NBMPS 50

The fiftieth meeting of the North British Mathematical Physics Seminar will take place on

Friday 12th May 2017 at the King's Manor, University of York.

The King's Manor is in the centre of the city, 5 minutes' walk from the railway station. To get there, turn left out of the station, under the wall, left over the bridge over the river, then left after 100m at the crossroads (see map). The King's Manor is in Exhibition Square, to the left of the fountain and the city art gallery.

Refreshments will be in the refectory and lunch in cafes nearby. To get to the refectory go through the porters' lodge and up the stone staircase towards the end of the first court on the left. Talks will be in K/133, entered either through the refectory (back of the theatre) or at the far left-hand corner of the furthest court (which brings you in at the front of the theatre).

Programme

1100-1130

Mirjam Weilenmann (York)

Analysis of the entropy vector approach to distinguish classical and quantum causal structures

Bell's theorem shows that our intuitive understanding of causation must be revisited in light of quantum correlations. Nevertheless, quantum mechanics does not permit signalling and hence a notion of cause remains. Understanding this notion is not only important at a fundamental level, but also for technological applications such as key distribution and randomness expansion. It has recently been shown that a useful way to determine which classical causal structures give rise to a given set of correlations is to use entropy vectors. We consider the question of whether such vectors can lead to useful certificates of non-classicality. We find that for a family of causal structures that include the usual bipartite Bell structure and the bilocality scenario they do not, in spite of the existence of non-classical correlations. Furthermore, we find that for many causal structures non-Shannon entropic inequalities give additional constraints on the sets of possible entropy vectors in the classical case. They hence lead to tighter outer approximations of the set of realisable entropy vectors, which we are able to supplement with inner approximations. This enables a sharper distinction of different causal structures. Whether our improved characterisations are also valid for the quantum case remains an open problem whose resolution would have implications for the discrimination of classical and quantum cause and would give novel insights into the question of whether there exist new inequalities for the von Neumann entropy.

1130-1200

Lennart Schmidt (Heriot-Watt)

The Non-Abelian Self-Dual String

This talk is based on work with Christian Saemann detailed in arxiv:1705.02353. In there, we argue that the relevant higher gauge group for the non-abelian generaliza- tion of the self-dual string equation is the string 2-group. After deriving the corresponding equations of motion we present explicitly the elementary solution to these, which is the categorified analogue of the ’t Hooft–Polyakov monopole and passes the relevant consistency checks; in particular, it is globally defined on R^4 and approaches the abelian self-dual string of charge one at infinity. In this talk, I will aim to present the framework of this solution and discuss its properties.

1345-1445

Arthur Jaffe (Harvard)

Some Recent Insights with Pictures

1530-1600

Robert Parini (York)

Algebro-geometric solutions to integrable defects

Several 1+1 dimensional integrable PDEs permit point-like defects or impurities which do not break the integrability of the model. The effect of such an integrable defect on an incoming soliton (stable solitary wave) is well known but many nonlinear integrable PDEs also permit a class of algebro-geometric (or finite-gap) solutions which are more general than solitons. I will show how algebro-geometric solutions in the presence of integrable defects can be constructed using a Darboux transformation and discuss how they compare to the known soliton solutions which can all be recovered in a suitable limit. This is the subject of joint work with Ed Corrigan detailed in arXiv:1612.06904.

1600-1700

Yang-Hui He (Oxford)

Calabi-Yau Volumes and Reflexive Polytopes

We study various geometrical quantities for Calabi-Yau varieties realized as cones over Gorenstein Fano varieties, obtained as toric varieties from reflexive polytopes in various dimensions. We concentrate on reflexive polytopes up to dimension 4 and calculate the minimized volume of the Sasaki-Einstein base of the corresponding Calabi-Yau cone. By doing so we conjecture new bounds for the Sasaki-Einstein volume with respect to many topological quantities of the corresponding toric varieties. We give interpretations about these volume bounds in the context of associated field theories via the AdS/CFT correspondence. Based on joint work with R.-K. Seong and S.-T. Yau.

Practical Information

If you come by car I'm afraid you'll need to take your chances in the city centre car parks. Bootham Row is the closest council car park, but the much larger Marygate is the next closest.

Limited funds are available to help with travel expenses of those with no other source of funding, especially postgraduate students and postdocs. Please book early to take advantage of the cheaper advance-purchase train fares. For how to claim please see the main NBMPS page.

If you plan to attend the meeting, or for further questions, please email the local organiser, Eli Hawkins. Please mention if you wish to attend the dinner, so that we can estimate numbers.

North British Mathematical Physics Seminar 50

Programme

Practical Information