28 June 2018

Lorenzo De Biase (Cardiff)

Generalised braid categorification

Ordinary braid group Br_n is a well-known algebraic structure which encodes configurations of n non-touching strands (“braids”) up to continuous transformations (“isotopies”). A classical result of Khovanov and Thomas states that this group acts categorically on the space Fl_n of complete flags in Cⁿ. Generalised braids are the braids whose strands are allowed to touch in a certain way. They have multiple endpoint configurations and can be non-invertible, thus forming a category rather than a group. In this talk I will present  some progress that have been made towards extending the result of Khovanov and Thomas to the categorification of the generalised braid category.

4 October 2018

Stuart White (Glasgow)

To be confirmed

5 October 2017

Room M1.02

Gerard Watts (King's)

Conformal Field Theory defects - old and new

I will try to summarise some old and some new work on defects in two dimensional conformal field theory. Defects have played important roles from the Jordan-Wigner transformation onwards, but there are still interesting questions to ask and some hope that they can be answered.

16 October 2017

16:10-17:00

Rolf Gohm (Aberystwyth)

Star generators of S_∞ as a noncommutative exchangeable sequence

Gohm and Koestler developed an interpretation of Thoma's formula for extremal characters of S_∞ as a de Finetti type theorem. Here a basic observation is that the so-called star generators form a noncommutative exchangeable sequence. We discuss the method and explore its potential by looking at more general states for which this basic observation still holds.

26 October 2017

Paweł Dłotko (Swansea)

Practical problems, theory and computations: A few simple stories on topology in action

In this talk I will present a few problems in applied science that have been solved using methods from computational topology and in general computational mathematics. Starting from down-to-earth material science, via dynamical systems, ending up in brain research. I will present a feedback loop between theory and algorithms: how those two works together to solve problems, how they get mutual inspiration and why in applied sciences they should not be separated.

2 November 2017

Simon Wassermann (Glasgow)

Free groups and operator algebras

Operator algebras arising from free groups have provided important examples in the subject, starting with von Neumann's celebrated construction of non-isomorphic factors in the 1930s. Another milestone was the proof by Pimsner and Voiculescu in the 1980s that the regular C*-algebras of free groups on n generators are nonisomorphic, for different n. In this talk I shall present an extension of the the latter result to products of free groups and more general free product algebras and discuss some open problems.

8 November 2017

Maths Colloquium

Speaker: Constantin Teleman (Oxford)

9 November 2017

Alexander Kasprzyk (Nottingham)

23 November 2017

Ilke Canakci (Newcastle)

Cluster algebras, snake graphs and continued fractions

Snake graphs are planar graphs first appeared in the context of cluster algebras associated to marked surfaces. In their first incarnation, snake graphs were used to give formulas for generators of cluster algebras. Along with further investigations and several applications, snake graphs were also studied from a more abstract point of view as combinatorial objects. In this talk, I will report on joint work with Ralf Schiffler where we introduce a link to continued fractions. More precisely, we give a combinatorial realisation of continued fractions in terms of 'perfect matchings' of snake graphs. I will also discuss applications to cluster algebras as well as to elementary number theory.

30 November 2017

David Ridout (Melbourne)

Weight modules for sl₃ and conformal field theory

One of the most fundamental families of conformal field theories, the Wess-Zumino-Witten models, relies heavily on the theory of irreducible highest-weight representations of affine Kac-Moody algebras. However, there are many other interesting models with affine symmetry for which one needs representations that have neither of these properties. This motivates studying more general classes of weight modules, starting with those for simple Lie algebras. I will review what's known, concentrating on sl₂ and sl₃, and explain the relevance to conformal field theory.

7 December 2017

Kazuya Kawasetsu (Melbourne)

The characters of relaxed highest-weight modules over affine Kac-Moody algebras

The relaxed highest-weight modules over affine Kac-Moody algebras play an important role in the Creutzig-Ridout Verlinde formula for admissible affine vertex algebras. In this talk, we compute the characters of the irreducible relaxed highest-weight modules over the affine Kac-Moody algebra $\hat{sl}_2$ induced from the dense irreducible modules over $sl_2$, using Mathieu's coherent families. We show that the characters are ``coherent", that is, they are the product of a $q$-series and a formal delta function in $z$. If time allows, we will also consider the characters of relaxed highest-weight modules over $\hat{osp}(1|2)$ and $\hat{sl}_3$.

This is a joint work with David Ridout.

13-15 December 2017

LMS South Wales & South West Regional Meeting and Workshop on Algebraic Structures and Quantum Physics

Speakers include: Shahn Majid (Queen Mary), Ingo Runkel (Hamburg), Chris Fewster (York), Veronique Fisher (Bath), Christian Korff (Glasgow), Pieter Naaijkens (Aachen), Ulrich Pennig (Cardiff), Ko Sanders (Dublin), Anne Taormina (Durham), Michael Tuite (Galway)

1 February 2018

Oscar Bandtlow (QMUL)

13 February 2018

Calf in Cardiff

13:00-17:00, Queen's Buildings, South Building room S/3.21

Speakers: Oliver E. Anderson (Liverpool), Mirko Mauri (LSGNT), Vladimir Eremichev (Warwick)

15 February 2018

Nelly Villamizar (Swansea)

Geometric realizations of spline spaces on a simplicial complex

We consider the space of C^r-continuous splines (or piecewise polynomial functions) defined on a simplicial complex. Besides the practical applications of splines, including the solution of partial differential equations by the finite element method, and the approximation of shapes in geometric modeling, the space of C^r-continuous splines forms a ring, and one can study its algebraic structure. More precisely, the space of C⁰-continuous splines is a quotient of the Stanley-Reisner ring of the corresponding simplicial complex, and the geometric realization of the Stanley-Reisner ring reflects the structure of the simplicial complex. In the talk, we shall consider the generalized Stanley-Reisner rings associated to a simplicial complex, namely the ring of spline functions with higher order of global continuity on the simplicial complex, and give a description of their geometric realizations for particular instances of the dual graph of the complex. We will also discuss related open problems in this area.

22 March 2018

Gandalf Lechner (Cardiff)

Examples and deformations of algebraic quantum field theories

In this talk, I will first explain how so-called Borchers triples - consisting of an algebra of operators acting on a Hilbert space, a representation of the Poincaré group on that space, and an invariant vector satisfying certain compatibility assumptions - gives rise to examples of quantum field theories. I will then discuss a procedure ("warped convolution") related to Rieffel's deformation that can be used to deform such triples in a certain sense and define non-trivial quantum field theories. Following suggestions from within the GAPT group, my plan is to avoid the technical details of the construction and rather include a post seminar discussion in the Pen & Wig.

12 April 2018

15.10-15.55

Daniela Cadamuro (TU Munich)

An introduction to quantum integrable models in the algebraic framework

Quantum integrable models are a special class of quantum field theories in 1+1 dimensional Minkowski space. A consistent mathematical framework for the construction of these models can be formulated in the language of C*- or von Neumann algebras. In particular, it makes use of the concept of “wedge algebras”, an intermediate step to the construction that helps controlling the functional analytic properties of physically relevant operators.

12 April 2018

16.10-16.55

Henning Bostelmann (York)

The status of pointlike fields in integrable quantum field theories

Integrable QFTs are heuristically thought to be generated by interacting pointlike quantum fields. However, these objects are mathematically very difficult to control. in this talk, we explicitly construct pointlike fields in a specific situation (the massive Ising model), show that they correspond to closable operators affiliated with the local net of von Neumann algebras, and verify that they generate all local quantities in a certain sense.

19 April 2018

Simon Blackburn (Royal Holloway)

Cryptography using group theory

Over the past 20 years, there have been frequent proposals to use group-theoretic techniques in the design of cryptosystems. I will provide a brief introduction to the area, and I will talk about some of the techniques that can be used to attack some of these schemes. I will assume no knowledge of cryptography, and very little group theory.

26 April 2018

Claudia Scheimbauer (Oxford)

From topological field theories to “higher” algebra

We will start this talk with an introduction to the Atiyah-Segal approach to topological field theories. This approach has encouraged many developments of so-called "higher" algebra and "higher" categories in the last three decades. We will see how a classification of so called "fully extended" topological field theories leads to studying algebraic "dualizability" conditions, generalizing a finite dimensional vector space and its dual. The study of these conditions has led to many interesting connections to different fields of mathematics, e.g. in representation theory.

3 May 2018

Michael Joachim (Münster)

On applications of twisted spin cobordism theory

Hebestreit and Joachim generalized the Anderson-Brown-Peterson splitting for spin cobordism to the twisted set-up. In our talk we will  show how classical applications, which use the Anderson-Brown-Peterson  splitting, can be generalized to give results for twisted spin cobordism  and twisted K-theory.

10 May 2018

Olalla Castro-Alvaredo (City)

Entanglement Measures in 1+1 Dimensional Quantum Field Theory

In this talk I will present a brief introduction to a research area I have been contributing to for the past 11 years. My research addresses the question of how to compute measures of entanglement for 1+1 dimensional quantum field theories, especially those that are not conformal but are integrable. In this context, my research has focused on employing one particular technique we have called the branch point twist field approach that we introduced in [Cardy, Castro-Alvaredo, Doyon'07] which I will briefly summarise in my talk. The basic premise of this technique is that measures of entanglement can be expressed in terms of correlation functions of a particular class of local quantum fields and once this is established one may use generalisations of well-known methods to obtain information about the amount of entanglement that can be "distilled" from a particular quantum state and the universal properties of this measure. I will then present some of the main results we have obtained by using this technique and discuss some future developments and open problems.

The work has been carried out in collaboration mainly with Benjamin Doyon and several other collaborators over many years. View a list of related publications.

16 May 2018

(Wednesday this week)

COW seminar

To be confirmed

1-2 June 2018

ICFT 22 - UK Meeting on Integrable and Conformal Field Theory and Related Topics

Speakers include: Kasia Rejzner (York), Ana Ros Camacho (Utrecht), Cornelius Schmidt-Colinet (Munich), Yoh Tanimoto (Rome)