Consider an ideal I ⊂ R = C[x] = C[x 1 ,. .. , x n ] defining a complex affine variety X = V (I) = {x ∈ C n | ∀f ∈ I, f (x) = 0}. We describe the associated components VAss(I) = {V (P) | P ∈ Ass(I)} by means of numerical primary decomposition (NPD). The method is based on the construction of deflation ideal I (d) that defines the deflated variety X (d) = V (I (d)) in a higher-dimensional comple...

I will discuss some recent results on marginally outer trapped surfaces, apparent horizons and the trapped region. A couple of applications of the results developed for marginally outer trapped surfaces to coalescence of black holes and to the characterization of the trapped region are given.

Given a suitable functor T : C → D between model categories, we define a long exact sequence relating the homotopy groups of any X ∈ C with those of TX , and use this to describe an obstruction theory for lifting an object G ∈ D to C. Examples include finding spaces with given homology or homotopy groups.

This talk describes some of the precision electroweak measurements from around the world, namely those related to the Z and W bosons, the top quark mass, sin 2 θ W at NuTeV, and three other fundamental measurements: α −1 (m 2 Z), (g − 2) µ at the E821 BNL experiment as well as the atomic parity violation (APV) measurement for the Cesium atom. These and other measurements are set in the context ...

We geometrically construct a homology theory that generalizes the Euler characteristic mod 2 to objects in the unoriented cobordism ring N∗(X) of a topological space X. This homology theory Eh∗ has coefficients Z/2 in every nonnegative dimension. There exists a natural transformation N∗(X) → Eh∗(X) that for X = pt assigns to each smooth manifold its Euler characteristic mod 2. The homology theo...