Elliptic integrable systems, special functions and quantum field theory

16 Jun 2019, 09:00 → 20 Jun 2019, 18:00 Europe/Stockholm

FB42, AlbaNova (Nordita, Stockholm)

Edwin Langmann, Hjalmar Rosengren, Martin Hallnäs

Venue

Nordita, Stockholm, Sweden

Scope

In recent years there have been exciting new developments at the interface between elliptic integrable systems, special functions and quantum field theory. The aim of this workshop is to obtain a better understanding of the emerging links between these topics and to help bring out further unexpected connections in the future. This will be achieved by bringing together researchers from diverse areas in mathematics and physics, for a week of lectures and informal discussions. The workshop is the continuation of a series (Kyoto 2004, Bonn 2008, Leiden 2013, Vienna 2017). It is a satellite meeting of String Math 2019, which takes place in Uppsala 1-5 July. The main themes of the meeting are:

• Elliptic integrable systems
• Elliptic hypergeometric functions
• Elliptic and classical Painlevé equations
• New special functions emerging from quantum field theory

Programme with abstracts

See the linked pdf file at the bottom of this page.

Invited speakers

Oleg Chalykh, Leeds University Rinat Kashaev, University of Geneva Oleg Lisovyy, LMPT, Tours Marta Mazzocco, University of Birmingham Nobutaka Nakazono, Tokyo University of Agriculture and Technology Eric Rains, Caltech Simon Ruijsenaars, Leeds University Jun'ichi Shiraishi, University of Tokyo Vyacheslav Spiridonov, JINR, Dubna and NRU HSE, Moscow Alexander Varchenko, University of North Carolina

Confirmed participants

Arash Ardehali, Uppsala University Carlos Arreche, University of Texas at Dallas Farrokh Atai, Kobe University Bjorn Berntson, KTH, Stockholm Oleg Chalykh, University of Leeds Dmitry Chernyak, ENS, Paris László Fehér, University of Szeged Masayuki Fukuda, University of Tokyo Ilmar Gahramanov, Mimar Sinan University, Istanbul Tamás Görbe, University of Leeds Christian Hagendorf, Université Catholique de Louvain Martin Hallnäs, Chalmers University, Gothenburg Linnea Hietala, University of Gothenburg Masahiko Ito, University of the Ryukyus Shahriyar Jafarzade, Mimar Sinan University, Istanbul Rinat Kashaev, University of Geneva Makoto Katori, Chuo University, Tokyo Andrew Kels, SISSA, Trieste Rob Klabbers, Humboldt Universität zu Berlin Hitoshi Konno, Tokyo University of Marine Science and Technology Tom Koornwinder, University of Amsterdam Jules Lamers, University of Melbourne Edwin Langmann, KTH, Stockholm Oleg Lisovyy, LMPT, Tours Rebecca Lodin, Uppsala University Yongchao Lu, Uppsala University Marta Mazzocco, University of Birmingham Kohei Motegi, Tokyo University of Marine Science and Technology Nobutaka Nakazono, Tokyo University of Agriculture and Technology Yury Neretin, ITEP, Moscow and University of Vienna Masatoshi Noumi, Kobe University Matej Penciak, University of Illinois Eric Rains, Caltech Hjalmar Rosengren, Chalmers University, Gothenburg Daria Rudneva, NRU HSE, Moscow Simon Ruijsenaars, University of Leeds Paul Ryan, Trinity College, Dublin Matteo Sacchi, University of Milano-Bicocca Michael Schlosser, University of Vienna Samil Shakirov, Uppsala University Jun'ichi Shiraishi, University of Tokyo Vyacheslav Spiridonov, JINR, Dubna and NRU HSE, Moscow Alex Takeda, UC Berkeley Takashi Takebe, NRU HSE, Moscow Alexander Varchenko, University of North Carolina Vidya Venkateswaran, Center for Communications Research, Princeton Dmytro Volin, Nordita, Stockholm Ole Warnaar, University of Queensland Tobias Zingg, Nordita, Stockholm

Scientific committee

Edwin Langmann, KTH, Stockholm Masatoshi Noumi, Kobe University Hjalmar Rosengren, Chalmers University, Gothenburg Simon Ruijsenaars, University of Leeds Vyacheslav Spiridonov, JINR, Dubna and NRU HSE, Moscow Ole Warnaar, University of Queensland

Organizing committee

Martin Hallnäs, Chalmers University, Gothenburg Edwin Langmann, KTH, Stockholm Hjalmar Rosengren, Chalmers University, Gothenburg

Sponsored by:

Programme nordita-schedule.pdf

Sunday, 16 June

09:30 → 10:30 Registration and Coffee

10:30 → 11:15 The endless beta integrals

Speaker: Vyacheslav Spiridonov

11:25 → 12:10 Painlevé functions, Fredholm determinants and combinatorics

Speaker: Oleg Lisovyy

12:10 → 14:00 Lunch

14:00 → 14:30 Elliptic hypergeometric integrals and black holes

Speaker: Arash Ardehali

14:30 → 15:00 Solving q-Virasoro constraints

Speaker: Rebecca Lodin

15:00 → 15:30 Coffee

15:30 → 16:00 The q-deformed Haldane-Shastry spin chain: from the affine Hecke algebra, via 'freezing', to exact eigenvectors

Speaker: Jules Lamers

16:00 → 16:30 Rationalizing Inozemtsev's elliptic spin chain with the Legendre relation

Speaker: Rob Klabbers

Monday, 17 June

09:00 → 09:45 Quantum dilogarithms over LCA groups

Speaker: Rinat Kashaev

09:45 → 10:15 Coffee

10:15 → 11:00 Consistency around a cuboctahedron

Speaker: Nobutaka Nakazono

11:10 → 11:40 Discrete integrability from hypergeometric integrals

Speaker: Andrew Kels

11:40 → 12:10 The Bailey lemma and 3d mirror symmetry

Speaker: Ilmar Gahramanov

12:10 → 14:00 Lunch

14:00 → 14:30 An analog of the Dougall formula and of the de Branges-Wilson integral

Speaker: Yury Neretin

14:30 → 15:30 Coffee and poster session

Masayuki Fukuda: Macdonald functions from topological vertex and its elliptic analogue Daria Rudneva: TBA Paul Ryan: Separated variables + factorized wave functions in gl(n) spin chains Matteo Sacchi: From 3d dualities to 2d free field correlators and back

15:30 → 16:00 Elliptic extension of Gustafson's q-integral of type G2

Speaker: Masahiko Ito

16:00 → 16:30 On some theta-function conjectures

Speaker: Ole Warnaar

Tuesday, 18 June

09:00 → 09:45 Painlevé-Calogero correspondence: The elliptic 8-parameter level

Speaker: Simon Ruijsenaars

09:45 → 10:15 Coffee

10:15 → 11:00 Elliptic double affine Hecke algebras

Speaker: Eric Rains

11:10 → 11:40 Differential transcendence of elliptic hypergeometric functions through Galois theory

Speaker: Carlos Arreche

11:40 → 12:10 Double elliptic generalization of Ruijsenaars-Schneider model

Speaker: Shamil Shakirov

12:10 → 14:00 Lunch

14:00 → 14:30 Elliptic quantum (toroidal) algebras and their representations

Speaker: Hitoshi Konno

14:30 → 15:00 Izergin–Korepin method to elliptic identities

Speaker: Kohei Motegi

15:00 → 15:30 Coffee

15:30 → 16:00 Source identities for relativistic models of Calogero–Moser–Sutherland type

Speaker: Farrokh Atai

16:00 → 16:30 Second quantization of elliptic Calogero-Sutherland models

Speaker: Bjorn Berntson

Wednesday, 19 June

09:00 → 09:45 From Dunkl and Cherednik operators to Lax pairs

Speaker: Oleg Chalykh

09:45 → 10:15 Coffee

10:15 → 11:00 Affine screening operators, affine Laumon spaces, and conjectures concerning non-stationary Ruijsenaars functions

Speaker: Jun’ichi Shiraishi

11:10 → 11:40 Formal eigenfunctions for the elliptic Ruijsenaars difference operators

Speaker: Masatoshi Noumi

11:40 → 12:10 Perturbative solution of the elliptic Ruijsenaars model

Speaker: Edwin Langmann

12:10 → 14:00 Lunch

14:00 → 14:30 Two-dimensional elliptic determinantal point processes and related systems

Speaker: Makoto Katori

14:30 → 15:00 Soliton scattering in the hyperbolic relativistic Calogero–Moser system

Speaker: Martin Hallnäs

15:00 → 15:30 Coffee

18:30 → 22:00 Boat tour and conference dinner

Thursday, 20 June

09:00 → 09:45 Quantum uniformisation and Calabi–Yau algebras

Speaker: Marta Mazzocco

09:45 → 10:15 Coffee

10:15 → 11:00 Dynamical elliptic Bethe algebra, KZB eigenfunctions, and theta-polynomials

Speaker: Alexander Varchenko

11:10 → 11:40 Elliptic Stirling and Lah numbers

Speaker: Michael Schlosser

11:40 → 12:10 Q-operators for higher spin eight vertex models with a rational anisotropy parameter

Speaker: Takashi Takebe

12:10 → 14:00 Lunch

14:00 → 14:30 A combinatorial description of certain polynomials related to the XYZ spin chain

Speaker: Linnea Hietala

14:30 → 15:00 Correlations for the XYZ spin chain and Painlevé VI

Speaker: Hjalmar Rosengren

15:00 → 15:30 Coffee

15:30 → 16:15 Open problem session, concluding discussion