Program
The use of dynamical invariants has long been a staple of geometry and topology, from rigidity theorems, to classification theorems, to the general study of lattices and of the mapping class group. More recently, random structures in topology and notions of probabilistic geometric convergence have played a critical role in testing the robustness of conjectures in the arithmetic setting. The program will focus on invariants in topology, geometry, and the dynamics of group actions linked to random constructions.
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Keywords and Mathematics Subject Classification (MSC)
Tags/Keywords
Arithmetic group
Symmetric space
Invariant random subgroup
torsion growth
Benjamin-Schramm convergence
probability measure preserving actions
Measure equivalence relations
sofic entropy
hyperbolic manifold
20P05 - Probabilistic methods in group theory [See also 60Bxx]
22E40 - Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]
22F10 - Measurable group actions [See also 22D40, 28Dxx, 37Axx]
37A20 - Orbit equivalence, cocycles, ergodic equivalence relations
37A35 - Entropy and other invariants, isomorphism, classification
37C40 - Smooth ergodic theory, invariant measures [See also 37Dxx]
57M25 - Knots and links in $S^3$ {For higher dimensions, see 57Q45}