The fourth meeting of the
South East Mathematical Physics Seminar will be held on
Wednesday 8th April 2015
at the University of Hertfordshire in room E351.
The meeting is partially supported by supported by a London Mathematical Society Joint Research Groups grant.
There is no registration fee. If you plan to attend, it would be helpful if you could register here.
|11.00 - 11.30||Coffee|
|11.30 - 12.20||Rafael Maldonado (Cambridge)||Abelian-Higgs vortices on compact hyperbolic surfaces|
|12.20 - 13.20||lunch|
|13.20 - 14.10||Andrew Singleton (Cambridge)||Geometry in superconformal quantum mechanics|
|14.10 - 15.00||Lotte Hollands (Oxford)||Fenchel-Nielsen coordinates from spectral networks|
|15.00 - 15.40||Tea & Biscuits|
|15.40 - 16.30||Brenda Penante (Queen Mary)||Non-planar on-shell diagrams|
|16.30 - 17.20||Vincent Caudrelier (City)||Yang-Baxter and reflection equations: unifying structures behind quantum and classical integrable systems|
|Vincent Caudrelier (City)|
|Yang-Baxter and reflection equations: unifying structures behind quantum and classical integrable systems|
|The Yang-Baxter equation (YBE) is central in the theory of quantum integrable systems. For decades, together with its companion for problems with boundaries (the quantum reflection equation), it has been studied and used in the quantum realm. But it was suggested by Drinfeld in 1990 that the general study of the so-called "set-theoretical YBE" is also important. It turns out that classical integrable field theories provide a means to construct solutions to this equation, called Yang-Baxter maps, by looking at soliton collisions. Using the vector nonlinear Schrödinger (NLS) equation as the main example, we will review this notion of "classical solutions of the quantum YBE". Then, we will show how the new concept of set-theoretical reflection equation naturally emerges by studying the vector NLS on the half-line. Solutions to this equation, which we call reflection maps, arise from the reflection of solitons on the boundary. In the present context, factorization of interactions is the unifying principle behind integrability. This is of course well-know for quantum field theories but is essentially unexplored classically.|
|Lotte Hollands (Oxford)|
|Fenchel-Nielsen coordinates from spectral networks|
|Gauge theory in four dimensions is closely tied to the geometry of Riemann surfaces. For instance, its spectrum is encoded in a so-called spectral network, which is a collection of lines on a Riemann surface defined by a tuple of k-differentials. I will show that spectral networks generate interesting sets of Darboux coordinates on the moduli space of flat connections on a Riemann surface, such as (higher rank generalizations of) Fenchel-Nielsen coordinates. These coordinates in turn teach us about the strongly coupled regime of the gauge theory.|
|Rafael Maldonado (DAMTP, Cambridge)|
|Abelian-Higgs vortices on compact hyperbolic surfaces|
|I will show how to solve the Abelian-Higgs vortex equations on the highly symmetric genus 2 Bolza surface. The Higgs field can be computed analytically at certain points on the surface, which is represented by a regular tiling of the Poincare disk.|
|Brenda Penante (Queen Mary)|
|Non-planar on-shell diagrams|
| Among the many recent developments in the study of scattering amplitudes in N=4 super Yang-Mills is its dual formulation in terms of an integral over the Grassmannian Gr(k,n) -- the space of k planes in n dimensions. This formulation is tied to the concept of on-shell diagrams, bipartite graphs which beautifully relate field theory with combinatorics and graph theory.
The planar limit of the theory (SU(N) gauge group with N large) is well understood, but the effects of having a finite N are only starting to be explored. In this talk I will review these concepts in the planar limit and present some new features that arise when going beyond to non-planar on-shell diagrams.
|Andrew Singleton (DAMTP, Cambridge)|
|Geometry in superconformal quantum mechanics|
|The framework of discrete light-cone quantisation (DLCQ) offers a potential window into superconformal field theories via models with finitely many degrees of freedom. These models exhibit a superconformal invariance whose details are closely tied to the existence of extra geometrical structure in the target space. Of particular relevance to DLCQ are those with a scale-invariant special Kaehler target. We will describe a construction of a broad class of these models and discuss their application to N=4 SUSY Yang-Mills.|
Room E351 on College Lane Campus of the University of Hertfordshire. Here are maps of the campus; in particular this one.
Local travel information including maps may be found here.
By Train: The nearest station is Hatfield (change at King's Cross, London). Uno bus numbers 653 and 695 run between Hatfield station and the College Lane campus.
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 Clare Dunning (tcd at kent.ac.uk) in advance if you would like to apply for support.
To return to the South East Mathematical Physics Seminar webpage and to find information about claiming travel expenses please follow this link.