 10:00  11:00 Coffee in 39/40AA04
 The venue for the morning session is LTM.
 11:00  11:50
Nicholas Manton (DAMTP, Cambridge)
Hyperbolic Vortices
 11:50  12:40 Fedor LevkovichMaslyuk
(King's College, London)
Numerical Solution of the Spectral Problem and BFKL at
NexttoNexttoLeading Order in N=4 SYM
 12:40  14:00 Lunch
 The venue for the afternoon session is 24AA04.
 14:00  14:50 Yvonne Geyer (Oxford)
Loop Integrands for Scattering Amplitudes from the Riemann sphere
 14:50  15:40 Benoit Vicedo (Hertfordshire)
From Classical Rmatrices to Deformed Integrable Sigma Models
 15:40  16:10 Tea & Coffee in 39/40AA04
 16:10  17:00 Giulia Ferlito (Imperial College, London)
Coulomb Branch and Moduli Space of Instantons
Seminar Programme
 Nicholas Manton (DAMTP, University of Cambridge)
 Hyperbolic Vortices
 Abelian Higgs vortices on the hyperbolic plane are integrable, and explicitly known. Vortices on compact hyperbolic surfaces are trickier to construct
but some especially symmetric examples have now been found (work with Rafael Maldonado). The vortices have a clear, purely geometrical interpretation.
 Seminar 1 by Nicholas Manton
 Fedor LevkovichMaslyuk (King's College, University of London)
 Numerical Solution of the Spectral Problem and BFKL at
NexttoNexttoLeading Order in N=4 SYM
 I will present a simple numerical method for computing the spectrum of anomalous dimensions in planar N=4 super YangMills at finite coupling.
It is based on the Quantum Spectral Curve originating from integrability of the theory. The method allows us for the first time to obtain the exact spectrum of a nontrivial interacting QFT
in 4d with almost unlimited precision. I will show examples with 80 digits accuracy and also explore numerically the rich cut structure for twist operators with complexified spin.
Inspired by these numerical results, a new analytic method will be presented which gives a systematic weak coupling expansion for any operator. In particular it leads to a new analytic result
for the BFKL (BalitskyFadinKuraevLipatov) eigenvalue at nexttonexttoleading order.
 Seminar 2 by Fedor LevkovichMaslyuk
 Yvonne Geyer (University of Oxford)
 Loop Integrands for Scattering Amplitudes from the Riemann sphere
 Worldsheet formulations of quantum field theories have had wide ranging impact on the study of scattering amplitudes.
However, the mathematical framework becomes very challenging on the highergenus worldsheets required to describe loop effects. I will describe how, in such
worldsheet models based on the scattering equations, formulae on highergenus surfaces can be transformed to ones on the Riemann sphere.
My talk will focus on the remarkably simple new formulae emerging for superYangMills and gravity, and discuss the proposal for the allloop integrands.
 Seminar 3 by Yvonne Geyer
 Benoit Vicedo (University of Hertfordshire)
 From Classical Rmatrices to Deformed Integrable Sigma Models
 I will present a general framework for constructing integrable deformations of integrable sigma models
within the Hamiltonian formalism. It can be applied to a large class of nonultralocal models, including the AdS_{5} x S^{5} superstring,
and can be used to describe both 'YangBaxter' type and 'gauged WZW' type deformations which are currently the subject of intensive study.
The construction also makes it apparent why these two types of integrable deformations are related by PoissonLie Tduality.
 Giulia Ferlito (Imperial College, University of London)
 Coulomb Branch and Moduli Space of Instantons
 Moduli spaces of instantons are a very rich laboratory where physicists and mathematicians enjoy a fruitful interaction.
Some of the most exciting corners of this lab are unveiled using supersymmetric gauge theories. It has long been known, for example, that the Higgs branch of certain quiver gauge theories
with 8 supersymmetries is isomorphic to the moduli space of Ginstantons of charge k, where G is any of the classical groups.

In this talk I exploit another avenue, namely that the moduli space of k G instantons is isomorphic to the Coulomb branch of some particular quiver gauge theories in 3d.
I will show how we have learnt to calculate a partition function that counts gauge invariant operators on the chiral ring of the Coulomb branch, making use of some special objects called monopole operators.
The construction of this partition function allows us to study the moduli space of instantons for any group G, including nonsimply laced exceptionals.
 Seminar 5 by Giulia Ferlito
Practical Information
Local Venue and Travel Information
Trains. There is a fast train from London (Waterloo) to Guildford which takes about 35 minutes.
See the south west trains schedule and the Unversity of Surrey
travel information website for further train and bus information.
It is a 10 minute walk from the train station to the University of Surrey
(see this
university googlemap).
Exit the train station towards Guildford town centre. Turn left and walk along Walnut Tree Close for about 5 minutes. Take the first nontrivial left and walk along the bridge over the railway to reach the
university campus. Turn right and walk up the hill with the lake on your right. The AA building is next to Senate House at the top of this hill, with the LT building behind it.
Parking. The university has a limited number of visitors parking spots, which should be requested in advance by contacting Andrea Prinsloo (a.prinsloo@surrey.ac.uk),
and there is also a large public car park adjacent to the university campus (its location is shown on this
parking googlemap).
Venues. On arrival, please go to 39/40AA04 (on the 4th floor of the AA building) for coffee and snacks, which will be available from 10:00 onwards. The venues for the morning and afternoon sessions are
LTM (on the top floor of the LT building) and 24AA04. The AA and LT buildings are shown on this University of Surrey Stag Hill
campus map. Lunch will take place at Wates House in the WA building near the cathedral.
After the meeting, participants are most welcome to join us for drinks and/or dinner at the
Britannia
in Guildford town centre.
Please contact Andrea Prinsloo (a.prinsloo@surrey.ac.uk) in 29bAA04 or Alessandro Torrielli (a.torrielli@surrey.ac.uk) in 33AA04 for any further local information.
Funding Information

The meeting is partially supported by a London Mathematical Society Joint Research Groups grant.
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@kent.ac.uk) in advance if you would like to apply for support.
Participants
 List of Registered Participants
 Andrea Prinsloo (Surrey)
 Alessandro Torrielli (Surrey)
 Clare Dunning (Kent)
 Nicholas Manton (DAMTP)
 Fedor LevkovichMaslyuk (King's)
 Yvonne Geyer (Oxford)
 Benoit Vicedo (Hertfordshire)
 Giulia Ferlito (Imperial)
 Aindriu Conroy (Lancaster)
 Andrea Fontanella (Surrey)
 Charles Young (Hertfordshire)
 Antonio Pittelli (Surrey)
 Martyna Kostacinska (Queen Mary)
 Jock McOrist (Surrey)
 Joakim Strömvall (Surrey)
 Spyridon Talaganis (Lancaster)
 Riccardo Borsato (Imperial)
 Jan Gutowski (Surrey)
 Vincent Caudrelier (City)
 Thomas Winyard (Durham)
 Martin Wolf (Surrey)
 Steffen Krusch (Kent)
 Nicholas Iles (King's)
 Gerard Watts (King's)
 Paul Dempster (Surrey)
 Sara Pasquetti (Surrey)
 Amihay Hanany (Imperial)

Go to the Department of Mathematics, University of Surrey home page.