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Professor Willems is primarily conducting research on Roman Law. The main focus is on the law of late antiquity, in particular the lawmaking of Emperor Justinian I. The usual spectrum of methods Romanists use is extended—where opportune—by a Law & Economics approach, utilizing above all the tools and ideas of (New) Institutional Economics. Together with Professor Catherine Hezser (SOAS, University of London, United Kingdom), Professor Willems is Principal Investigator of the project Rabbinic Civil Law in the Context of Ancient Legal History: A Legal Compendium to the Bavot Tractates of the Talmud Yerushalmi, which started in September 2023 and is funded for a period of three years by the Arts and Humanities Research Council (AHRC) and by the Deutsche Forschungsgemeinschaft (DFG). In cooperation with other disciplines in Classics, Professor Willems is involved in the Marburg Center for the Ancient World (MCAW); since November 2023, he is also one of the Principal Investigators of the Center's DFG-Graduiertenkolleg 2844: Inszenzierung religiöser Atmosphäre in Antiken Kulturen. Furthermore, the chair forms the core of the Institute for Legal History, which is part of the School of Law, and is in charge of the Papyrus Collection of Philipps-Universität Marburg.

In European Legal History, one focus is on the connections between the continental European Ius Commune and English Common Law. Other projects deal with historical developments in areas such as service contract law or unethical and illegal testamentary dispositions, in each case starting from Roman Law in a pan-European comparison. Another local research focus is on various chapters of the long history of the School of Law in Marburg, such as the role of the Marburg law faculty as a panel of judges in witch trials or the origins of the Historical School of Law with Friedrich-Carl von Savigny and his Marburg student Jacob Grimm.

In the area of German Civil Law, current and fundamental issues—especially concerning the general principles of contract law and the law of sales, leases, and service contracts—are investigated; in doing so, the historical-legal comparative perspective is used as well.

German and European antitrust and competition law is another focus of interest and research; in particular, aspects of merger control and procedural issues are examined.

A list of publications and papers can be found here.