Vanishing cotangent cohomology for Pl\"ucker algebras

We use representation theory and Bott's theorem to show vanishing of higher cotangent cohomology modules for the homogeneous coordinate ring of Grassmannians in the Pl\"ucker embedding. As a biproduct we answer a question of Wahl about the cohomology of the square of the ideal sheaf for the case of Pl\"ucker relations.Comment: Some results generalized to isotropic Grassmannian

Workshopping the Heart: New and Selected Poems by Jeri Kroll (Wakefield Press, 2013): Speech given at the Launch at Flinders University Library, 15 May 2014

Workshopping the Heart: New and Selected Poems by Jeri Kroll (Wakefield Press, 2013): Speech given at the Launch at Flinders University Library, 15 May 201

Poems

Loquats, Nightfall, Dividend, Day Trip, Pian

Hilbert Schemes and Toric Degenerations for Low Degree Fano Threefolds

For fixed degree $d\leq 12$, we study the Hilbert scheme of degree $d$ smooth Fano threefolds in their anticanonical embeddings. We use this to classify all possible degenerations of these varieties to toric Fano varieties with at most canonical Gorenstein singularities.Comment: 24 pages, 2 figures; v2 simplified exposition by using rolling factors format where applicable; v3 further revisions to exposition, changed titl

Staggered School Hours To Spread Peak Demand For Public Transport – Benefits And Costs

Institute of Transport and Logistics Studies. Faculty of Economics and Business. The University of Sydne

Staggered School Hours To Spread Peak Demand For Public Transport – Benefits And Costs

Institute of Transport and Logistics Studies. Faculty of Economics and Business. The University of Sydne

A comparison of two model averaging techniques with an application to growth empirics

Parameter estimation under model uncertainty is a difficult and fundamental issue in econometrics. This paper compares the performance of various model averaging techniques. In particular, it contrasts Bayesian model averaging (BMA) — currently one of the standard methods used in growth empirics — with a new method called weighted-average least squares (WALS). The new method has two major advantages over BMA: its computational burden is trivial and it is based on a transparent definition of prior ignorance. The theory is applied to and sheds new light on growth empirics where a high degree of model uncertainty is typically present

Optimal randomized multilevel algorithms for infinite-dimensional integration on function spaces with ANOVA-type decomposition

In this paper, we consider the infinite-dimensional integration problem on weighted reproducing kernel Hilbert spaces with norms induced by an underlying function space decomposition of ANOVA-type. The weights model the relative importance of different groups of variables. We present new randomized multilevel algorithms to tackle this integration problem and prove upper bounds for their randomized error. Furthermore, we provide in this setting the first non-trivial lower error bounds for general randomized algorithms, which, in particular, may be adaptive or non-linear. These lower bounds show that our multilevel algorithms are optimal. Our analysis refines and extends the analysis provided in [F. J. Hickernell, T. M\"uller-Gronbach, B. Niu, K. Ritter, J. Complexity 26 (2010), 229-254], and our error bounds improve substantially on the error bounds presented there. As an illustrative example, we discuss the unanchored Sobolev space and employ randomized quasi-Monte Carlo multilevel algorithms based on scrambled polynomial lattice rules.Comment: 31 pages, 0 figure