49th North British Mathematical Physics Seminar

The joint 49th meeting of the North British Mathematical Physics Seminar and Edinburgh Mathematical Physics seminar will be held on Wednesday 8 March 2017 in Edinburgh at ICMS, 15 South College Street in the main lecture hall . For all general information about the North British Mathematical Physics Seminar, including instruction for claiming travel expenses follow this link

Programme

Edinburgh Mathematical Physics Group Seminar

Abstract: Many quantities in mathematical physics are periods in the sense of Kontsevich and Zagier. Francis Brown's theory of motivic periods enriches these mere numbers to algebraic objects and thereby provides an extremely powerful new tool to understand their relations, namely the motivic coaction (dual to an action of a motivic Galois group). I shall explain this structure in the case of multiple zeta values, where Goncharov's formula allows us to compute the coaction explicitly. Then I will focus on the example of Feynman integrals in perturbative phi^4 quantum field theory and briefly review methods of computing such periods in terms of multiple polylogarithms (based on hyperlogarithms and single-valued integration). These results show a remarkable feature: the Feynman periods appear to be closed under the motivic coaction, which explains their highly constrained structure. This is joint work with Oliver Schnetz.

Abstract:In this talk I will present some recent results regarding Darboux transformations of the vector nonlinear Schrodinger equation (vNLS). I will discuss the dressing and Backlund transformations for vNLS, and present the general higher rank one-soliton as well as the n-soliton solution as a ratio of determinants.

Abstract: Berry phase is a well-known feature of quantum mechanics. In this talk I will describe several new results about Berry phase in quantum field theory. We will see that even simple quantum field theories can exhibit non-trivial Berry phases. We will discuss an explicit example in axion electrodynamics. We will also discuss a general relation between the Berry connection in conformal field theories and the connections on conformal manifolds considered previously by several authors in conformal perturbation theory. The implementation of this relation in 2d N=(2,2) and 4d N=2 superconformal field theories leads to a useful re-derivation of the tt* equations. The latter have important implications on the non-perturbative structure of certain correlation functions, which I will briefly review.

Abstract: Dyson-Schwinger equations (DSEs) are integral equations which appear as the equations of motion for Green's functions in quantum field theories. Here we will look at combinatorial DSEs, which generate families of graphs through the action of grafting operators. We will see how this combinatorial version of the DSE relates to the traditional version, and why it is useful for the renormalisation of quantum field theories.

Abstract:The transition between Hall conductance plateaus of the integer quantum Hall effect stands out as a possible paradigm for quantum phase transitions of Anderson-localization type. Yet, in spite of numerous efforts and a renewed interest coming from the expanding field of topological phases, understanding this transition has so far defied an analytical solution by the methods of conformal field theory and/or the theory of integrable systems. In this talk I will review our approach based on a supersymmetric vertex model and the construction of conformal primary fields on the lattice from highest weight vectors of the vertex model in the presence of point contacts. The outcome of the analysis will be an effective free field description of critical wave intensities leading to a parabolic multifractality spectrum.

Abstract:In this talk I will summarise the construction of Bloch bundles and the Kane-Mele invariant from quantum mechanics along the lines of Freed and Moore's "Twisted equivariant matter". I will indicate how this abstract formalism lines up with the more commonly used topological set-up of time-reversal symmetric topological insulators and outline new perspectives on the Kane-Mele invariant.

Practical Information

ICMS is a 15-20 minute walk from Waverley train station. Here is a link to ICMS web page here .

Limited funds are available to help with travel expenses of participants with no other source of funding. We hope that this will encourage postgraduate students and postdocs to attend the meeting. Please email Douglas Smith in advance if you would like to apply for support.

Postscript: The meeting took place successfully. Click here to view a list of people who took part.