Overview

The program “New Trends in Integrable Models” to be held at the InternationalInstitute of Physics in Natal, is planned to review the recent developments in the field of integrability, attempt to develop a new approaches to the long-standingfundamental problems of mathematical physics and discuss future applications in various modern branches of theoretical physics, such as string theory, condensed matter physics, statistical physics and quantum information theory. Early attempts to resolve the challenging problems of quantum gravity andconfinement in the (non-critical) string theory approach produced a great deal of attention to low-dimensional integrable models and/or (supersymmetric) nonabelian gauge theories in various dimensions. A particularly important aspect of integrability of those models is the access to exact information about their strong coupling regime. Consequently, the quest for achieving a tractable description of strongly coupled phenomena was marked with such milestones as the random matrix theory approach to non-critical strings, solutions of 2D and 3D gravity theories, quantization of Chern-Simons theories and relation with CFT’s and knots, solution of the N = 2 supersymmetric Yang-Mills theory, application of integrability to test the AdS/CFT correspondence and so on.

Last decade has confirmed the defining role of integrability in the developmentof various fields of mathematical physics. It has been a period of productive activity in investigations of a range of problems including 2D integrable models (form-factor problem, applications to condensed matter physics), 3D integrable models (tetrahedron equations, Kitaev model with a great potential of possible application to quantum computing and to construction of new matrix models, which are capable to extend non-critical string theories beyond c = 1), low dimensional dualities (AGT correspondence, new integrable structures) and Chern-Simons/knot theories (Khovanov-Rozansky calculus, refined invariants, possible applications to quantum gravity and quantum information theory). The aim of the program in Natal is to promote further developments in these investigations.

Program of the event

The program is roughly divided into the following four interrelated subjects: 2Dand 3D integrable models, non-critical strings and matrix models, integrability in AGT conjecture and integrability in knot theory. The activities planned in the scope of the event are intended to create a stimulative atmosphere for the discussion of recent developments in those fields as well to explore theirconnections and  possible applications.

The total duration of the program will be 15 weeks. Slow weekly activities will consist of seminars, lectures and open discussions. Each of the four main subjects of the program will unfold consecutively culminating in an intense oneor two-week workshop, one for each subject. The tentative schedule of the program is as follows:

Local Organizing Committee

Dmitry Melnikov, IIP-UFRN

Rodrigo Pereira, IIP-UFRN

Jacopo Viti, UFRN

Activities

• Aug’15 - Sep’16, 2016: Two and three dimensional integrable models
• Aug’29 - Sep’30, 2016: Non-critical strings and matrix models: integrable structures
• Sep’26 - Oct’28, 2016: AGT conjecture, CFT and Chern-Simons theories
• Oct’24 - Nov’25, 2016: Knots invariants and quantum integrable systems

Workshops

• Aug'24 - Sep'02: "Boundary Degrees of Freedom and Thermodynamics of Integrable Models" (satellite workshop organized by Andreas Kluemper, Vladimir Korepin and Giuliano Ribeiro)
• Sep'05 - Sep'09:  "Non-critical strings and matrix models"
• Oct'23 - Oct'28:    "AGT duality and beyond"
• Nov'21 - Nov'25:   "Quantum integrable systems"

Schools

• Oct'17 - Oct'21: mini-school on conformal field theories and AGT correspondence
  

Main parts of the program are intended to overlap to allow participants in related areas to share their experience and ideas.

Location

The city of Natal is located at the north-western part of Brazil, closest to Africa and Europe. Home of sandy dunes and magnificent beaches, it is an attractive destination for South American and, more recently, European tourists. We recommend to visit the Wikipedia page of Natal for general information about the city.

The event is expected to take place in the new building of the International Institute of Physics on the campus of the Federal University of Rio Grande do Norte (UFRN) in Natal. The participants will enjoy the newly inaugurated facilities of the IIP, including auditorium, seminar rooms, discussion and office spaces.

Accommodation

We expect the participants to select their preferred accommodation type. Forthose participants staying for a short period (up to two weeks) the reasonable choice of the accommodation would be a room in the hotel. In the case of a longer stay, it is advisable to rent an apartment. The recommended location for the accommodation of the IIP guests is Ponta Negra, the coastal district of Natal. Both hotel and apartment reservations can be made through the organizing committee. During the program workshops there expected to be an organized transportation to the IIP.