Bridgeland's work helped to establish the coherent derived category as a key invariant of algebraic varieties and stimulated world-wide enthusiasm for what had previously been a technical backwater.

[3] Bridgeland's 2002 Annals paper introduced spaces of stability conditions on triangulated categories, replacing the traditional rational slope of moduli problems by a complex phase.

This far-reaching innovation gives a rigorous mathematical language for describing D-branes and creates a new area of deep interaction between theoretical physics and algebraic geometry.

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