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Jinsung Park

Publications and source records attributed to Jinsung Park.

At least 19 recordsLinked to original sources
arXiv2026

Maximal discs of Weil-Petersson class in $\mathbb{A}\mathrm{d}\mathbb{S}^{2,1}$

We introduce maximal discs of Weil-Petersson class in the 3-dimensional Anti-de Sitter space $\mathbb{A}\mathrm{d}\mathbb{S}^{2,1}$, whose parametrization space can be identified with the cotangent bundle $T^*T_0(1)$ of Weil-Petersson universal Teichmüller space $T_0(1)$. We prove that the Mess map defines a symplectic diffeomorphism from $T^*T_0(1)$ to $T_0(1)\times T_0(1)$, with respect to the canonical symplectic form on $T^*T_0(1)$ and the difference of pullbacks of the Weil-Petersson symplectic forms from each factor of $T_0(1)\times T_0(1)$. Furthermore, we show that the functional given by the anti-holomorphic energies of the induced Gauss maps associated with maximal discs of Weil-Petersson class serves as a Kähler potential for the restriction of the canonical symplectic form to certain submanifolds $T_0(1)^\pm \subset T^*T_0(1)$, which bijectively parametrize the space of maximal discs of Weil-Petersson class in $\mathbb{A}\mathrm{d}\mathbb{S}^{2,1}$.

math.SG↗
arXiv2026

Robust Nonlinear Transform Coding: A Framework for Generalizable Joint Source-Channel Coding

This paper proposes robust nonlinear transform coding (Robust-NTC), a generalizable digital joint source-channel coding (JSCC) framework that couples variational latent modeling with channel-adaptive transmission. Unlike learning-based JSCC methods that implicitly absorb channel variations, Robust-NTC explicitly models element-wise latent distributions via a variational objective with a Gaussian proxy for quantization and channel noise, allowing encoder-decoder to capture latent uncertainty without channel-specific training. Using the learned statistics, Robust-NTC also facilitates rate-distortion optimization to adaptively select element-wise quantizers and bit depths according to online channel conditions. To support practical deployment, Robust-NTC is integrated into an orthogonal frequency-division multiplexing (OFDM) system, where a unified resource allocation framework jointly optimizes latent quantization, bit allocation, modulation order, and power allocation to minimize transmission latency while guaranteeing learned distortion targets. Simulation results demonstrate that for practical OFDM systems, Robust-NTC achieves superior rate-distortion efficiency and stable reconstruction fidelity compared to both a conventional separated coding scheme and digital JSCC baselines across various channel conditions.

eess.SP↗
arXiv2025

Rate-Adaptive Semantic Communication via Multi-Stage Vector Quantization

This paper proposes a novel framework for rate-adaptive semantic communication based on multi-stage vector quantization (VQ), termed \textit{MSVQ-SC}. Unlike conventional single-stage VQ approaches, which require exponentially larger codebooks to achieve higher fidelity, the proposed framework decomposes the quantization process into multiple stages and dynamically activates both stages and individual VQ modules. This design enables fine-grained rate adaptation under varying bit constraints while mitigating computational complexity and the codebook collapse problem. To optimize performance, we formulate a module selection problem that minimizes task loss subject to a rate constraint and solve it using an incremental allocation algorithm. Furthermore, we extend the framework by incorporating entropy coding to exploit non-uniform codeword distributions, further reducing communication overhead. Simulation results on the CIFAR-10 dataset demonstrate that the proposed framework outperforms existing digital semantic communication methods, achieving superior semantic fidelity with lower complexity while providing flexible and fine-grained rate control.

eess.SP↗
arXiv2025

ESC-MVQ: End-to-End Semantic Communication With Multi-Codebook Vector Quantization

This paper proposes a novel end-to-end digital semantic communication framework based on multi-codebook vector quantization (VQ), referred to as ESC-MVQ. Unlike prior approaches that rely on end-to-end training with a specific power or modulation scheme, often under a particular channel condition, ESC-MVQ models a channel transfer function as parallel binary symmetric channels (BSCs) with trainable bit-flip probabilities. Building on this model, ESC-MVQ jointly trains multiple VQ codebooks and their associated bit-flip probabilities with a single encoder-decoder pair. To maximize inference performance when deploying ESC-MVQ in digital communication systems, we devise an optimal communication strategy that jointly optimizes codebook assignment, adaptive modulation, and power allocation. To this end, we develop an iterative algorithm that selects the most suitable VQ codebook for semantic features and flexibly allocates power and modulation schemes across the transmitted symbols. Simulation results demonstrate that ESC-MVQ, using a single encoder-decoder pair, outperforms existing digital semantic communication methods in both performance and memory efficiency, offering a scalable and adaptive solution for realizing digital semantic communication in diverse channel conditions.

eess.SP↗
arXiv2021

Liouville Action for Harmonic Diffeomorphisms

In this paper, we introduce a Liouville action for a harmonic diffeomorphism from a compact Riemann surface to a compact hyperbolic Riemann surface of genus $g\ge 2$. We derive the variational formula of this Liouville action for harmonic diffeomorphisms when the source Riemann surfaces vary with a fixed target Riemann surface.

math.DG↗
arXiv2017

Liouville action and Holography on quasi-Fuchsian deformation spaces

We study the Liouville action for quasi-Fuchsian groups with parabolic and elliptic elements. In particular, when the group is Fuchsian, the contribution of elliptic elements to the classical Liouville action is derived in terms of the Bloch-Wigner functions. We prove the first and second variation formulas for the classical Liouville action on the quasi-Fuchsian deformation space. We prove an equality expressing the holography principle, which relates the Liouville action and the renormalized volume for quasi-Fuchsian groups with parabolic and elliptic elements. We also construct the potential functions of the Kähler forms corresponding to the Takhtajan-Zograf metrics associated to the elliptic elements in the quasi-Fuchsian groups.

math-ph↗
arXiv2015

Potentials and Chern forms for Weil-Petersson and Takhtajan-Zograf metrics on moduli spaces

For the TZ metric on the moduli space $\mathscr{M}_{0,n}$ of $n$-pointed rational curves, we construct a Kähler potential in terms of the Fourier coefficients of the Klein's Hauptmodul. We define the space $\mathfrak{S}_{g,n}$ as holomorphic fibration $\mathfrak{S}_{g,n}\rightarrow\mathfrak{S}_{g}$ over the Schottky space $\mathfrak{S}_{g}$ of compact Riemann surfaces of genus $g$, where the fibers are configuration spaces of $n$ points. For the tautological line bundles $\mathscr{L}_{i}$ over $\mathfrak{S}_{g,n}$ we define Hermitian metrics $h_{i}$ in terms of Fourier coefficients of a covering map $J$ of the Schottky domain. We define the regularized classical Liouville action $S$ and show that $\exp\{S/π\}$ is a Hermitian metric in the line bundle $\mathscr{L}=\otimes_{i=1}^{n}\mathscr{L}_{i}$ over $\mathfrak{S}_{g,n}$. We explicitly compute the Chern forms of these Hermitian line bundles $$c_{1}(\mathscr{L}_{i},h_{i})=\frac{4}{3}ω_{\mathrm{TZ},i},\quad c_{1}(\mathscr{L},\exp\{S/π\})=\frac{1}{π^{2}}ω_{\mathrm{WP}}.$$ We prove that a smooth real-valued function $-\mathscr{S}=-S+π\sum_{i=1}^{n}\log h_{i}$ on $\mathfrak{S}_{g,n}$, a potential for this special difference of WP and TZ metrics, coincides with the renormalized hyperbolic volume of a corresponding Schottky $3$-manifold. We extend these results to the quasi-Fuchsian groups of type $(g,n)$.

math.AG↗
arXiv2012

Tau function and Chern-Simons invariant

We define a Chern-Simons invariant for a certain class of infinite volume hyperbolic 3-manifolds. We then prove an expression relating the Bergman tau function on a cover of the Hurwitz space, to the lifting of the function $F$ defined by Zograf on Teichmüller space, and another holomorphic function on the cover of the Hurwitz space which we introduce. If the point in cover of the Hurwitz space corresponds to a Riemann surface $X$, then this function is constructed from the renormalized volume and our Chern-Simons invariant for the bounding 3-manifold of $X$ given by Schottky uniformization, together with a regularized Polyakov integral relating determinants of Laplacians on $X$ in the hyperbolic and singular flat metrics. Combining this with a result of Kokotov and Korotkin, we obtain a similar expression for the isomonodromic tau function of Dubrovin. We also obtain a relation between the Chern-Simons invariant and the eta invariant of the bounding 3-manifold, with defect given by the phase of the Bergman tau function of $X$.

math.DG↗
arXiv2010

Bergman and Calderón projectors for Dirac operators

For a Dirac operator $D_{\bar{g}}$ over a spin compact Riemannian manifold with boundary $(\bar{X},\bar{g})$, we give a natural construction of the Calderón projector and of the associated Bergman projector on the space of harmonic spinors on $\bar{X}$, and we analyze their Schwartz kernels. Our approach is based on the conformal covariance of $D_{\bar{g}}$ and the scattering theory for the Dirac operator associated to the complete conformal metric $g=\bar{g}/ρ^2$ where $ρ$ is a smooth function on $\bar{X}$ which equals the distance to the boundary near $\partial\bar{X}$. We show that $({\rm Id}+\tilde{S}(0))/2$ is the orthogonal Calderón projector, where $\tilde{S}(λ)$ is the holomorphic family in $\{\Re(λ)\geq 0\}$ of normalized scattering operators constructed in our previous work, which are classical pseudo-differential of order $2λ$. Finally we construct natural conformally covariant odd powers of the Dirac operator on any spin manifold.

math.DG↗
arXiv2009

Eta invariant and Selberg Zeta function of odd type over convex co-compact hyperbolic manifolds

We show meromorphic extension and analyze the divisors of a Selberg zeta function of odd type $Z_{Γ,Σ}^{\rm o}(λ)$ associated to the spinor bundle $Σ$ on odd dimensional convex co-compact hyperbolic manifolds $X:=Γ\backslash\hh^{2n+1}$. We define a natural eta invariant $η(D)$ associated to the Dirac operator $D$ on $X$ and prove that $η(D)=\frac{1}{πi}\log Z_{Γ,Σ}^{\rm o}(0)$, thus extending Millson's formula to this setting. As a byproduct, we do a full analysis of the spectral and scattering theory of the Dirac operator on asymptotically hyperbolic manifolds. We also define an eta invariant for the odd signature operator and, under some conditions, we describe it on the Schottky space of 3-dimensional Schottky hyperbolic manifolds and relate it to Zograf factorization formula.

math.SP↗
arXiv2009

Regularity of the eta function on manifolds with cusps

On a spin manifold with conformal cusps, we prove under an invertibility condition at infinity that the eta function of the twisted Dirac operator has at most simple poles and is regular at the origin. For hyperbolic manifolds of finite volume, the eta function of the Dirac operator twisted by any homogeneous vector bundle is shown to be entire.

math.DG↗
arXiv2008

The ubiquitous $ζ$-function and some of its "usual" and "unusual" meromorphic properties

In this contribution we announce a complete classification and new exotic phenomena of the meromorphic structure of $\z$-functions associated to conic manifolds proved in \cite{KLP1}. In particular, we show that the meromorphic extensions of these $\z$-functions have, in general, countably many logarithmic branch cuts on the nonpositive real axis and unusual locations of poles with arbitrarily large multiplicity. Moreover, we give a precise algebraic-combinatorial formula to compute the coefficients of the leading order terms of the singularities.

math-ph↗
arXiv2007

Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone

In this article we consider the zeta regularized determinant of Laplace-type operators on the generalized cone. For {\it arbitrary} self-adjoint extensions of a matrix of singular ordinary differential operators modelled on the generalized cone, a closed expression for the determinant is given. The result involves a determinant of an endomorphism of a finite-dimensional vector space, the endomorphism encoding the self-adjoint extension chosen. For particular examples, like the Friedrich's extension, the answer is easily extracted from the general result. In combination with \cite{BKD}, a closed expression for the determinant of an arbitrary self-adjoint extension of the full Laplace-type operator on the generalized cone can be obtained.

math-ph↗
arXiv2006

Exotic expansions and pathological properties of $ζ$-functions on conic manifolds

We give a complete classification and present new exotic phenomena of the meromorphic structure of $ζ$-functions associated to general self-adjoint extensions of Laplace-type operators over conic manifolds. We show that the meromorphic extensions of these $ζ$-functions have, in general, countably many logarithmic branch cuts on the nonpositive real axis and unusual locations of poles with arbitrarily large multiplicity. The corresponding heat kernel and resolvent trace expansions also exhibit exotic behaviors with logarithmic terms of arbitrary positive and negative multiplicity. We also give a precise algebraic-combinatorial formula to compute the coefficients of the leading order terms of the singularities.

math.SP↗
arXiv2006

The very unusual properties of the resolvent, heat kernel, and zeta function for the operator $-d^2/dr^2 - 1/(4r^2)$

In this article we analyze the resolvent, the heat kernel and the spectral zeta function of the operator $-d^2/dr^2 - 1/(4r^2)$ over the finite interval. The structural properties of these spectral functions depend strongly on the chosen self-adjoint realization of the operator, a choice being made necessary because of the singular potential present. Only for the Friedrichs realization standard properties are reproduced, for all other realizations highly nonstandard properties are observed. In particular, for $k\in \N$ we find terms like $(\log t)^{-k}$ in the small-$t$ asymptotic expansion of the heat kernel. Furthermore, the zeta function has $s=0$ as a logarithmic branch point.

math-ph↗