In my research, I have applied mathematical techniques such as homology, catastrophy, integral geometry and Picard-Lefschetz theory to problems in cosmology. I have applied these techniques to the formation and properties of the cosmic microwave background radiation field, the formation of the large-scale structure and the study of the big bang in Lorentzian quantum cosmology. In my work, I attempt to study observable phenomena, using conservative assumptions in a critical and mathematically rigorous fashion. See links below for a summary of my main projects.
Job Feldbrugge, Matti van Engelen, Rien van de Weygaert, Pratyush Pranav, Gert Vegter. Stochastic Homology of Gaussian vs. non-Gaussian Random Fields: Graphs towards Betti Numbers and Persistence Diagrams. 2019. [arXiv][pdf]
Pratyush Pranav, Rien van de Weygaert, Gert Vegter, Bernard J. T. Jones, Robert J. Adler, Job Feldbrugge, Changbom Park, Thomas Buchert, Michael Kerber. Topology and Geometry of Gaussian random fields I: on Betti Numbers, Euler characteristic and Minkowski functionals. 2018. [arXiv][pdf]
R. van de Weygaert, G. Vegter, H. Edelsbrunner, B. Jones, P. Pranav, C. Park, W. Hellwing, B. Eldering, N. Kruithof, E. Bos, J. Hidding, Job Feldbrugge, E. ten Have, M. van Engelen, M. Caroli, M. Teillaud Alpha, Betti and the Megaparsec Universe: on the Topology of the Cosmic Web. 2013. [arXiv][pdf]