"Mathematics is music of the mind - music is mathematics of the soul" (Daniil Iwanowitsch Charms)
Last but not least, the introduction of axiomatic probability theory by Kolmogorov in 1933 rendered the laws of chance presentable in Mathematics. And whoever needs to extract information from data nowadays makes use of stochastic modelling in the form of big data , data science , knowledge discovery and pattern recognition .
Gentle introduction (in German) well suited for non-mathematicians: PDF (6MB) on Randomness and Monkeys, reprinted
with the friendly permission of NOEO.
Estimation of the entropy of Markov chains and asymptotics of related divergence measures for defining stringent tests for pseudorandom number generators.
Pattern classification, clustering and data mining: development of new methods and algorithms in the areas of bioinformatics (HMMs), image processing (medical image processing, sport sciences) and natural language processing (topic mapping, sentiment analysis).
Signal processing: non-linear figures (Lyapunov exponent, approximate entropy) and pattern recognition in the areas of sport sciences and EKG/EEG processing.