The modular degree and the congruence number of a weight 2 cusp form

Let f be a weight 2 normalized newform on the congruence subgroup Γ0(N) with integral Fourier coefficients. There are two important numerical invari-ants attached to f: its congruence number and its modular degree. By definition, the congruence number of f is the largest integer Df suc

The Physics of the B Factories

This work is on the Physics of the B Factories. Part A of this book contains a brief description of the SLAC and KEK B Factories as well as their detectors, BaBar and Belle, and data taking related issues. Part B discusses tools and methods used by the experiments in order to obtain results. The results themselves can be found in Part C

Fundus-controlled perimetry (microperimetry): Application as outcome measure in clinical trials

YesFundus-controlled perimetry (FCP, also called 'microperimetry') allows for spatially-resolved mapping of visual sensitivity and measurement of fixation stability, both in clinical practice as well as research. The accurate spatial characterization of visual function enabled by FCP can provide insightful information about disease severity and progression not reflected by best-corrected visual acuity in a large range of disorders. This is especially important for monitoring of retinal diseases that initially spare the central retina in earlier disease stages. Improved intra- and inter-session retest-variability through fundus-tracking and precise point-wise follow-up examinations even in patients with unstable fixation represent key advantages of these technique. The design of disease-specific test patterns and protocols reduces the burden of extensive and time-consuming FCP testing, permitting a more meaningful and focused application. Recent developments also allow for photoreceptor-specific testing through implementation of dark-adapted chromatic and photopic testing. A detailed understanding of the variety of available devices and test settings is a key prerequisite for the design and optimization of FCP protocols in future natural history studies and clinical trials. Accordingly, this review describes the theoretical and technical background of FCP, its prior application in clinical and research settings, data that qualify the application of FCP as an outcome measure in clinical trials as well as ongoing and future developments

Intersections of Humbert surfaces and binary quadratic forms

Humbert surfaces are certain surfaces embedded in the moduli space $A_2$ of principally polarized abelian surfaces. In this talk I will explain the connection between the components of the intersection of two Humbert surfaces and classes of certain binary quadratic forms. More precisely, for each positive quadratic form $q$ in $r$ variables one can associate a closed subvariety $H(q)$ of $A_2$ (which depends only on the equivalence class of the form). If $r = 1$, then we recover the Humbert surfaces. For $r = 2$ we get curves which can be used to describe the intersection of two Humbert surfaces. (Using the reduction theory of binary quadratic forms, this can be done quite explicitly.) If q is a primitive binary quadratic form, then $H(q)$ is irreducible, but in the general case $H(q)$ is a union of the images of modular curves (modular correspondences) lying on $X(N) x X(N)$ (or on Hilbert modular surfaces). By studying conjugacy classes of matrices mod $N$, the irreducible components of $H(q)$ can be identified. Thus, one gets an explicit description of all irreducible components of the intersection of two Humbert surfaces.Non UBCUnreviewedAuthor affiliation: Queen's UniversityFacult