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Abstract by Alex Safsten

Personal Infomation


Presenter's Name

Alex Safsten

Degree Level

Masters

Abstract Infomation


Department

Mathematics

Faculty Advisor

Denise Halverson

Title

Busemann spaces: the role of curvature and the infinite dimensional case

Abstract

Busemann Geodesic spaces (g-spaces) are metric spaces endowed with a several properties which together guarantee the existence of geodesics. A long standing conjecture suggests that all g-spaces are manifolds. We show that g-spaces with locally bounded Alexandrov curvature do indeed posess manifold properties such as the existence of a local projection to a geodesic. We will present a standard definition for an infinite-dimensional metric space, and outline an unfinished argument for the non-existence of an infinite dimensional g-space.