Here are the titles and abstracts of their talks:
Abstract. In this talk, I will present some of the recent advances in the understanding of concurrent computations made with geometric (and of course category-theoretic) reasoning. One very important tool is the fundamental category functor which associates a category of "essential schedules" to the semantics of concurrent processes (seen as some form of partially ordered topological space for instance); hence giving a lot of information about how processes coordinate themselves. I will show how to compute inductively, in some simple cases, this fundamental category; this is part of the "compositionality" problem in concurrency theory. One of the defects is that this category is huge, so I will show how to "compress it" through several constructions of categories of fractions, which again reveal to be fundamental and natural constructions in this framework. This is joint work with Martin Raussen and Emmanuel Haucourt.
Abstract. Scott's graph model is a lambda-algebra based on the observation that continuous endofunctions on can be represented via their graphs. A graph consists of a set of pairs (S, n) where n is a natural and S is a finite set of naturals.
We consider a similar model based on sets of pairs (s,n), where s is a finite sequence rather than a set. Intuitively, this alteration means that we are taking into account the order in which observations are made. This new notion of graph gives rise to a model of affine lambda-calculus which admits an interpretation of imperative constructs including variable assignment, dereferencing and allocation.
The category arising as the Karoubi envelope of this untyped model provides a model of typed higher-order imperative computation with an affine type system. An appropriate language of this kind is Reynolds's Syntactic Control of Interference. Our model turns out to be fully abstract for this language. At a concrete level, the model is the same as Reddy's object spaces model, which was the first ``state-free'' model of a higher-order imperative programming language and an important precursor of games models. Our graph model can therefore be seen as a universal domain for Reddy's model. We also give a simple construction of a category of monoids and relations in which all of this work can be seen to live.
Abstract. The field of quantum computation suffers from a lack of syntax. In the absence of a convenient programming language, algorithms are frequently expressed in terms of circuits or Turing machines. Neither approach particularly encourages structured programming or abstractions such as data types. In this talk, I describe the syntax and semantics of a simple quantum programming language. The semantics is interesting because it combines notions from geometry of interaction, linear algebra, category theory, and complete partial orders.
Abstract. Anonymous communication techniques obscure who is talking to whom and are an important aspect of secure communication. This talk will be an introduction to anonymous communications theory and will be in two parts.
The first part of the talk will introduce some of the basic building blocks of anonymous communications systems: proxies, Chaum mixes, DC nets, etc. These offer varying amounts of protection. Typically the stronger the protection afforded by some primitive, the less practical the system that uses it. We will also briefly describe implemented systems, such as Onion Routing and Crowds.
In the second part of the talk we will look at some of the ways that have been proposed to define anonymity and related properties. As difficult as it has been to define notions such as authentication and confidentiality, anonymity is even more subtle. For example, protection generally depends on other legitimate users of the system. Otherwise the communicants are exposed. We will set out the various properties in the area, e.g., unobservability or plausible deniability, as well as the attempts to formalize them, e.g., using notions from process algebra and epistemic logic. We will also describe some of the nonformal work on probabilistic and information-theoretic characterizations of anonymity properties.