Dessins, their delta-matroids and partial duals

Given a map $\mathcal M$ on a connected and closed orientable surface, the delta-matroid of $\mathcal M$ is a combinatorial object associated to $\mathcal M$ which captures some topological information of the embedding. We explore how delta-matroids associated to dessins d'enfants behave under the action of the absolute Galois group. Twists of delta-matroids are considered as well; they correspond to the recently introduced operation of partial duality of maps. Furthermore, we prove that every map has a partial dual defined over its field of moduli. A relationship between dessins, partial duals and tropical curves arising from the cartography groups of dessins is observed as well.Comment: 34 pages, 20 figures. Accepted for publication in the SIGMAP14 Conference Proceeding

On 3d extensions of AGT relation

An extension of the AGT relation from two to three dimensions begins from connecting the theory on domain wall between some two S-dual SYM models with the 3d Chern-Simons theory. The simplest kind of such a relation would presumably connect traces of the modular kernels in 2d conformal theory with knot invariants. Indeed, the both quantities are very similar, especially if represented as integrals of the products of quantum dilogarithm functions. However, there are also various differences, especially in the "conservation laws" for integration variables, which hold for the monodromy traces, but not for the knot invariants. We also discuss another possibility: interpretation of knot invariants as solutions to the Baxter equations for the relativistic Toda system. This implies another AGT like relation: between 3d Chern-Simons theory and the Nekrasov-Shatashvili limit of the 5d SYM.Comment: 23 page

Athlome Project Consortium: a concerted effort to discover genomic and other "omic" markers of athletic performance.

Despite numerous attempts to discover genetic variants associated with elite athletic performance, injury predisposition, and elite/world-class athletic status, there has been limited progress to date. Past reliance on candidate gene studies predominantly focusing on genotyping a limited number of single nucleotide polymorphisms or the insertion/deletion variants in small, often heterogeneous cohorts (i.e., made up of athletes of quite different sport specialties) have not generated the kind of results that could offer solid opportunities to bridge the gap between basic research in exercise sciences and deliverables in biomedicine. A retrospective view of genetic association studies with complex disease traits indicates that transition to hypothesis-free genome-wide approaches will be more fruitful. In studies of complex disease, it is well recognized that the magnitude of genetic association is often smaller than initially anticipated, and, as such, large sample sizes are required to identify the gene effects robustly. A symposium was held in Athens and on the Greek island of Santorini from 14-17 May 2015 to review the main findings in exercise genetics and genomics and to explore promising trends and possibilities. The symposium also offered a forum for the development of a position stand (the Santorini Declaration). Among the participants, many were involved in ongoing collaborative studies (e.g., ELITE, GAMES, Gene SMART, GENESIS, and POWERGENE). A consensus emerged among participants that it would be advantageous to bring together all current studies and those recently launched into one new large collaborative initiative, which was subsequently named the Athlome Project Consortium