Let k be a field and let G be a finite group. There is a canonical element in the Hochschild cohomology of the Tate cohomology γG ∈ HH3,−1Ĥ∗(G, k) with the following property. Given a graded Ĥ∗(G, k)-module X, the image of γG in Ext 3,−1 Ĥ∗(G,k) (X,X) vanishes if and only if X is isomorphic to a direct summand of Ĥ∗(G,M) for some kG-module M . The description of the realizability obstruction wo...

Due to the orbifold singularities, the intersection numbers on the moduli space of curves Mg,n are in general rational numbers rather than integers. We study the properties of the denominators of these intersection numbers and their relationship with the orders of automorphism groups of stable curves. We also present a conjecture about a multinomial type numerical property for a general class o...

A polymorphic function is parametric if it has uniform behavior for all type parameters. This property is useful when writing, reasoning about, and compiling functional programs. We show how to syntactically deene and reason about parametricity in a language with intersection types and bounded polymorphism. Within this framework, parametricity is subtyping, and reasoning about para-metricity be...

We prove that for a topological spaceX with the property that H∗(U) = 0 for ∗ ≥ d and every open subset U of X, a finite family of open sets in X has nonempty intersection if for any subfamily of size j, 1 ≤ j ≤ d+1, the (d−j)-dimensional homology group of its intersection is zero. We use this theorem to prove new results concerning transversal affi ne planes to families of convex sets

We give an example of a direct summand of a serial module that does not admit an indecomposable decomposition.

We study the strict type assignment system, a restriction of the intersection type discipline [6], and prove that it has the principal type property. We define, for a term M, the principal pair (of basis and type). We specify three operations on pairs, and prove that all pairs deducible for M can be obtained from the principal one by these operations, and that these map deducible pairs to deduc...

We give a uniform short proof of the fact that the intersection of every non-central conjugacy class in a Chevalley group and a big Gauss cell is non-empty and that this intersection contains elements with any prescribed semisimple part. The interest in this property stems at least in part from its relation to Ore's and Thompson's conjectures in the theory of nite groups.

Using automata-theoretic approach, Giambruno and Restivo have investigated on the intersection of two finitely generated submonoids of the free monoid over a finite alphabet. In particular, they have obtained Hanna Neumann property for a special class of submonoids generated by finite prefix sets. This work continues their work and provides a sufficient condition for Hanna Neumann property for ...