Varieties with too many rational points

We investigate Fano varieties defined over a number field that contain subvarieties whose number of rational points of bounded height is comparable to the total number on the variety.Comment: 23 page

Implementing RFID at Leeds Met

What benefits does the introduction of radio frequency identification bring to students, staff and university, and what should you be looking for in a supplier? Helen Loughran and Dilys Young take us through the Leeds Met experience

Failures of weak approximation in families

Given a family of varieties $X\to \mathbb{P}^n$ over a number field $k$, we determine conditions under which there is a Brauer-Manin obstruction to weak approximation for $100\%$ of the fibres which are everywhere locally soluble.Comment: 44 pages; there is a new application to integral points (Theorem 1.4) and Cor 1.5 recovers a well-known result concerning the Hasse principl

Integral Hasse principle and strong approximation for Markoff surfaces

We study the failure of the integral Hasse principle and strong approximation for Markoff surfaces, as studied by Ghosh and Sarnak, using the Brauer-Manin obstruction

Rank jumps on elliptic surfaces and the Hilbert property

Given an elliptic surface over a number field, we study the collection of fibres whose Mordell-Weil rank is greater than the generic rank. Under suitable assumptions, we show that this collection is not thin. Our results apply to quadratic twist families and del Pezzo surfaces of degree 1

Fibrations with few rational points

We study the problem of counting the number of varieties in families which have a rational point. We give conditions on the singular fibres that force very few of the varieties in the family to contain a rational point, in a precise quantitative sense. This generalises and unifies existing results in the literature by Serre, Browning-Dietmann, Bright-Browning-Loughran, Graber-Harris-Mazur-Starr, et al.Comment: 34 pages. Major revision. More details added and examples section moved to the end of the paper. Main theorems unchanged. To appear in GAF

Pseudo-split fibres and arithmetic surjectivity

Let f : X → Y be a dominant morphism of smooth, proper and geometrically integral varieties over a number field k, with geometrically integral generic fibre. We give a necessary and sufficient geometric criterion for the induced map X ( k v ) → Y ( k v ) to be surjective for almost all places v of k. This generalises a result of Denef which had previously been conjectured by Colliot-Th ́el`ene, and can be seen as an optimal geometric version of the celebrated Ax–Kochen theorem

HYDROGEN BONDING IN betabeta-NITRO ALCOHOLS. III. PYRIDINE COMPLEXES

BETA -Nitro alcohols form stable 1:1 complexes with pyridine, examples of which were prepared. In solvents such as dichloromethane and carbon tetrachloride the complexes partially dissociate into their components. The dissociation constants for the equilibria were determined by infrared methods and may be used as a measure of the strength of the complex hydrogen bond. The dissociation constants decrease with increasing number of BETA -nitro groups. Some reactions of the pyridine complexes are described. (auth

New insight into the causes, consequences, and correction of hematopoietic stem cell aging

Aging of hematopoietic stem cells (HSCs) is characterized by lineage bias, increased clonal expansion, and functional decrease. At the molecular level, aged HSCs typically display metabolic dysregulation, upregulation of inflammatory pathways, and downregulation of DNA repair pathways. Cellular aging of HSCs, driven by cell-intrinsic and cell-extrinsic factors, causes a predisposition to anemia, adaptive immune compromise, myelodys, plasia, and malignancy. Most hematologic diseases are strongly associated with age. But what is the biological foundation for decreased fitness with age? And are there therapeutic windows to resolve age-related hematopoietic decline? These questions were the focus of the International Society for Experimental Hematology (ISEH) New Investigator Committee Fall 2022 Webinar. This review touches on the latest insights from two leading laboratories into inflammatory- and niche-driven stem cell aging and includes speculation on strategies to prevent or correct age-related decline in HSC function