Add to ORKGWe show that a large family of groups is uniformly stable relative to unitary groups equipped with submultiplicative norms, such as the operator, Frobenius, and Schatten $p$-norms. These include lamplighters $\Gamma \wr \Lambda$ where $\Lambda$ is infinite and amenable, as well as several groups of dynamical origin such as the classical Thompson groups $F, F', T$ and $V$. We prove this by means of vanishing results in asymptotic cohomology, a theory introduced by the second author, Glebsky, Lubotzky and Monod, which is suitable for studying uniform stability. Along the way, we prove some foundational results in asymptotic cohomology, and use them to prove some hereditary features of Ulam stability. We further discuss metric approximation pr...
We prove a statement concerning hyperlinearity for central extensions of property (T) groups in the ...
We prove that Thompson’s group V is acyclic. The strategy of our proof stems from the context of hom...
Open access via the Springer Compact Agreement Acknowledgements: My thanks to Rachael Boyd, Anssi La...
We show that a large family of groups is uniformly stable relative to unitary groups equipped with s...
It is, by now, classical that lattices in higher rank semisimple groups have various rigidity proper...
It is, by now, classical that lattices in higher rank semisimple groups have various rigidity proper...
Using cohomological methods, we show that lattices in semisimple groups are typically stable with re...
A countable discrete group is said to be Frobenius stable if every function from the group to unitar...
In this thesis, we consider various notions of approximate representations of groups. Loosely speaki...
In this thesis, we consider various notions of approximate representations of groups. Loosely speaki...
A discrete group is matricially stable if every function from the group to a complex unitary group t...
Let Γ be a relatively hyperbolic group and let µ be an admissible symmetric finitely supported proba...
We give an effective bound on how much time orbits of a unipotent group $U$ on an arithmetic quotien...
We introduce a notion of "local stability in permutations" for finitely generated groups. If a group...
We relate the group structure of van der Kallen on orbit sets of unimodular rows with values in a sm...
We prove a statement concerning hyperlinearity for central extensions of property (T) groups in the ...
We prove that Thompson’s group V is acyclic. The strategy of our proof stems from the context of hom...
Open access via the Springer Compact Agreement Acknowledgements: My thanks to Rachael Boyd, Anssi La...
We show that a large family of groups is uniformly stable relative to unitary groups equipped with s...
It is, by now, classical that lattices in higher rank semisimple groups have various rigidity proper...
It is, by now, classical that lattices in higher rank semisimple groups have various rigidity proper...
Using cohomological methods, we show that lattices in semisimple groups are typically stable with re...
A countable discrete group is said to be Frobenius stable if every function from the group to unitar...
In this thesis, we consider various notions of approximate representations of groups. Loosely speaki...
In this thesis, we consider various notions of approximate representations of groups. Loosely speaki...
A discrete group is matricially stable if every function from the group to a complex unitary group t...
Let Γ be a relatively hyperbolic group and let µ be an admissible symmetric finitely supported proba...
We give an effective bound on how much time orbits of a unipotent group $U$ on an arithmetic quotien...
We introduce a notion of "local stability in permutations" for finitely generated groups. If a group...
We relate the group structure of van der Kallen on orbit sets of unimodular rows with values in a sm...
We prove a statement concerning hyperlinearity for central extensions of property (T) groups in the ...
We prove that Thompson’s group V is acyclic. The strategy of our proof stems from the context of hom...
Open access via the Springer Compact Agreement Acknowledgements: My thanks to Rachael Boyd, Anssi La...