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LFCS seminar: Ross Duncan: Interacting Frobenius Algebras are Hopf but Quantum Theory is not Petri-nets

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What
  • LFCS Seminar
When Feb 02, 2016
from 04:00 PM to 05:00 PM
Where IF 4.31/4.33
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Abstract:

 

Theories featuring the interaction between a Frobenius algebra and a Hopf algebra have recently appeared in several areas in computer science: concurrent programming, control theory, and quantum computing, among others. Bonchi, Sobocinski, and Zanasi (2014) have shown that, given a suitable distributive law, a pair of Hopf algebras forms two Frobenius algebras. Here we take the opposite approach, and show that interacting Frobenius algebras form Hopf algebras. We generalise (BSZ 2014) by including non-trivial dynamics of the underlying object---the so-called phase group---and investigate the effects of finite dimensionality of the underlying model. We recover the system of Bonchi et al as a subtheory in the prime power dimensional case, but the more general theory does not arise from a distributive law.

 

 

The talk is based on: http://arxiv.org/abs/1601.04964

 

 

Brief Bio: Ross Duncan is a lecturer at Strathclyde since October 2013. He completed BSc Hons Edinburgh 2001; DPhil from Oxford 2007; Following which he was a post-doc ion Oxford, then in Brussels.  He likes category theory, graphical languages and quantum computing.

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