# Isaac Ren: Algebraic rewriting

**Time: **
Fri 2022-02-18 13.15 - 14.15

**Location: **
KTH, 3721 and Zoom (meeting ID: 68578498723)

**Participating: **
Isaac Ren (KTH)

**Abstract**

How can we effectively check if two elements of a quotient algebra are equal? This is one of the problems that algebraic rewriting theory addresses. In this talk, I will give an overview of algebraic rewriting theory. Its history begins in computational mathematics, with abstract rewriting and the word decision problem. On the algebraic side, rewriting emerged in the form of Gröbner-Shirshov bases for commutative and Lie algebras. Since then, rewriting has been generalized to higher dimensional rewriting using polygraphs (or computads), which are especially interesting for computational aspects of homological algebra: in particular, algebraic rewriting allows for the computation of small resolutions of algebraic objects.