Hecke grids and congruences for weakly holomorphic modular forms

Let $U(p)$ denote the Atkin operator of prime index $p$. Honda and Kaneko proved infinite families of congruences of the form $f|U(p) \equiv 0 \pmod{p}$ for weakly holomorphic modular forms of low weight and level and primes $p$ in certain residue classes, and conjectured the existence of similar congruences modulo higher powers of $p$. Partial results on some of these conjectures were proved recently by Guerzhoy. We construct infinite families of weakly holomorphic modular forms on the Fricke groups $\Gamma^*(N)$ for $N=1,2,3,4$ and describe explicitly the action of the Hecke algebra on these forms. As a corollary, we obtain strengthened versions of all of the congruences conjectured by Honda and Kaneko

"We're on the Same Page": A Usability Study of Secure Email Using Pairs of Novice Users

Secure email is increasingly being touted as usable by novice users, with a push for adoption based on recent concerns about government surveillance. To determine whether secure email is for grassroots adoption, we employ a laboratory user study that recruits pairs of novice to install and use several of the latest systems to exchange secure messages. We present quantitative and qualitative results from 25 pairs of novice users as they use Pwm, Tutanota, and Virtru. Participants report being more at ease with this type of study and better able to cope with mistakes since both participants are "on the same page". We find that users prefer integrated solutions over depot-based solutions, and that tutorials are important in helping first-time users. Hiding the details of how a secure email system provides security can lead to a lack of trust in the system. Participants expressed a desire to use secure email, but few wanted to use it regularly and most were unsure of when they might use it.Comment: 34th Annual ACM Conference on Human Factors in Computing Systems (CHI 2016

Euler-like recurrences for smallest parts functions

We obtain recurrences for smallest parts functions which resemble Euler's recurrence for the ordinary partition function. The proofs involve the holomorphic projection of non-holomorphic modular forms of weight 2

On pp-filtrations of Weyl modules

This paper considers Weyl modules for a simple, simply connected algebraic group over an algebraically closed field $k$ of positive characteristic $p\not=2$. The main result proves, if $p\geq 2h-2$ (where $h$ is the Coxeter number) and if the Lusztig character formula holds for all (irreducible modules with) regular restricted highest weights, then any Weyl module $\Delta(\lambda)$ has a $\Delta^p$-filtration, namely, a filtration with sections of the form $\Delta^p(\mu_0+p\mu_1):=L(\mu_0)\otimes\Delta(\mu_1)^{[1]}$, where $\mu_0$ is restricted and $\mu_1$ is arbitrary dominant. In case the highest weight $\lambda$ of the Weyl module $\Delta(\lambda)$ is $p$-regular, the $p$-filtration is compatible with the $G_1$-radical series of the module. The problem of showing that Weyl modules have $\Delta^p$-filtrations was first proposed as a worthwhile ("w\"unschenswert") problem in Jantzen's 1980 Crelle paper.Comment: Latest version corrects minor mistakes in previous versions. A reference is made to Williamson's recent arXiv posting, providing some relevant discussion in a footnote. [Comments on earlier versions: Previous v. 1 with minor errors and statements corrected. Improved organization. Should replace v. 2 which is an older version (even older than v.1) and was mistakenly posted.

Multispecies, trait and community size spectrum ecological modelling in R (mizer)

Size spectrum ecological models have emerged as a conceptually simple way to model a large community of individuals which grow and change trophic level during their lives. They are a subset of physiologically structured models where growth (and thus maturation) is food dependent, and processes are formulated in terms of individual level processes. A key feature is that of a size spectrum, where the total abundance of individuals at size scales negatively with size: there are more small things than big things. Mizer is a software package for implementing size spectrum ecological models using the R statistical programming environment. The package has been developed to model marine ecosystems that are subject to fishing.JRC.G.4-Maritime affair