Geiger's research involves studying aspects of plant-animal interactions, such as, pollinator services, seed predation, and herbivory. His hypotheses center on how these facets affect plant 's breeding system, demography (e.g. population growth/decline, persistence/extinction probabilities), population genetic structure, and invasive success.
He has worked with common and endangered plants of the globally imperiled pine rockland habitat of the Everglades in southern Florida. Geiger has been a part of a team studying the invasive exotic plant Brazilian pepper throughout Florida and in its native range of southeastern Brazil.