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Abstract
| Asymptotic analysis has been a powerful and versatile technique within mathematics and physics for over a century, but recent breakthroughs have led to radical changes in the mathematical understanding of these methods. By exploiting the idea of ‘resurgence’, researchers have been able to extend asymptotic analysis beyond the boundaries of the traditional asymptotic analysis of Poincaré. This is an exciting area where with significant current transfer of technology between mathematical analysts, applied mathematicians and theoretical physics. This new mathematical landscape was the focus of the 2022 Newton Institute Programme ‘Applicable resurgent asymptotics: towards a universal theory’. Much of the work contained in this issue was conceptualised or developed during this programme. This focus issue collects recent results on resurgent asymptotics, and highlights ongoing advances in the study of Painlevé equations and quantum field theory. The interplay between these two subjects has seen considerable progress in recent years, with major advances such as the discovery of the so-called ‘Kyiv formula’ [6]. This formula relates tau-functions of the Painlevé equations to partition functions supersymmetric quantum field theories, or equivalently, c = 1 Liouville conformal blocks. This new connection unleashed a wave of enthusiasm, as it opens up exciting avenues for reaching new insights and making significant discoveries in both fields. This is just one example of the many recent results whose impact spans across both applied mathematics and theoretical physics. The aim of this focus issue is to present other new results from across mathematics and physics that can generate such enthusiasm, and open up their own new avenues of further study |