equality when the difference between the dimension and the depth is at most two. The purpose of this paper is to prove Benson’s Regularity Conjecture as a corollary of the following result.

Examples of Support Varieties for Hopf Algebras with Noncommutative Tensor Products Dave Benson and Sarah Witherspoon

The representations of some Hopf algebras have curious behavior: Nonprojective modules may have projective tensor powers, and the variety of a tensor product of modules may not be contained in the intersection of their varieties. We explain a family of examples of such Hopf algebras and their modules, and classify left, right, and two-sided ideals in their stable module categories.

Spin modules for symmetric groups

Stably Splitting Bg

In the early nineteen eighties, Gunnar Carlsson proved the Segal conjecture on the stable cohomotopy of the classifying space BG of a finite group G. This led to an algebraic description of the ring of stable self-maps of BG as a suitable completion of the “double Burnside ring”. The problem of understanding the primitive idempotent decompositions of the identity in this ring is equivalent to u...