Hyperbolic string vertices by Kevin Costello, Barton Zwiebach

“…Abstract The string vertices of closed string field theory are subsets of the moduli spaces of punctured Riemann surfaces that satisfy a geometric version of the Batalin-Vilkovisky master equation. …”
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E-Polynomials of Generic $\mathbf {\operatorname {\mathrm {GL}}_n\rtimes \!<\!\sigma \!>\!}~$ -Character Varieties: Branched Case by Cheng Shu

“…For any branched double covering of compact Riemann surfaces, we consider the associated character varieties that are unitary in the global sense, which we call $\operatorname {\mathrm {GL}}_n\rtimes \!…”
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Hyperbolic string vertices by Costello, Kevin, Zwiebach, Barton

“…Abstract The string vertices of closed string field theory are subsets of the moduli spaces of punctured Riemann surfaces that satisfy a geometric version of the Batalin-Vilkovisky master equation. …”
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Hyperbolic string vertices by Costello, Kevin, Zwiebach, Barton

“…Abstract The string vertices of closed string field theory are subsets of the moduli spaces of punctured Riemann surfaces that satisfy a geometric version of the Batalin-Vilkovisky master equation. …”
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On the singular sets of solutions to the Kapustin–Witten equations and the Vafa–Witten ones on compact Kähler surfaces by Tanaka, Y

“…These equations can be seen as real four-dimensional analogues of the Hitchin equations on Riemann surfaces, and one of common obstacles to be overcome is a certain unboundedness of solutions to these equations, especially of the “Higgs fields”. …”

Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz by Hausel, T, Rodriguez-Villegas, F

“…We calculate the E-polynomials of certain twisted GL(n,ℂ)-character varieties Mn of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type GL(n, q) and a theorem proved in the appendix by N. …”

Mixed Hodge polynomials of character varieties by Hausel, T, Rodriguez-Villegas, F

“…We calculate the E-polynomials of certain twisted GL(n,C)-character varieties M_n of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type GL(n,F_q) and a theorem proved in the appendix by N. …”

Manipulating spectral topology and exceptional points by nonlinearity in non-Hermitian polariton systems by Jan Wingenbach, Stefan Schumacher, Xuekai Ma

“…Not only do we find that EPs can be intentionally shifted in parameter space by the saturable gain, but we also observe intriguing rotations and intersections of Riemann surfaces and find nonlinearity-enhanced sensing capabilities. …”
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Trinions for the 3d compactification of the 5d rank 1 E N f + 1 $$ {E}_{N_{f+1}} $$ SCFTs by Matteo Sacchi, Orr Sela, Gabi Zafrir

“…In this paper, we study compactifications of the rank 1 5d Seiberg E N f + 1 $$ {E}_{N_{f+1}} $$ SCFTs to 3d on Riemann surfaces of genus g > 1. We rely on the recent progress in the study of compactifications of 6d SCFTs to 4d and torus compactifications of 5d SCFTs to conjecture 3d N $$ \mathcal{N} $$ = 2 theories corresponding to the reduction of said 5d SCFTs on three punctured spheres. …”
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Quantum Jackiw-Teitelboim gravity, Selberg trace formula, and random matrix theory by Antonio M. García-García, Salomón Zacarías

“…We show that the partition function of quantum Jackiw-Teitelboim (JT) gravity, including topological fluctuations, is equivalent to the partition function of a Maass-Laplace operator of large (imaginary) weight acting on noncompact, infinite-area, hyperbolic Riemann surfaces of arbitrary genus. The resulting spectrum of this open quantum system for a fixed genus is semiclassically exact and given by a regularized Selberg trace formula; namely, it is expressed as a sum over the lengths of primitive periodic orbits of these hyperbolic surfaces. …”
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Counting surface-kernel epimorphisms from a co-compact Fuchsian group to a cyclic group with motivations from string theory and QFT by Khodakhast Bibak, Bruce M. Kapron, Venkatesh Srinivasan

“…As a consequence, we obtain an ‘equivalent’ form of Harvey's famous theorem on the cyclic groups of automorphisms of compact Riemann surfaces. Our main tool is an explicit formula for the number of solutions of restricted linear congruence recently proved by Bibak et al. using properties of Ramanujan sums and of the finite Fourier transform of arithmetic functions.…”
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Solving 3d gravity with Virasoro TQFT by Scott Collier, Lorenz Eberhardt, Mengyang Zhang

“…We propose a precise reformulation of 3d quantum gravity with negative cosmological constant in terms of a topological quantum field theory based on the quantization of the Teichmüller space of Riemann surfaces that we refer to as "Virasoro TQFT". This TQFT is similar, but importantly not equivalent, to SL(2, $\mathbb{R}$) Chern-Simons theory. …”
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Non-analytic behavior of the Loschmidt echo in XXZ spin chains: Exact results by Piroli, L, Pozsgay, B, Vernier, E

“…Our exact results are expressed in terms of “excited-state” thermodynamic Bethe ansatz equations, whose solutions involve non-trivial Riemann surfaces. By evaluating our formulas, we provide explicit numerical results for the quench from the Néel state, and we determine the first few non-analytic points.…”

Entanglement and topology in RG flows across dimensions: caps, bridges and corners by Evan Deddo, Leopoldo A. Pando Zayas, Christoph F. Uhlemann

“…As concrete examples we discuss twisted compactifications of 4d N $$ \mathcal{N} $$ = 4 SYM on T 2, S 2 and hyperbolic Riemann surfaces.…”
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Entanglement and topology in RG flows across dimensions: caps, bridges and corners by Deddo, E, Pando Zayas, LA, Uhlemann, CF

“…As concrete examples we discuss twisted compactifications of 4d <em>N</em> = 4 SYM on T², S² and hyperbolic Riemann surfaces.</p>…”

Dynamics of Ion Channels via Non-Hermitian Quantum Mechanics by Tobias Gulden, Alex Kamenev

“…Non-Hermiticity elevates WKB action integrals from the real line to closed cycles on a complex Riemann surfaces where direct calculations are not attainable. …”
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Bordered Heegaard Floer Homology and four-manifolds with corners by Brown, Tova Helen Fell

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Log-lightning computation of capacity and Green's function by Baddoo, P, Trefethen, LN

“…It also extends to "domains of negative measure" and other Riemann surfaces.…”

Supersyrnmetric AdS(5) solutions of M-theory by Gauntlett, J, Martelli, D, Sparks, J, Waldram, D

“…We find a large family of new explicit regular solutions where M6 is a compact, complex manifold which is topologically a 2-sphere bundle over a four-dimensional base, where the latter is either (i) Kähler-Einstein with positive curvature, or (ii) a product of two constant-curvature Riemann surfaces. After dimensional reduction and T-duality, some solutions in the second class are related to a new family of Sasaki-Einstein spaces which includes T1,1/ℤ2. …”

Weierstrass points on modular curves X0(N) fixed by the Atkin–Lehner involutions by Mustafa Bojakli, Hasan Sankari

“…For example, in algebraic number theory, they have been used by Schwartz and Hurwitz to determine the group structure of the automorphism groups of compact Riemann surfaces of genus g ≥ 2. Whereas in algebraic geometric coding theory, if one knows a Weierstrass nongap sequence of a Weierstrass point, then one is able to estimate parameters of codes in a concrete way. …”
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