Moduli Spaces & Stability Conditions

The fundamental objects of algebraic geometry are spaces defined by polynomial equations, called algebraic varieties. The main goal of algebraic geometry is ultimately the classification of algebraic varieties. Recent developments have explained that in order for this question to be tractable, one must restrict to a nicer class of “stable” varieties. For this more well-behaved class of varieties, it is expected that one can classify them into parameter spaces called moduli spaces. An important aspect of the theory is then to understand of the geometry of these moduli spaces.