##### Department of Mathematics,

University of California San Diego

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### Algebra Colloquium

## Tullio Ceccherini-Silberstein

#### UCSD

## Linear cellular automata, sofic groups and stable finiteness of group rings

##### Abstract:

In this talk I'll first recall the notion of a "cellular automaton over a group" (also presenting celebrated Conway's "Game of Life") and then consider the linear version of the so-called "Garden of Eden Theorem" and Gottshalk's "Surjunctivity problem" which arise from symbolic dynamics. After recalling the notion of "amenability" for groups, I'll discuss the Gromov-Weiss notion of a "sofic group". Finally, I'll discuss Kaplansky's conjectures on the non-existence of idempotents and on stable finiteness of group rings and relate these problems to the theory of linear cellular automata.

Host: Efim Zelmanov

### November 6, 2006

### 2:00 PM

### AP&M 7218

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