### Higher-Dimensional Rewriting in Warsaw

#### Posted by John Baez

This summer there will be a conference on higher-dimensional algebra and rewrite rules in Warsaw. They want people to submit papers! I’ll give a talk about presentations of symmetric monoidal categories that are important in electrical engineering and control theory. There should also be interesting talks about combinatorial algebra, homotopical aspects of rewriting theory, and more:

- Higher-Dimensional Rewriting and Applications, 28-29 June 2015, Warsaw, Poland. Co-located with the RDP, RTA and TLCA conferences. Organized by Yves Guiraud, Philippe Malbos and Samuel Mimram.

Here’s a description…

### Description

Over recent years, rewriting methods have been generalized from strings and terms to richer algebraic structures such as operads, monoidal categories, and more generally higher-dimensional categories. These extensions of rewriting fit in the general scope of higher-dimensional rewriting theory, which has emerged as a unifying algebraic framework. This approach allows one to perform homotopical and homological analysis of rewriting systems (Squier theory). It also provides new computational methods in combinatorial algebra (Artin-Tits monoids, Coxeter and Garside structures), in homotopical and homological algebra (construction of cofibrant replacements, Koszulness property). The workshop is open to all topics concerning higher-dimensional generalizations and applications of rewriting theory, including

• higher-dimensional rewriting: polygraphs / computads, higher-dimensional generalizations of string/term/graph rewriting systems, etc.

• homotopical invariants of rewriting systems: homotopical and homological finiteness properties, Squier theory, algebraic Morse theory, coherence results in algebra and higher-dimensional category theory, etc.

• linear rewriting: presentations and resolutions of algebras and operads, Gröbner bases and generalizations, homotopy and homology of algebras and operads, Koszul duality theory, etc.

• applications of higher-dimensional and linear rewriting and their interactions with other fields: calculi for quantum computations, algebraic lambda-calculi, proof nets, topological models for concurrency, homotopy type theory, combinatorial group theory, etc.

• implementations: the workshop will also be interested in implementation issues in higher-dimensional rewriting and will allow demonstrations of prototypes of existing and new tools in higher-dimensional rewriting.

### Submitting

Important dates:

• Submission: April 15, 2015

• Notification: May 6, 2015

• Final version: May 20, 2015

• Conference: 28-29 June, 2015

Submissions should consist of an extended abstract, approximately 5 pages long, in standard article format, in PDF. The page for uploading those is here. The accepted extended abstracts will be made available electronically before the workshop.

### Organizers

Program committee:

• Vladimir Dotsenko (Trinity College, Dublin)

• Yves Guiraud (INRIA / Université Paris 7)

• Jean-Pierre Jouannaud (École Polytechnique)

• Philippe Malbos (Université Claude Bernard Lyon 1)

• Paul-André Melliès (Université Paris 7)

• Samuel Mimram (École Polytechnique)

• Tim Porter (University of Wales, Bangor)

• Femke van Raamsdonk (VU University, Amsterdam)