Weekly Bulletin

We consider generic translation surfaces of genus g>0 with marked points and take covers branched over the marked points such that the monodromy of every element in the fundamental group lies in a cyclic group of order d. Given a translation surface, the number of cylinders with waist curve of length at most L grows like L^2. By work of Veech and Eskin-Masur, when normalizing the number of cylinders by L^2, the limit as L goes to infinity exists and the resulting number is called a Siegel-Veech constant. The same holds true if we weight the cylinders by their area. Remarkably, the Siegel-Veech constant resulting from counting cylinders weighted by area is independent of the number of branch points n. All necessary background will be given.  This is joint work with Aaron Calderon, Carlos Matheus, Nick Salter, and Martin Schmoll.

We provide a finite element discretization of $\ell$-form-valued $k$ form in $n$ dimensions for general $k$, $\ell$ and $n$ and polynomial degree. The construction generalizes finite element Whitney forms for the de~Rham complex and their higher-order and distributional versions, the Regge finite elements and the Christiansen--Regge elasticity complex, the TDNNS element for symmetric stress tensors, the MCS element for traceless matrix fields, the Hellan--Herrmann--Johnson (HHJ) elements for biharmonic equations, and discrete divdiv and Hessian complexes in [Hu, Lin, and Zhang, 2025]. The construction discretizes the Bernstein--Gelfand--Gelfand (BGG) diagrams. Applications of the construction include discretization of strain and stress tensors in continuum mechanics and metric and curvature tensors in differential geometry in any dimension. This talk is based on a joint work with Kaibo Hu (Edinburgh).

We study the long time behavior for the distribution of a critical birth and death diffusion process, motivated by population dynamics in changing environment (cf. a recent paper by Calvez, Henry, Méléard, Tran). The birth rates are bounded but death rates are unbounded. Our analysis is based on the spectral properties of the associated Feynman Kac semigroup. We require a standard spectral gap property for this semigroup with a dominant eigenfunction vanishing at infinity. Some examples of diffusions, diffusions with jump, pure jump dynamics are given for which it is true. We consider situations where the underlying diffusion process doesn't come down rapidly from infinity but the compactness properties follow from the divergence of the death rate at infinity. We prove the convergence in law of the branching diffusion process suitably normalized and conditioned to non-extinction. We also prove the existence of the $Q$-process. The main tool is the convergence of suitably normalized moments of the process, which follows from recursive relations for these moments. This is a joint work with Pierre Collet and Jaime San Martin.

data.table is an R package with C code that is one of the most efficient open-source in-memory database packages available today. First released to CRAN by Matt Dowle in 2006, it continues to grow in popularity, and now over 1500 other CRAN packages depend on data.table. This talk will discuss basic and advanced data manipulation topics, and end with a discussion about how you can contribute to data.table.