$\mathcal{N}$ = 1 supersymmetric indices and the four-dimensional A-model by Closset, C, Kim, H, Willett, B

“…<p>We compute the supersymmetric partition function of $\mathcal{N}$ = 1 supersymmetric gauge theories with an R-symmetry on $\mathcal{M}$₄ ≅ $\mathcal{M}$_<em>g,p</em> × <em>S</em>¹, a principal elliptic fiber bundle of degree <em>p</em> over a genus-<em>g</em> Riemann surface, Σ_<em>g</em> . Equivalently, we compute the generalized supersymmetric index <em>I</em>_{$\mathcal{M}$_<em>g,p</em>} , with the supersymmetric three-manifold $\mathcal{M}$_<em>g,p</em> as the spatial slice. …”

The ASD equations in split signature and hypersymplectic geometry by Roeser, MK

“…</p> <p>Hitchin's harmonic map equations are the split signature analogue of the self-duality equations on a Riemann surface, in which case it is known that there is a smooth hyperkähler moduli space. …”

Symplectic quotients of unstable Morse strata for normsquares of moment maps by Kirwan, F

“…There is an analogous infinite-dimensional picture for the Yang&#x2013;Mills functional over a Riemann surface with strata determined by Harder&#x2013;Narasimhan type. …”

A Method of the Riemann–Hilbert Problem for Zhang’s Conjecture 2 in a Ferromagnetic 3D Ising Model: Topological Phases by Zhidong Zhang, Osamu Suzuki

“…Following the procedures of realizing the representation of knots on the Riemann surface and formulating the Riemann–Hilbert problem in our preceding paper [O. …”
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Consistent truncations to 3-dimensional supergravity by Michele Galli, Emanuel Malek

“…We also show how to construct consistent truncations of IIB supergravity on S 5 fibred over a Riemann surface. These result in 3-dimensional N $$ \mathcal{N} $$ = 4 gauged supergravities with scalar manifold M = SO 6 4 SO 6 × SO 4 × SU 2 1 S U 1 × U 2 $$ \mathcal{M}=\frac{\mathrm{S}\mathrm{O}\left(6,4\right)}{\mathrm{S}\mathrm{O}(6)\times \mathrm{SO}(4)}\times \frac{\mathrm{S}\mathrm{U}\left(2,1\right)}{\mathrm{S}\left(\mathrm{U}(1)\times \mathrm{U}(2)\right)} $$ with a ISO(3) × U(1)4 gauging and for hyperboloidal Riemann surfaces contain N $$ \mathcal{N} $$ = (2, 2) AdS3 vacua.…”
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Analysis of contact Cauchy–Riemann maps III: Energy, bubbling and Fredholm theory by Yong-Geun Oh

“…The asymptotic limit of a contact instanton is a ‘spiraling’ instanton along a ‘rotating’ Reeb orbit near each puncture on a punctured Riemann surface [Formula: see text]. Each limiting Reeb orbit carries a ‘charge’ arising from the integral of [Formula: see text]. …”
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Topological semimetals with helicoid surface states by Fang, Chen, Lu, Ling, Liu, Junwei, Fu, Liang

“…Each helicoid or multi-helicoid is shown to be the non-compact Riemann surface representing a multi-valued holomorphic function (generating function). …”
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Isotropic to anisotropic transition in a fractional quantum Hall state by Mulligan, Michael, Nayak, Chetan, Kachru, Shamit

“…Nevertheless, there are chiral edge modes when the theory is placed on a space with boundary and a nontrivial ground-state degeneracy kg when it is placed on a finite-size Riemann surface of genus g. The coefficient of ei2 is the only relevant coupling; it tunes the system through a quantum phase transition between an isotropic fractional quantum Hall state and an anisotropic fractional quantum Hall state. …”
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G2 geometry and integrable systems by Baraglia, D

“…We study the Hitchin component in the space of representations of the fundamental group of a Riemann surface into a split real Lie group in the rank 2 case. …”

Coherent-resonance enhancement of sensing at the exceptional points by Chen, Jingming, Xie, Qinnan, Zhang, Jingjing, Li, Zhuo, Cui, Tie Jun, Luo, Yu

“…The branch point singularities in the Riemann surface of the parameter space are known as the exceptional points (EPs), at which two or more eigenvalues and their associated eigenvectors simultaneously coalesce. …”
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Prime Geodesic Theorems for Compact Locally Symmetric Spaces of Real Rank One by Dženan Gušić

“…First, following classical Randol’s appraoch in the compact Riemann surface case, we improve the error term in the corresponding result. …”
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Higgs bundles, Lagrangians and mirror symmetry by Branco, L

“…<p>Let Σ be a compact Riemann surface of genus <em>g</em> ≥ 2. This thesis is dedicated to the study of certain loci of the Higgs bundle moduli space. …”

Methods in wave propagation and scattering by Braunisch, Henning, 1969-

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Dynamics of Fricke–Painlevé VI Surfaces by Michel Planat, David Chester, Klee Irwin

“…The symmetries of a Riemann surface <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="sans-serif">Σ</mi><mo>∖</mo><mo>{</mo><msub><mi>a</mi><mi>i</mi></msub><mo>}</mo></mrow></semantics></math></inline-formula> with <i>n</i> punctures <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>a</mi><mi>i</mi></msub></semantics></math></inline-formula> are encoded in its fundamental group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>π</mi><mn>1</mn></msub><mrow><mo>(</mo><mi mathvariant="sans-serif">Σ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. …”
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Algebraic Construction of the Sigma Function for General Weierstrass Curves by Jiryo Komeda, Shigeki Matsutani, Emma Previato

“…It is known that every compact Riemann surface has a Weierstrass curve <i>X</i>, which is birational to the surface. …”
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Discriminant and Root Trajectories of Characteristic Equation of Fractional Vibration Equation and Their Effects on Solution Components by Jun-Sheng Duan, Yun-Yun Zhang

“…It is proved that for any <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>c</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo><mo>∪</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula>, the characteristic equation always has a pair of conjugated simple complex roots with a negative real part on the principal Riemann surface. Particular attention is paid to the problem as to how the couple conjugated complex roots approach the two roots of the integer case <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>, especially to the two different real roots in the case of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>c</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula>. …”
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A study of horizontally weakly conformal maps and their distributions by Mehran Aminian

“…Corollary 2.8. [3]  A smooth map from Riemannian manifold $ (M,g) $ into a Riemann surface $ \overline{M}^2 $, is a horizontally weakly conformal map if and only if for any local complex coordinate $ z $ on $ \overline{M}^2 $, $ \nabla z $ is isotropic. …”
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Large genus bounds for the distribution of triangulated surfaces in moduli space by Vasudevan, Sahana

“…Triangulated surfaces are compact Riemann surfaces equipped with a conformal triangulation by equilateral triangles. …”
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Supermoduli and PCOs at genus two by Charles Wang, Xi Yin

“…Abstract We illustrate the relation between supermoduli integration and picture changing operators (PCOs) particularly concerning the role of vertical integration, in the context of superstring vacuum amplitudes, by an explicit comparison of different parameterizations of the supermoduli space of genus two super Riemann surfaces.…”
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A metal-free photoactive nitrogen-doped carbon nanosolenoid with broad absorption in visible region for efficient photocatalysis by Yu Zhou, Xinyu Zhang, Guan Sheng, Shengda Wang, Muqing Chen, Guilin Zhuang, Yihan Zhu, Pingwu Du

“…Abstract Riemann surfaces inspired chemists to design and synthesize such multidimensional curved carbon architectures. …”
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