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1. Liouville properties

   https://doi.org/10.4310/ICCM.2019.v7.n1.a10  

   Colding, Tobias H.; Minicozzi, William P. (January 2019, Notices of the International Congress of Chinese Mathematicians)

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2. Liouville dynamical percolation

   https://doi.org/10.1007/s00440-021-01057-1  

   Garban, Christophe; Holden, Nina; Sepúlveda, Avelio; Sun, Xin (August 2021, Probability Theory and Related Fields)
3. Liouville closed HT-fields

   Kaplan, Elliot (April 2023, Journal of algebra)

   Let T be a complete, model complete o-minimal theory extending the theory of real closed ordered fields. An HT-field is a model K of T equipped with a T-derivation ∂ such that the underlying ordered differential field of (K,∂) is an H-field. We study HT-fields and their extensions. Our main result is that if T is power bounded, then every HT-field K has either exactly one or exactly two minimal Liouville closed HT-field extensions up to K-isomorphism. The assumption of power boundedness can be relaxed to allow for certain exponential cases, such as T = Th(Ran,exp). 

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4. Yang-Mills as a Liouville theory

   https://doi.org/10.1016/j.physletb.2023.138229  

   Stieberger, Stephan; Taylor, Tomasz R; Zhu, Bin (November 2023, Physics Letters B)

   We propose a description of the gluon scattering amplitudes as the inverse Mellin transforms of the conformal correlators of light operators in two-dimensional Liouville theory tensored with WZW-like chiral currents on the celestial sphere. The dimensions of operators are Mellin dual to gluon light cone energies while their positions are determined by the gluon momentum directions. Tree-level approximation in Yang-Mills theory corresponds to the semiclassical limit of Liouville theory. By comparing subleading corrections, we find b^2=(8π^2)^{−1}b_0g^2(M), where b is the Liouville coupling constant, g(M) is the Yang Mills coupling at the renormalization scale M and b_0 is the one-loop coefficient of the Yang-Mills beta function. 

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5. Baxter permuton and Liouville quantum gravity

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   Borga, Jacopo; Holden, Nina; Sun, Xin; Yu, Pu (April 2023, Probability Theory and Related Fields)