TMCCT 2027

About the workshop

TMCCT 2027 (Topological Methods in Computability and Complexity Theory) brings together researchers from India and France for a workshop in Chennai. Its common thread is the use of topology, geometry and dynamics to understand computation, information and randomness.

Algorithmic information theory uses Kolmogorov complexity to give a precise meaning to the randomness and compressibility of individual infinite sequences and real numbers. Viewed in Cantor space or Euclidean space, these notions become geometric: effective versions of Hausdorff dimension (constructive, polynomial-time and finite-state dimension) measure the information content of individual points, and the point-to-set principle turns them into a tool for classical fractal geometry.

Dynamical systems offer a second perspective. Normal numbers, equidistribution and Weyl-type criteria link finite-state compression to the dynamics of base-b expansions and of the Gauss map behind continued fractions. Subshifts and tilings, which are topological dynamical systems on Cantor space, raise computability questions of their own, including games played on tilings.

Topics may also include topological aspects of computable analysis, and resource-bounded versions of these ideas, which connect to complexity theory and cryptography, for instance through the link between one-way functions and polynomial-time dimension.

The programme will be posted here soon.