Alex Rutar (University of Jyväskylä): Non-convex optimization in fractal geometry

What does non-convex optimization have to do with fractal geometry? I will discuss two such applications: the first, more well known, in multifractal analysis; and the second, more recent, in the dimension theory of dynamically invariant sets. In these two settings, fractal geometric problems can often be reduced to an abstract optimization problem over some measure space. A technical difficulty is that the objective functions which arise are often non-convex and non-smooth. To understand how to work around these difficulties, a key perspective is the parametric geometry of Lagrange multipliers. The new results are based on joint work with (different subsets of) Amlan Banaji, Jonathan Fraser, Thomas Jordan and István Kolossváry.