The Virasoro minimal string by Scott Collier, Lorenz Eberhardt, Beatrix Muehlmann, Victor A. Rodriguez

“…The main observables of the Virasoro minimal string are quantum analogues of the Weil-Petersson volumes, which are computed as absolutely convergent integrals of worldsheet CFT correlators over the moduli space of Riemann surfaces. By exploiting a relation of the Virasoro minimal string to three-dimensional gravity and intersection theory on the moduli space of Riemann surfaces, we are able to give a direct derivation of the duality. …”
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On the equivalence between SRS and PCO formulations of superstring perturbation theory by Charles Wang, Xi Yin

“…Abstract We establish the equivalence between two formulations of superstring perturbation theory, one based on integration over the supermoduli space of super Riemann surfaces (SRS), the other based on integration over the bosonic moduli space with insertions of picture changing operators (PCO) on the worldsheet and the vertical integration prescription, by showing how the latter arises from a specific construction of the supermoduli integration contour.…”
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Cyclic products of Szegö kernels and spin structure sums. Part I. Hyper-elliptic formulation by Eric D’Hoker, Martijn Hidding, Oliver Schlotterer

“…In this paper we discover that, for Riemann surfaces of genus two and even spin structures, a collection of novel identities leads to a dramatic simplification of the spin structure sum. …”
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$\alpha$-Differentiable functions in complex plane by Ronak Pashaei, Amir Pishkoo, Mohammad Sadegh Asgari, Davood Ebrahimi Bagha

“…Then, we discuss about two complex conformable differential equations and solutions with their Riemann surfaces. For some values of order of derivative, $\alpha$, we compare their plots.…”
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Gravitational action for a massive Majorana fermion in 2d quantum gravity by Corinne de Lacroix, Harold Erbin, Vincent Lahoche

“…Abstract We compute the gravitational action of a free massive Majorana fermion coupled to two-dimensional gravity on compact Riemann surfaces of arbitrary genus. The structure is similar to the case of the massive scalar. …”
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Topological invariants and Holomorphic Mappings by Greene, Robert E., Kim, Kang-Tae, Shcherbina, Nikolay V.

“…Invariants for Riemann surfaces covered by the disc and for hyperbolic manifolds in general involving minimizing the measure of the image over the homotopy and homology classes of closed curves and maps of the $k$-sphere into the manifold are investigated. …”
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Ground state wavefunctions of elliptic relativistic integrable Hamiltonians by Belal Nazzal, Anton Nedelin, Shlomo S. Razamat

“…The models we discuss appear in computations of superconformal indices of four-dimensional theories obtained by compactifying six-dimensional models on Riemann surfaces. These include, among others, the Ruijsenaars-Schneider model and the van Diejen model. …”
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Gravitational action for a massive Majorana fermion in 2d quantum gravity by de Lacroix, Corinne, Erbin, Harold, Lahoche, Vincent

“…We compute the gravitational action of a free massive Majorana fermion coupled to two-dimensional gravity on compact Riemann surfaces of arbitrary genus. The structure is similar to the case of the massive scalar. …”
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AdS2 holography and effective QFT by Sangmin Choi, Finn Larsen

“…It also puts the non-compact AdS2 topology on the same footing as compact Riemann surfaces.…”
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Ricci solitons and geometric analysis by Wink, M

“…<p>This thesis studies Ricci solitons of cohomogeneity one and uniform Poincaré inequalities for differentials on Riemann surfaces. </p> <p>In the two summands case, which assumes that the isotropy representation of the principal orbit consists of two inequivalent Ad-invariant irreducible summands, complete steady and expanding Ricci solitons have been detected numerically by Buzano-Dancer-Gallaugher-Wang. …”

Gas of Baby Universes in JT Gravity and Matrix Models by Irina Aref’eva, Igor Volovich

“…It has been shown recently by Saad, Shenker and Stanford that the genus expansion of a certain matrix integral generates partition functions of Jackiw-Teitelboim (JT) quantum gravity on Riemann surfaces of arbitrary genus with any fixed number of boundaries. …”
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Liouville theory and the Weil-Petersson geometry of moduli space by Sarah M. Harrison, Alexander Maloney, Tokiro Numasawa

“…Abstract Liouville theory describes the dynamics of surfaces with constant negative curvature and can be used to study the Weil-Petersson geometry of the moduli space of Riemann surfaces. This leads to an efficient algorithm to compute the Weil-Petersson metric to arbitrary accuracy using Zamolodchikov’s recursion relation for conformal blocks. …”
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Topological strings on compact Calabi-Yau's by Hollands, L

“…Some steps towards solving topological string amplitudes on Calabi-Yau spaces have been taken lately: all-genus amplitudes have been computed for non-compact toric Calabi-Yau threefolds, local Riemann surfaces and K3-fibrations, while progression has been made for the Fermat quintic threefold. …”

On the mathematical contributions of Giorgio Valli by James Eells

“…In quite a new and different direction — in collaboration with Stefano Trapani: An existence theorem for 1-harmonic diffeomorphisms between compact Riemann surfaces. That has broken new ground-first steps along a path with much promise.…”
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Wilson loops and wormholes by Panos Betzios, Olga Papadoulaki

“…Such observables lead to a generalisation and refinement of the characterisation in [1] based on the compressibility of cycles and the pinching limit of higher genus Riemann surfaces, since they carry information about the dynamics and phase structure of the dual gauge theory of an arbitrary dimensionality. …”
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Some boundedness properties of solutions to the Vafa–Witten equations on closed 4-manifolds by Tanaka, Y

“…They are similar to Hitchin’s equations over compact Riemann surfaces, and as part of the resemblance, there is no L2-bound on the curvature without an L2-bound on the extra fields. …”

Connections between reflected entropies and hyperbolic string vertices by Peng Wang, Houwen Wu, Haitang Yang

“…We show that the reflected surfaces, which are bulk duals of the reflected entropies, share the same Riemann surfaces with the hyperbolic string vertices. This observation enables us to build quantitative relations between the reflected entropies and hyperbolic string vertices. …”
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Hyperbolic three-string vertex by Fırat, Atakan H.

“…We note the relevance of our construction to the calculations of the higher-order string vertices using the pants decomposition of hyperbolic Riemann surfaces.…”
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Spectral Fukaya Categories for Liouville Manifolds by Large, Tim

“…We then develop a basic TQFT formalism, in the stable homotopy category, for producing operations on these Floer homotopy types from families of punctured Riemann surfaces. As a byproduct, we can generalize many familiar algebraic constructions in traditional Floer homology over the integers to Floer homotopy theory: among them symplectic cohomology, wrapped Floer cohomology, and the Donaldson-Fukaya category.…”
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Infinite loop spaces from operads with homological stability by Basterra, M, Bobkova, I, Ponto, K, Tillmann, U, Yeakel, S

“…Motivated by the operad built from moduli spaces of Riemann surfaces, we consider a general class of operads in the category of spaces that satisfy certain homological stability conditions. …”