NMR spectroscopy as a playground for armchair mathematicians

Nuclear magnetic resonance (NMR) spectroscopy is a branch of chemical analysis, finding applications in material science, structural biology, chemical synthesis, pharma industry, food profiling, medical screening and many other fields.

To apply NMR, we need to have a basic knowledge at many levels, ranging from the quantum mechanics of nuclear spins through the fundamentals of hardware and software signal processing to interpreting results in chemical and biological contexts. Moreover, in all activities of a spectroscopist, knowledge of practical aspects of mathematical methods is needed: Fourier, Laplace or Hilbert transforms, compressed sensing methods, statistical data analysis and many others.

In the laboratory of NMR spectroscopy at the Centre of New Technologies, we work on methods of obtaining and analysing NMR signals, making practical use of the achievements of mathematicians. In my presentation, I will give an overview of mathematical methods whose application in practice brings joy to spectroscopists and provides benefits to chemists and biologists.