Professor Purnhagen is a leading authority on European Union law, international trade law and globalization. His publications include over 80 articles and book chapters in legal, natural science and social science outlets. His work is both, doctrinal and cross-disciplinary, addressing topics concerning European integration and international trade, as well as national regulation in a global context. He previously was lecturer at the Universities of Lucerne and Giessen, post-doc at the University of Amsterdam, and Akademischer Rat aZ at the Ludwig Maximilian University Munich, where he also co-directed a university research center on risk regulation. He received his State Exam, and his M.J.I. with dictinction, obtained an LL.M. at Wisconsin-Madison and a PhD at the European University Institute in Florence.His early research focused on the increasing role of systematisation in the harmonisation of risk regulation in EU law. He also co-led a project on European legal culture at the LMU in Munich and at Oxford University, funded by a Thyssen grant. This work led to the well-received book Towards a European Legal Culture, which was commented inter alia by Hugh Collins, Steven Weatherill, Eric Jayme, Ewoud Hondius, Kåre Lilleholt, Norbert Reich, Gerhard Dannemann, and Thomas Wilhelmsson.

More recently, Kai has worked broadly on various aspects of risk regulation in WTO law, EU law and German law, with a focus on the implementation of findings from behavioural, economic and safety sciences into law and regulation. His works have appeared in prestigious journals such as the European Law Journal, The Journal of World Trade, Nature, Journal of Consumer Policy, Nature Biotechnology, Risk Analysis, the European Law Review and the Rabel Journal of Comparative and International Private Law. He is also (co-)editor of various prestigious outlets, most prominently of the forthcoming Oxford Encyclopedia on EU law and the Springer Science Series Studies in European Economic Law and Regulation. Kai was also Founding Associate Editor of the European Journal of Risk Regulation (Cambridge University Press).

His works regularly influence law-making and interpretation at various levels. Among others, his works were taken up by the European Commission in marketing law, the German government in energy and consumer law and the German Supreme Court in contract law. In this respect, he regularly serves as an expert to various governments and consulting agencies such as the Chinese government, the European Commission, the German government and the Austrian government.

He was responsible for the legal part of interdisciplinary projects such as the Nudging project with the German ministry for the environment (Anstossen nachhaltiger Konsummuster, 2014-2016), and the ZaNexus project for several German ministries (2015-2017).

Kai has taught and researched at various institutions including the Ludwig-Maximilian University Munich, the University of Lucerne, the European University Institute, Wageningen University, the London School of Economics and Political Science, the University of Wisconsin-Madison, the Justus-Liebig-University Giessen, and the University of Amsterdam.