Some Homotopical Aspects of Ergodic Structure TheoryGraduate Colloquium

by Noa Bihlmaier (IAM)

Wednesday Feb 4, 2026, 3:15 PM → 4:45 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

Abstract:

A central theme in ergodic theory is the decomposition of systems into structured and random components. In the study of multiple ergodic averages, the structured part is captured by the Host–Kra–Ziegler tower. We will introduce this tower; which will lead us to nilspaces, axiomatizing the cubical configurations underlying these factors. We then discuss the resulting weak structure theory of nilspaces, which can be seen as a cubical analogue of simplicial homotopy theory. For example, there are similar notions of fibrations, homotopy groups and Postnikov towers. We make these analogies explicit and indicate routes toward a precise formalization.

 

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