##### Department of Mathematics,

University of California San Diego

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### Math 211 A00 - Algebra Seminar

## Keivan Mallahi-Karai

#### Jacobs University

## Optimal linear sofic approximation of countable groups

##### Abstract:

Various notions of metric approximation for countable groups have been introduced and studied in the last decade, with sofic and hyperlinear approximations being two notable examples among them. The class of linear sofic groups was introduced by Glebsky and Rivera and was subsequently studied by Arzhantseva and Paunescu. This mode of approximation uses the general linear group over, say, the field of complex numbers as model groups, equipped with the distance defined using the normalized rank. Among their other interesting results, Arzhantseva and Paunescu prove that every linear sofic group is 1/4-linear sofic, where the constant 1/4 quantifies how well non-identity elements can be separated from the identity matrix. In this talk, which is based on joint work with Maryam Mohammadi Yekta, we will address the question of optimality of the constant 1/4 and report on some progress in this direction.

### November 22, 2021

### 1:00 PM

### Meeting ID: 939 5383 2894 Password: structures

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