- Research Advisor, responsibility for externally funded applications and projects (EU and NFR in particular).
- Project Manager for EU3D (EU Differentiation, Dominance and Democracy), a four year (2019-2023) RIA project funded by the EU's Horizon 2020, coordinated by ARENA and with partner institutions in Belgium, Denmark, France, Germany, Greece, Italy, Poland, Slovakia, and the UK.
Kværk has been employed at ARENA since 2003, and was Administrative Director at the centre from 2011-2015.
From 2016-2020 Kværk was Project Manager for GLOBUS (Reconsidering European Contributions to Global Justice), a RIA project funded by the EU's Horizon 2020, coordinated by ARENA and with partner institutions in Brazil, China, Germany, India, Ireland, Italy and South Africa.
From 2007-2011 Kværk was Project Manager for RECON (Reconstituting Democracy in Europe), a five year Integrated Project funded by the European Commission's Sixth Framework Programme (FP6), with 24 partner institutions in 12 European countries as well as New Zealand, and with an FP6 contribution of 5 million €.
Kværk was Project Manager for the research project CIDEL (Citizenship and Democratic Legitimacy in Europe), funded by the European Commission's Fifth Framework Programme (FP5).
Kværk holds a master's degree in political science from the University of Oslo, with a master's thesis on the involvement of civil society in the EU's Charter Convention (ARENA Report 6/2003). His undergraduate degree (cand.mag.) includes studies in French and the history and politics of Western Europe and North America.