Quadrangular Sets in Projective LIne and in Moebius Space and Geometric Interpretation of the Non-Commutative Discrete Schwarzian Kadomtsev-Petviashvili Equation (Doliwa et al.).- Complexity and integrability in 4D bi-rational maps with two invariants (Gubbiotti et al.).- A non-linear relation for certain hypergeometric functions(Schmalz et al.).- An algebraically stable variety for a four-dimensional dynamical system reduced from the lattice super-KdV equation (Carstea et al.).- On the Lattice Potential KP Equation(Cao et al.).- Opers for higher states of the quantum Boussinesq model (Masoero et al.).- Nonsingular Rational Solutions to Integrable models (Gegenhasi et al.).- Stokes phenomenon arising in the confluence of the Gauss hypergeometric equation (Horrobin et al.).- Periodic trajectories of ellipsoidal billiards in the 3-dimensional Minkowski space (Dragovi´c et al.).- Analogues of Kahan’s method for higher order equations of higher degree (Hone et al.).- On some explicit representations of the elliptic Painlev´e equation (Noumi et al.).

This proceedings volume gathers together selected works from the 2018 “Asymptotic, Algebraic and Geometric Aspects of Integrable Systems” workshop that was held at TSIMF Yau Mathematical Sciences Center in Hainan China, honoring Nalini Joshi on her 60th birthday. The papers cover recent advances in asymptotic, algebraic and geometric methods in the study of discrete integrable systems.The workshop brought together experts from fields such as asymptotic analysis, representation theory and geometry, creating a platform to exchange current methods, results and novel ideas.This volume's articles reflect these exchanges and can be of special interest to a diverse group of researchers and graduate students interested in learning about current results, new approaches and trends in mathematical physics, in particular those relevant to discrete integrable systems.

Covers recent advances in asymptotic, algebraic and geometric methods applied to discrete integrable systems Gathers together works from fields such as asymptotic analysis, representation theory and geometry Showcases current results, new approaches and trends in the field