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The Erwin Schroedinger Institute for Mathematical Physics

Higher topological quantum field theory and categorical quantum mechanics

Workshop Schedule (pdf), Abstracts (pdf)

Recently new parallels between the foundations of quantum mechanics, quantum computation and topological quantum field theory (TQFT) have begun to take shape. Categorical quantum mechanics was conceived by Abramsky and Coecke about ten years ago in an attempt to clarify the conceptual foundations of the subject, while TQFT (pioneered by Atiyah, Segal and Witten) is one of the finest modern examples of the interaction between pure mathematics and theoretical physics. The two subjects are founded on a common mathematical language: symmetric monoidal categories (both ordinary categories and higher categories) with duals at various levels.

In recent years higher categories, under for example the headings of ‘categorification’ and ‘defects’, have generated a lot of activity in the field of TQFT. This has led to insights in algebra, geometry, topology, condensened matter physics, supersymmetric gauge theory, and string theory; the rich and growing literature on categorified knot invariants is a prime example here. These developments have many unexplored implications for categorical quantum mechanics, and for quantum computation more specifically. In the opposite direction, researchers in categorical quantum mechanics have made rapid progress on clarifying the conceptual problems of quantum information; this insight, as well as an emphasis on categorical structures not traditionally studied in TQFT, is an opportunity to examine the latter subject from a new angle.

The time is right for a workshop to intensify cross-fertilisation between TQFT and categorical quantum mechanics, by bringing together experts in higher category theory, TQFT, and quantum mechanics. The first intention of this workshop is to review recent progress in these directions and discuss important open problems such as a unified 2-categorical treatment of open quantum systems including infinite-dimensional state spaces, or a 2-categorical version of homological mirror symmetry. The second and main purpose is to contribute to solutions of these challenges, in the spirit of earlier successes such as the idea of an anyonic topological quantum computer based on the understanding of three-dimensional TQFT. Accordingly, higher-dimensional TQFTs will be another focus. 

At a glance

Type: Workshop
When: Oct 19, 2015 to
Oct 23, 2015
Where: ESI, Boltzmann Lecture Hall
Organizers: Nils Carqueville (U Vienna), Daniel Murfet (U Melbourne), Ingo Runkel (Hamburg U)
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