New derived autoequivalences of Hilbert schemes and generalised Kummer varieties

We show that for every smooth projective surface X and every $n\ge 2$ the push-forward along the diagonal embedding gives a $P^{n-1}$-functor into the $S_n$-equivariant derived category of X^n. Using the Bridgeland--King--Reid--Haiman equivalence this yields a new autoequivalence of the derived category of the Hilbert scheme of n points on X. In the case that the canonical bundle of X is trivial and n=2 this autoequivalence coincides with the known EZ-spherical twist induced by the boundary of the Hilbert scheme. We also generalise the 16 spherical objects on the Kummer surface given by the exceptional curves to n^4 orthogonal $P^{n-1}$-Objects on the generalised Kummer variety.Comment: Mistakes in Lemma 3.3, Prop. 4.4, and Remark 4.7 corrected. The changes do not affect the main result

Formality of P\mathbb{P}-objects

We show that a $\mathbb{P}$-object and simple configurations of $\mathbb{P}$-objects have a formal derived endomorphism algebra. Hence the triangulated category (classically) generated by such objects is independent of the ambient triangulated category. We also observe that the category generated by the structure sheaf of a smooth projective variety over the complex numbers only depends on its graded cohomology algebra.Comment: 23 pages, many changes to improve presentation, strengthened results in Section 5, same content as published versio

Decay, interference, and chaos: How simple atoms mimic disorder

We establish a close quantitative analogy between the excitation and ionization process of highly excited one electron Rydberg states under microwave driving and charge transport across disordered 1D lattices. Our results open a new arena for Anderson localization - a disorder induced effect - in a large class of perfectly deterministic, decaying atomic systems.Comment: 6 pages, 4 figures (2 in colour), proceedings of The International Conference on Multiphoton Processes (ICOMP IX), October 2002: http://www.iesl.forth.gr/icomp9 ;submitted to EP

The physiological significance of insemination in programming pregnancy outcome

The cellular and molecular environment of the uterus during the pre - and peri - implantation period of early pregnancy is critical for implantation success and optimal fetal and placental development. Perturbations to this environment not only have consequences for the success of pregnancy and neonatal health and viability, but can also drive adverse health outcomes in the offspring after birth, particularly the development of metabolic disorders such as obesity, hypertension and insulin resistance. The influence of seminal plasma on the cytokine and immune uterine environment has been previously well characterised in mice, however the effects of disruption in uterine seminal plasma exposure for pregnancy outcome have not been investigated. The studies described in this thesis employed the use of surgical seminal vesicle ablation in males and embryo transfer experiments to investigate the physiological significance of uterine seminal plasma exposure on programming fetal and neonatal outcomes, and growth and metabolic status in adult offspring. We demonstrate that in the absence of seminal plasma, oocyte fertilisation and embryo implantation are reduced, showing that seminal plasma acts primarily to facilitate fertilisation, possibly by promoting sperm transport and survival in the reproductive tract. In addition we show that pregnancies initiated in the absence of seminal plasma give rise to offspring which display accelerated growth after birth and increased adiposity in adulthood, compared to those developed in a tract exposed to seminal plasma at the time of conception. Offspring conceived in the absence of seminal plasma also displayed alterations in serum leptin and adiponectin content, similar to those known to be associated with obesity in the mouse. Using embryo transfer experiments, we showed that some, but not all aspects of the perturbed postnatal development are recapitulated when embryos fertilised in the presence of what semen are transferred to a recipient tract which has not been exposed to seminal plasma. More severe perturbations were seen in 2 - cell transfer than in blastocyst transfer experiment. Additionally, there was a significant effect of the embryo transfer procedure, irrespective of seminal plasma exposure, on fetal and postnatal development that confounded interpretation of these experiments. In addition, we investigated the potential mechanisms by which the influence of seminal plasma is exerted. Mediators of pre - implantation embryo development, implantation and the modulation of the maternal immune response to pregnancy were all assessed for regulation by seminal plasma using QRT - PCR. It was demonstrated that seminal plasma exposure induces the up - regulation of key embryotrophic factors, LIF, GM - CSF and IL - 6, in the oviduct following insemination. Factors important in tissue remodelling required for implantation and angiogenesis, MMP - 2, MMP - 3 and VEGF - C, were also shown to be increased at the time of implantation after seminal plasma exposure. Additionally the generation of T - regulatory cells in uterine tissues, demonstrated by the up - regulation of the transcription factor FOXp3 was shown to be dependent on semen exposure. The influence of seminal plasma on embryonic development, implantation and modulation of the maternal immune response to pregnancy may therefore be mechanisms which contribute to the adverse outcomes seen in pregnancies initiated in the absence of seminal plasma. Together these experiments show a role for seminal plasma signalling at the time of insemination in influencing the pre - implantation embryo to program later fetal and neonatal development, thereby impacting on the metabolic health of offspring. We conclude that seminal plasma is not simply a transport medium for sperm, but acts also as a key regulator of a female tract environment providing optimal support for the developing embryo.Thesis (Ph.D.)--School of Paediatrics and Reproductive Health, 2006