topics for bachelor-students

• random matrix theory - the circle law
• random Fibonacci series
• self-avoiding random walks and connectivity constants
• Markov-chains for fitting data
• random matrix theory - Marcenko-Pastur distribution of eigenvalues
• random walk models for polymers
• Polya's constants for random walks
• fluctuation-dissipation theorem
• central limit theorem
• Buffon-Laplace needle problem and the value of π
• integral geometry of a Gaussian random field
• fitting data with simulated annealing
• dynamics of the Lorenz attractor
• kicked oscillators and bifurcation
• double pendulum and Poincaré map
• correlation functions in the double pendulum system
• dynamics of a pendulum with an elastic string
• numerics of the triple, quadruple and quintuple pendulum
• Korteweg-deVries equation and solitons
• Kelvin-Helmholtz instability
• Gibbs-sampling in data fitting

topics for phd-, master- and diploma-students

integrated Sachs-Wolfe effect

• quantification of the non-Gaussianity of the nonlinear iSW-effect
• iSW parameter estimation, non-Gaussianity of the iSW-likelihood
• iSW-constraints on dark energy and neutrino masses
• bias evolution and scale dependent bias

correlations of galaxy ellipticities

• nonlinear tidal torquing, drifting model, statistics of tidal shear and inertia
• bi- and trispectrum of intrinsic ellipticity correlations
• combined alignment models for spirals and ellipticals
• non-Gaussianity in the angular momentum/ellipticity correlation function

weak gravitational flexions

• weak flexions from nonlinear structures
• cross correlations between shear and flexion
• combination of flexion and shear for removing intrinsic alignments