Abstract:
After introducing the standard cross-ratio, we discuss a generalization of the cross-ratio to higher-dimensional Grassmannians. As an application, we give a short proof of the following theorem in projective geometry: Any four n-plane subspaces in general position in a projective space of dimension 2n+1 over an algebraically closed field have exactly n+1 common transversals.
Abstract:
We give a complete combinatorial characterization of all possible polarizations of powers of the maximal ideal $(x_1,x_2,\dotsc,x_n)$ in a polynomial ring of $n$ variables. We also give a combinatorial description of the Alexander duals of such polarizations. In the three variable case we show that every polarization defines a (shellable) simplicial ball. We conjecture that any polarization of an artinian monomial ideal defines a simplicial ball. This is joint work with Gunnar Fløystad.
Abstract:
Abstract:
Abstract:
We prove the large deviation principle for the law of the solutions to a class of parabolic semilinear stochastic partial differential equations driven by multiplicative noise, in C[0,T] : Lρ(D) where D ⊂ Rd with d 1 is a bounded convex domain with smooth boundary and ρ is any real, positive and large enough number. The equation has nonlinearities of polynomial growth of any order, the space variable is of any dimension, and the proof is based on the weak convergence method.