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Explore the intricate relationship between infinite distance points in parameter space and string dualities, particularly T-duality, in curved or flux-supported internal spaces. Delve into the Swampland program's distance conjecture and its role in diagnosing viable low-energy effective theories. Examine evidence suggesting how divergent potentials indicate pathological infinite distance points, leading to a proposed extension of the Swampland distance conjecture. Consider the potential for defining distances in the space of geometries with scalar potentials using generalised Ricci flows. This 26-minute talk, part of the Thematic Programme on "The Landscape vs. the Swampland" at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI), presents collaborative work by Thomas Raml, Saskia Demulder, and Dieter Lüst, offering insights into infinite distances, scalar potentials, and non-geometry in theoretical physics.