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Each year wildfires result in billions of dollars in property damage. Being one of the major natural hazards, wildfires nowadays are also a global affair whose negative impact is particularly devastating in developing countries. As wildfires are expected to become more frequent and severe, more accurate models to predict wildfires are vital to mitigating risks and developing more informed decision-making. Artificial intelligence (AI) has a potential to enhance wildfire risk analytics on multiple fronts. For example, deep learning (DL) has been successfully used to classify active fires, burned scars, smoke plumes and to track the spread of active wildfires. Since wildfire spread tends to exhibit highly complex spatio-temporal dependencies which often cannot be accurately described with conventional Euclideanbased approaches, we postulate that the tools of topological and geometric deep learning, specifically designed for non-Euclidean objects such as manifolds and graphs, may offer a more competitive solution. We validate the proposed methodology to predict wildfire occurrences in Greece and several regions of Africa. Our results indicate that the Firecast Zigzag Convolutional Network (F-ZCN) outperforms the current baseline methods for wildfire prediction and opens a path for more accurate wildfire risk analytics, even in scenarios of limited and noisy data records.