The introduction of l-adic cohomology by M. Artin and Grothenieck was motivated by the Weil conjecture concerning the number of rational points of algebraic varieties over finite fields. Since its introduction in the early 60s, l-adic cohomology theory has been used in the representation theory of finite Chevalley groups in a “misterious way”. The first application of l-adic cohomology and inte...

Detecting whether two geometric objects intersect and computing the region of intersection are fundamental problems in computational geometry. Geometric intersection problems arise naturally in a number of applications. Examples include geometric packing and covering, wire and component layout in VLSI, map overlay in geographic information systems, motion planning, and collision detection. In s...

We discuss a possible characterization, by means of forbidden configurations, of posets which are embeddable in a product of finitely many scattered chains. Introduction and presentation of the results A fundamental result, due to Szpilrajn [26], states that every order on a set is the intersection of a family of linear orders on this set. The dimension of the order, also called the dimension o...

The intersection problem for block a..sks for values of k it is to find two B d and based on the V, with IBI n B:;d k; that is, k common blocks. We define to be the of cornDI.ete graph solve the intersection 1 1.1 Let G be a (undirected) which is some subgraph of another graph H. A G-decomposdion of H is a block (V, where V is the vertex set of Hand B decomposition of H into copies of G. In the...

Let X be a semi-stable regular curve over the spectrum S of the integers in a number field F , and L̄ = (L, h) an hermitian line bundle on X , i.e. L is an algebraic line bundle on X and h is a smooth hermitian metric (invariant by complex conjugation) on the restriction of L to the set X(C) of complex points of X . In this paper we are interested in the height hL̄(D) of irreducible divisors D on...

A small fraction of these functions are Boolean functions (including constants), that is functions that can be This paper discusses some classification and constructed from constants and variables, using union, The set p(r) is a enumeration problems in r-valued set logic, which is the intersection and complementation. logic of functions mapping n-tuples of subsets into subsets Boolean algebra (...

Let ƒ: N —• M be a C°° map of oriented compact manifolds, and let L be an oriented closed submanifold of codimension q > 1 in M. If w is a closed form Poincaré dual to L, we show that f~L, with multiplicities counted, is Poincaré dual to ƒ *w in N and is even meaningful on a "secondary" level. This leads to generalized versions of the Hopf invariant, the Hopf index theorem and the Bezout theore...

The quotient complexity of a regular language L, which is the same as its state complexity, is the number of left quotients of L. An atom of a non-empty regular language L with n quotients is a non-empty intersection of the n quotients, which can be uncomplemented or complemented. An NFA is atomic if the right language of every state is a union of atoms. We characterize all reduced atomic NFAs ...

L-functions in Number Theory Yichao Zhang Doctor of Philosophy Graduate Department of Mathematics University of Toronto 2010 As a generalization of the Riemann zeta function, L-function has become one of the central objects in Number Theory. The theory of L-functions, which produces a large family of consequences and conjectures in a unified way, concerns their zeros and poles, functional equat...