Related papers: A New Proof of the New Intersection Theorem

The subtyping rules for intersection types traditionally employ a transitivity rule (Barendregt et al. 1983), which means that subtyping does not satisfy the subformula property, making it more difficult to use in filter models for compiler…

The main result is a common generalization of results on lower bounds for the chromatic number of r-uniform hypergraphs and some of the major theorems in Tverberg-type theory, which is concerned with the intersection pattern of faces in a…

We study a relation between roots of characteristic polynomials and intersection points of line arrangements. Using these results, we obtain a lot of applications for line arrangements. Namely, we give (i) a generalized addition theorem for…

We show that certain sums studied in two recent papers are basically character coordinates (as they are called in the literature). These sums involve values of Dirichlet characters and powers of $\cot(\pi k/n)$, $1\le k\le n-1$. We also…

Following the method of Seifert surfaces in knot theory, we define arithmetic linking numbers and height pairings of ideals using arithmetic duality theorems, and compute them in terms of n-th power residue symbols. This formalism leads to…

The goal of the paper is two-fold. At first, we attempt to give a survey of some recent applications of symmetric polynomials and divided differences to intersection theory. We discuss: polynomials universally supported on degeneracy loci;…

In 1997, Bauschke, Borwein, and Lewis have stated a trichotomy theorem that characterizes when the convergence of the method of alternating projections can be arbitrarily slow. However, there are two errors in their proof of this theorem.…

We provide new Schmidt-type results through an investigation of two bijections, which are results involving partitions with parts counted only at given indices. Mork's bijection, the first of these, was originally given as a proof of…

Around 2001 we classified the Leonard systems up to isomorphism. The proof was lengthy and involved considerable computation. In this paper we give a proof that is shorter and involves minimal computation. We also give a comprehensive…

In this paper, we show that, given two down-sets (simplicial complexes) there is a matching between them that matches disjoint sets and covers the smaller of the two down-sets. This result generalizes an unpublished result of Berge from…

We give combinatorial proofs of two multivariate Cayley--Hamilton type theorems. The first one is due to Phillips (Amer. J. Math., 1919) involving $2k$ matrices, of which $k$ commute pairwise. The second one regards the mixed discriminant,…

Rotors were introduced in Graph Theory by W.Tutte. The concept was adapted to Knot Theory as a generalization of mutation by Anstee, Przytycki and Rolfsen in 1987. In this paper we show that Tristram-Levine signature is preserved by…

Using a certain well-posed ODE problem introduced by Shilnikov in the sixties, G. Minervini proved in his PhD thesis [17], among other things, the Harvey-Lawson Diagonal Theorem but without the restrictive tameness condition for Morse…

Inspired by the Finn-Osserman (1964), Chern (1969), do Carmo-Peng (1979) proofs of the Bernstein theorem, which characterizes flat planes as the only entire minimal graphs, we prove a new rigidity theorem for associate families connecting…

We show that \emph{No unbounded profit with bounded risk} (NUPBR) implies \emph{predictable uniform tightness} (P-UT), a boundedness property in the Emery topology which has been introduced by C. Stricker \cite{S:85}. Combining this insight…

We consider the following generalization of the seminal Erd\H{o}s-Ko-Rado theorem, due to Frankl. For k>= 2, let F be a k-wise intersecting family of r-subsets of an n element set X, i.e. any k sets in F have a nonempty intersection. If r<=…

In this thesis, we study the properties of String theory amplitudes within the framework of Intersection Theory (IT) for twisted (co)homology, which, as recently proposed, offered a novel approach to analyze relations between scattering…

Using the celebrated Witten-Kontsevich theorem, we prove a recursive formula of the $n$-point functions for intersection numbers on moduli spaces of curves. It has been used to prove the Faber intersection number conjecture and motivated us…

We prove the 3-fold DT/PT correspondence for K-theoretic vertices via wall-crossing techniques. We provide two different setups, following Mochizuki and following Joyce; both reduce the problem to q-combinatorial identities on word…

Following Bloch-Esnault-Kerz and Green-Griffiths' recent works on deformation of algebraic cycle classes, we use Chern character from K-theory to negative cyclic homology to show how to eliminate obstructions to deforming cycles.