We give new a proof of the general Briançon-Skoda theorem about ideals of holomorphic functions by means of multivariable residue calculus. The method gives new variants of this theorem for products of ideals. Moreover, we obtain a related result for the ideal generated by the the subdeterminants of a matrix-valued generically surjective holomorphic function, generalizing the duality theorem fo...

This paper defines reduction on derivations in the strict intersection type assignment system of [1], by generalising cut-elimination, and shows a strong normalisation result for this reduction. Using this result, new proofs are given for the approximation theorem and the characterisation of normalisability using intersection types.

This paper defines reduction on derivations in the strict intersection type assignment system of [2], by generalising cut-elimination, and shows a strong normalisation result for this reduction. Using this result, new proofs are given for the approximation theorem and the characterisation of normalisability using intersection types.

We give an alternative proof of the Witten-Di Francesco-ItzyksonZuber theorem —which expresses derivatives of the generating functional of intersection numbers as matrix integrals— using techniques based on diagrammatic calculus and combinatorial relations among intersection numbers on the moduli spaces of algebraic curves. Our techniques extend to a more general interaction potential.

obtain a new for the of a-(u, A) design the block intersection designs are eliminated by an ad hoc coding theoretic argument. A 2-(v, k, A) design 93 is said to be quasi-symmetric if there are two block intersection sizes s1 and s2. The parameters of the complementary design !3* are related to the parameters of 93 as follows: Here Ai denotes the number of blocks through a given i points (and A ...

Helly’s theorem is one of the fundamental results in discrete geometry [9]. It states that if every 6 d+1 sets in a set system S of convex sets in R have non-empty intersection then all of the sets in S have non-empty intersection. Equivalently, if the entire family S has empty intersection, then there is a subset S ′ ⊂ S (a witness) of size 6 d+1 which also has empty intersection. Over the yea...

In simply typed λ-calculus with one ground type the following theorem due to Loader holds. (i) Given the full model F over a finite set, the question whether some element f ∈ F is λ-definable is undecidable. In the λ-calculus with intersection types based on countably many atoms, the following is proved by Urzyczyn. (ii) It is undecidable whether a type is inhabited. Both statements are major r...

We prove that if X,X are closed subschemes of a torus T over a non-Archimedean field K, of complementary codimension and with finite intersection, then the stable tropical intersection along a (possibly positive-dimensional, possibly unbounded) connected componentC of Trop(X)∩Trop(X) lifts to algebraic intersection points, with multiplicities. This theorem requires potentially passing to a suit...

Intersection results for families of H-convex sets in H-spaces are given. These extend known results concerning families of convex sets in topological vector spaces, such as the Berge-Klee intersection theorem and a previous result of the author. MSC 2000. 52A01, 14E20.

“ This paper defines reduction on derivations (cut-elimination) in the Strict Intersection Type Assignment System of [1] and shows a strong normalisation result for this reduction. Using this result, new proofs are given for the approximation theorem and the characterisation of normalisability of terms, using intersection types. ”