Low-dimensional topology and non-Euclidean geometry in nature

Sergei Nechaev (ISCP)


In the talk I demonstrate on specific examples the emergence of a new actively developing field, the “statistical topology”, which unifies topology, noncommutative geometry, probability theory and random walks. In particular, I plan to discuss the following interlinked questions: (i) statistics of random walks on hyperbolic manifolds and graphs in connection with the topology and fractal structure of unknotted long polymer chain confined in a bounding box and hierarchical DNA folding, and (ii) optimal embedding in the three-dimensional space of exponentially growing tissues, like, for example, the salad leaf, and how the hierarchical ultrametric geometry emerges in that case.

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