Christian van Enckevort
Equivalence of D-brane categories

In this thesis, certain mathematical aspects of mirror symmetry are investigated. This symmetry originates in physics and gives a relation between seemingly very different geometrical properties of a pair of spaces. Kontsevich stated a conjecture which gives a precise mathematical formulation of this relation. This conjecture is discussed in detail and related to another important conjecture due to Strominger, Yau and Zaslow. In the case of tori, the latter conjecture can be made reasonably precise and used to prove Kontsevich's conjecture to a large extent. The relation with many properties of mirror symmetry that are described in the physics literature, is also discussed.