Debates on six controversial topics on the network theory of epilepsy were held during two debate sessions, as part of the International Conference for Technology and Analysis of Seizures, 2019 (ICTALS 2019) convened at the University of Exeter, UK, September 2-5 2019. The debate topics were (1) From pathologic to physiologic: is the epileptic network part of an existing large-scale brain network? (2) Are micro scale recordings pertinent for defining the epileptic network? (3) From seconds to years: do we need all temporal scales to define an epileptic network? (4) Is it necessary to fully define the epileptic network to control it? (5) Is controlling seizures sufficient to control the epileptic network? (6) Does the epileptic network want to be controlled? This article, written by the organizing committee for the debate sessions and the debaters, summarizes the arguments presented during the debates on these six topics.

Department of Epileptology University of Bonn Venusberg Campus 1 53127 Bonn Germany; Interdisciplinary Center for Complex Systems University of Bonn Brühler Str 7 53175 Bonn Germany

Department of Neurobiology and Anatomy Wake Forest School of Medicine Winston Salem NC USA

Department of Neurology Boston Children's Hospital 300 Longwood Ave Boston MA 02115 USA; Department of Neurology University Clinic Carl Gustav Carus Fetscherstrasse 74 01307 Dresden Germany

Department of Neurology Columbia University New York NY USA

Department of Neurology Yale University New Haven CT 06520 USA

Department of Physiology 2nd Faculty of Medicine Charles University Prague Czech Republic

Department of Physiology 2nd Faculty of Medicine Charles University Prague Czech Republic; Department of Pharmacology University of Oxford Oxford OX1 3QT UK

Epilepsy Center University Medical Center Freiburg Freiburg Germany

Institut de Neurosciences des Systèmes Aix Marseille University Marseille France

Institute for Complex Systems and Mathematical Biology University of Aberdeen Aberdeen AB24 3UE UK

Living Systems Institute University of Exeter Exeter UK; Wellcome Trust Centre for Biomedical Modelling and Analysis University of Exeter Exeter UK; EPSRC Centre for Predictive Modelling in Healthcare University of Exeter Exeter UK

Mayo Systems Electrophysiology Laboratory Departments of Neurology and Physiology and Biomedical Engineering Mayo Clinic Rochester MN 55905 USA

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