Srivatsav Kunnawalkam Elayavalli

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…

Selfless C-correspondences, operator valued C-probability spaces and completely positive maps

David Gao, Marius Junge, Srivatsav Kunnawalkam Elayavalli +2

We develop a general theory of selflessness for C*-correspondences, with several applications. Specializing this theory to completely positive maps, in particular to conditional ex…

Relative biexactness and mixing in von Neumann algebras

Srivatsav Kunnawalkam Elayavalli, Zhiyuan Yang

We develop a new technique to upgrade relative biexactness in general von Neumann algebras: suppose that ${N_{i}}_{i \in I} \subset M$ are mixing and biexact subalgebras of a separab…

Questions on the structure of random embeddings of $L (F_{2})$

Ben Hayes, David Jekel, Srivatsav Kunnawalkam Elayavalli

Motivated by recent developments at the interface of operator algebras and random matrix theory, we propose new conjectures concerning the asymptotic structure of random matrix mod…

Selfless reduced amalgamated free products and HNN extensions

David Gao, Srivatsav Kunnawalkam Elayavalli, Gregory Patchell +1

We find a general family of selfless inclusions in reduced amalgamated free products of C*-algebras. Apart from generalizing prior works due to McClanahan, Ivanov and Omland, our w…

math.GR2026

On free components of Artin and Coxeter groups

Guillaume Dumas, Jingyin Huang, Srivatsav Kunnawalkam Elayavalli +1

The number of connected components can be remembered by the von Neumann algebra among Artin groups, the only possible exception being the case that corresponds to the free group fa…

Toeplitz exactness for strong convergence

David Gao, Srivatsav Kunnawalkam Elayavalli

We prove a new "Toeplitz exactness" theorem for strong convergence. This is a machine to upgrade strong convergence in the general setting of $C^{*}$ -correspondences, and has seve…

math.GR2026

A new source of purely finite matricial fields

David Gao, Srivatsav Kunnawalkam Elayavalli, Aareyan Manzoor +1

A countable group $G$ is said to be \emph{matricial field} (MF) if it admits a strongly converging sequence of approximate homomorphisms into matrices; i.e, the norms of polynomial…

Strongly 1-bounded inner amenable groups

Ben Hayes, Srivatsav Kunnawalkam Elayavalli

It is shown that finitely presented icc inner amenable groups yield strongly 1-bounded II_1 factors.

Conjugacy co-amenability

Mehrdad Kalantar, Srivatsav Kunnawalkam Elayavalli

In this note we study a natural analytic property of inclusions of groups akin to co-amenability: the property of existence of a non-compactly supported invariant state for the con…

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}_…

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…

50 Open Problems: Ultraproduct II $_{1}$ factors

Srivatsav Kunnawalkam Elayavalli

A collection of 50 open problems around the structure theory of ultraproducts of II $_{1}$ factors is presented, along with some annotations and references.

Selfless Inclusions of C*-Algebras

Ben Hayes, Srivatsav Kunnawalkam Elayavalli, Gregory Patchell +1

We introduce and study a natural notion of selflessness for inclusions of C*-probability spaces, which in particular implies that all intermediate C*-algebras are selfless in the s…

math.GR2025

Some remarks on decay in countable groups and amalgamated free products

Srivatsav Kunnawalkam Elayavalli, Gregory Patchell, Lizzy Teryoshin

In this note, we first study the notion of subexponential decay (SD) for countable groups with respect to a length function, which generalizes the well-known rapid decay (RD) prope…

Selfless reduced free product $C^{*}$ -algebras

Ben Hayes, Srivatsav Kunnawalkam Elayavalli, Leonel Robert

We study selflessness in the general setting of reduced free products of $C^{*}$ -algebras. Towards this end, we develop a suitable theory of rapid decay for filtrations in arbitrary…

Negative resolution to the $C^{*}$ -algebraic Tarski problem

Srivatsav Kunnawalkam Elayavalli, Christopher Schafhauser

We compute the $K_{1}$ -group of ultraproducts of unital, simple $C^{*}$ -algebras with unique trace and strict comparison. As an application, we prove that the reduced free group $C^{*}$ -…

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…

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…

Simplices of maximally amenable extensions in II $_{1}$ factors

Srivatsav Kunnawalkam Elayavalli, Gregory Patchell

For every $n \in N$ we obtain a separable II $_{1}$ factor $M$ and a maximally abelian subalgebra $A \subset M$ such that the space of maximally amenable extensions of $A$ in $…

General solidity phenomena and anticoarse spaces for type $III_{1}$ factors

Ben Hayes, David Jekel, Srivatsav Kunnawalkam Elayavalli +1

By developing a theory of anticoarse spaces in the purely infinite setting and using 1-bounded entropy techniques along with recent strong convergence results in random matrix theo…

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 $H < G$ …