Epilepsy is a chronic neurological disorder affecting more than 65 million people worldwide and manifested by recurrent unprovoked seizures. The unpredictability of seizures not only degrades the quality of life of the patients, but it can also be life-threatening. Modern systems monitoring electroencephalography (EEG) signals are being currently developed with the view to detect epileptic seizures in order to alert caregivers and reduce the impact of seizures on patients' quality of life. Such seizure detection systems employ state-of-the-art machine learning algorithms that require a considerably large amount of labeled personal data for training. However, acquiring EEG signals of epileptic seizures is a costly and time-consuming process for medical experts and patients, currently requiring in-hospital recordings in specialized units. In this work, we generate synthetic seizure-like brain electrical activities, i.e., EEG signals, that can be used to train seizure detection algorithms, alleviating the need for recorded data. First, we train a Generative Adversarial Network (GAN) with data from 30 epilepsy patients. Then, we generate synthetic personalized training sets for new, unseen patients, which overall yield higher detection performance than the real-data training sets. We demonstrate our results using the datasets from the EPILEPSIAE Project, one of the world's largest public databases for seizure detection.