The dimension of self-affine sets: past, present and future.

The dimension of self-affine sets: past, present and future.

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Pablo Shmerkin, The University of Manchester
Fine Hall 401

Calculating the dimension of sets invariant under non-conformal dynamics is a formidable problem. My talk will be a survey on what is known and expected for self-affine sets, i.e. sets invariant under piece-wise affine expanding maps on Euclidean space. Some emphasis will be given to my joint work with A. Käenmäki on self-affine sets of Kakeya type, and the thermodynamic formalism for the singular value function.