Hildegard is professor of physics at Constructor University (formerly Jacobs University) Bremen since 2002, as emeritus there since 2020, and external professor at the CSH Vienna since 2023. She obtained her diploma in general relativity from the university of Cologne and her PhD in particle physics from the university of Hamburg at DESY.

After postdocs at the Werner Heisenberg-Institute in Munich and at the university and ETH in Zürich, she received her habilitation in theoretical physics from the university of Heidelberg. Later she completely switched to Network Science. Since then, she analyses complex systems with methods from statistical physics and nonlinear dynamics. Applications range from opinion formation, energy markets and power grids, to ecological, genetic, and neural networks. More recently she studies transient dynamics as framework for describing cognitive processes.

Further interests concern the role of stochastic fluctuations in evolution theory, in particular when demographic and environmental sources of noise are competing. From a broader perspective, she is interested in the impact of fundamental physical constraints on the cost of accuracy in (re-) production processes, moreover in the extent to which resources are optimally allocated in biological systems if their reservoirs are finite.

In relation to philosophy she gave lectures on the success and limitations of reductionism in physics, where the limitations demonstrate the need for interdisciplinary work.  Hildegard organized a number of interdisciplinary workshops, schools and conferences on interfaces between physics, life sciences and information science.