Mather has led or collaborated on work studying volcanoes around the world, both "in situ" and using remote sensing data from ground or satellite based platforms. Volcanoes Mather has studied include Bárðarbunga, Hekla, and Eyjafjallajökull in Iceland, the Santorini caldera in Greece, the Villarica, Lascar, Chaitén and Calbuco volcanoes in Chile, Masaya Volcano in Nicaragua (where she was held up at gunpoint), Mount Etna in Italy, Galeras in Colombia, the Santiaguito lava dome complex in Guatemala, and the Great Rift Valley, Ethiopia.