Information cohomology is computed in low degrees to establish multivariate mutual informations as k-coboundaries, with simplicial structures yielding free-energy interpretations and a topological minimum free energy complex.
Topological quantum field theories
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Following my plenary lecture on ICMP2000 I review my results concerning two closely related topics: topological quantum field theories and the problem of quantization of gauge theories. I start with old results (first examples of topological quantum field theories were constructed in my papers in late seventies) and I come to some new results, that were not published yet.
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The Poincar\'e-Boltzmann Machine: from Statistical Physics to Machine Learning and back
Information cohomology is computed in low degrees to establish multivariate mutual informations as k-coboundaries, with simplicial structures yielding free-energy interpretations and a topological minimum free energy complex.