Events Calendar
May 14
14:00 - 15:00
Mathematical Physics & Integrable Systems seminar: Ines Aniceto (Jagiellonian University, Krakow, Poland)
SMSAS Mathematical Physics seminars
From asymptotics to exact results in 2d gravity: Painlevé I and large-N Matrix models


Matrix models offer non-perturbative descriptions of quantum gravity in simple settings, allowing us to study important dualities, the so-called large-N dualities, between the seemingly very different gauge and string theories. However, the large-N expansions of matrix models lead divergent series, only defined as  asymptotic series. Furthermore, by fine-tuning the couplings of the matrix model we obtain models of pure gravity coupled to minimal conformal field theories. The simplest of these "minimal models" is 2d gravity, and the perturbative expansion of its partition function is asymptotic and formally satisfies the Painlevé I equation.

These asymptotic properties are connected to the existence of exponentially small contributions not captured by a perturbative analysis. The theory of resurgence perfectly captures this perturbative/non-perturbative connection and its consequences. Moreover, it allows us to construct a full non-perturbative solution from perturbative data. In this talk, I will analyse essential role of resurgence theory, coupled to exponentially accurate numerical methods, to go beyond the perturbative results and obtain (analytically and numerically) non-perturbative data. I will exemplify how these techniques can be applied to to the particular case of Painlevé I and the quartic matrix model.


Sibson Building (SibSR3)
United Kingdom


Open to All interested persons,

Contact: Dr Pavlos Xenitidis
School of Mathematics, Statistics and Actuarial Science


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Last Updated: 10/01/2012