David Gao

activity

20242026

collaborators

9 papers

math.OA2026

Strongly converging unitary representations for extensions by exact groups

David Gao, Srivatsav Kunnawalkam Elayavalli, Mahan Mj

We prove the existence of strongly converging unitary representations in various new settings of countable groups, in particular, arising as extensions by exact groups: semidirect…

math.OA2026

Non-isomorphism of reduced free group $C^{*}$ -algebras

David Gao, Srivatsav Kunnawalkam Elayavalli

Using a new approach involving embedding spaces in II $_{1}$ factors with plenty of freely independent Haar unitaries, we prove that $C^\ast_r(\mathbb{F}_n)\ncong C^\ast_r(\mathbb{F}_…

math.OA2026

Exotic full factors via weakly coarse bimodules

David Gao, David Jekel, Srivatsav Kunnawalkam Elayavalli +1

We are able to explicitly compute the bimodule structure of von Neumann algebra inclusions in handle constructions, which arise as inductive limits of iterated amalgamated free pro…

math.OA2025

Elementary embeddings into ultrapower $II_{1}$ factors without a UCP lift

David Gao, David Jekel

We show that there are $II_{1}$ factors $M$ and elementary embeddings $M \to M^{U}$ which do not lift to sequences of UCP maps, and in fact $M$ can be chosen from…

math.OA2025

3-handle construction on II $_{1}$ factors

David Gao, Srivatsav Kunnawalkam Elayavalli, Gregory Patchell

We find a subtle modification to the construction of Chifan-Ioana-Kunnawalkam Elayavalli, which yields a drastic simplification of the proof of the existence of two non Gamma non e…

math.OA2024

Strict comparison in reduced group $C^{*}$ -algebras

Tattwamasi Amrutam, David Gao, Srivatsav Kunnawalkam Elayavalli +1

We prove that for every $n \geq 2$ , the reduced group $C^{*}$ -algebras of the countable free groups $C_{r}^{*} (F_{n})$ have strict comparison. Our method works in a general setting…

math.GR2024

Sofic actions on graphs

David Gao, Greg Patchell, Srivatsav Kunnawalkam Elayavalli

We develop a theory of soficity for actions on graphs and obtain new applications to the study of sofic groups. We establish various examples, stability and permanence properties o…

math.GR2024

On soficity for certain fundamental groups of graphs of groups

David Gao, Srivatsav Kunnawalkam Elayavalli, Mahan Mj

In this note we study a family of graphs of groups over arbitrary base graphs where all vertex groups are isomorphic to a fixed countable sofic group $G$ , and all edge groups $H < G$ …

math.OA2024

Internal sequential commutation and single generation

David Gao, Srivatsav Kunnawalkam Elayavalli, Gregory Patchell +1

We extract a precise internal description of the sequential commutation equivalence relation introduced in [KEP23] for tracial von Neumann algebras. As an application we prove that…

Strongly converging unitary representations for extensions by exact groups

Non-isomorphism of reduced free group C∗-algebras

Exotic full factors via weakly coarse bimodules

Elementary embeddings into ultrapower II1​ factors without a UCP lift

3-handle construction on II1​ factors

Strict comparison in reduced group C∗-algebras

Sofic actions on graphs

On soficity for certain fundamental groups of graphs of groups

Internal sequential commutation and single generation

Non-isomorphism of reduced free group $C^{*}$ -algebras

Elementary embeddings into ultrapower $II_{1}$ factors without a UCP lift

3-handle construction on II $_{1}$ factors

Strict comparison in reduced group $C^{*}$ -algebras