Gert Heckman and Walter van Suijlekom both received a grant from the Free Competition of The Netherlands Organisation for Scientific Research NWO); both are intended for the hiring of a Ph.D. student.
The PhD research project of Gert Heckman is entitled “Reality Questions for ome Period Mappings”. In the past decade several period mappings from a moduli space to a ball quotient have been discovered, which bear a striking similarity with older work of Deligne and Mostow from the eighties. As conjectured by Allcock the highest dimensional ball quotient of this sort provides a geometric setting for Moonshine. We wish to understand the behavior over the real rather than complex numbers, with a special emphasis on the moduli space of quartic curves and the associated period map found by Kondo.
The PhD research project of Walter D. van Suijlekom is entitled “The noncommutative geometry of quantum gauge symmetries”. It lies at the intersection of the new mathematical field of noncommutative geometry and elementary particle physics. One goal will be to understand the perturbative structure of socalled Yang-Mills theories from a novel mathematical point of view, hopefully as a stepping stone towards the nonperturbative construction of such theories (as called for by one of the 1M$ Clay Millennium Problems in mathematics). Other participants in this project will be Klaas Landsman (RU) and Matilde Marcolli (Caltech), also expected to be promotores for the PhD student on this project. Including this project, IMAPP will now host three PhD students working in this area.