Topics in algebraic bundles

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The first topic to be considered is the essential dimension of moduli stacks of bundles. The dimension of a geometrical object is an important invariant. Stacks are an important generalisation of ordinary spaces that arise naturally when considering parameter spaces for objects. For example the most natural parameter "space" for curves is in fact not a space but a stack. One may view stacks as a modern theory of symmetries. For stacks there are two notions of dimension. Classical dimension, can be computed via methods from deformation theory that were developed many decades ago. The second notion of dimension, essential dimension, turns out to be a far more subtle invariant. It is the center of much intensive work and interesting conjectures. In our research we are interested in studying the essential dimension of certain stacks parametrising bundles over algebraic curves.