Event categories Archives:

Title: Extending CNOT to real stabilizer quantum mechanics Abstract: The stabilizer formalism for quantum mechanics is an important tool for implementing fault tolerant quantum circuits.  In this talk we first give a brief overview of the stabilizer formalism.  We also will discuss the angle-free fragment of the ZX calculus, which is complete for the real […]

Title: Abstract Symplectic Geometry Abstract: In recent years, symplectic geometry has used increasingly sophisticated categorical and homotopical machinery. We will consider how tangent categories may simplify some of these constructions.

Title: Differential Algebras in Codifferential Categories Abstract: Differential categories have lead to abstract formulations of several notions of differentiation such as, to list a few, the directional derivative, Kahler differentials, differential forms, smooth manifolds , and De Rham cohomology. Therefore, if the theory of differential categories wishes to champion itself as the axiomatization of the […]

Title: Additive Bundles and their Connection Theory Abstract: In this talk we consider the generalization of connection theory from the second tangent bundle of a smooth manifold to double additive bundles in an arbitrary category. We then extend this generalization to higher ordered connections on n-fold additive bundles. 

Title: Two dimensional Lie theory Abstract: This week I present an outline of a joint project with Ben MacAdam. The main aim is to generalise the theory of Lie groupoids and Lie algebroids by using 2-cubical sets. One advantage of this approach is that it avoids a certain quotient that is required in the classical […]

Title: The free Lie algebras in Tebbe’s calculation of the derivatives of atomic functors Abstract: A discrete module is a functor from finite pointed sets to chain complexes of R-modules. There are two ways to do functor calculus for discrete modules. The first is to find the Taylor tower in a way analogous to the […]

Title: Interpretations of algebraic theories, and the adjunctions they induce: Part II Abstract: Many cases of free/forgetful adjunctions are special cases of a more general theorem: any interpretation of algebraic theories induces an adjunction on their categories of models. Free monoid, free groups, free modules, tensor algebras, and polynomial rings are all instances of this. […]

Title: Interpretations of algebraic theories, and the adjunctions they induce Abstract: Many cases of free/forgetful adjunctions are special cases of a more general theorem: any interpretation of algebraic theories induces an adjunction on their categories of models. Free monoid, free groups, free modules, tensor algebras, and polynomial rings are all instances of this. In my […]

Title: Introduction to univalence in Coq IV Abstract: This week we conclude our sequence of talks on homotopy type theory (HoTT). We revisit the univalence axiom and use a simple example to illustrate its use. The audience is encouraged to follow the development of the theory on their own computers so please bring a laptop […]

Title: Introduction to univalence in Coq III Abstract: This week we continue our sequence of talks on homotopy type theory (HoTT) for which we are approaching the denouement. First we define h-propositions and what it means to be a contractible type. Then we distinguish between a couple of different types of equivalence and show that […]