arXiv subjects

Taegyu Kim

Publications and source records attributed to Taegyu Kim.

15 recordsLinked to original sources

arXiv2026

No bubble trees for the $1$-equivariant harmonic map heat flow and the radial energy-critical nonlinear heat equation in low dimensions

We consider the $1$-equivariant harmonic map heat flow (HMHF) from $\mathbb R^2$ to $\mathbb S^2$ and the radial energy-critical nonlinear heat equation (NLH) in dimensions $d=3,4,5$. We prove that every finite-energy solution of (HMHF) and every $\dot H^1$-bounded solution of (NLH) has at most one bubble: every finite-time blow-up has exactly one bubble, whereas every global solution has either no bubble or one bubble at infinite time. Starting from the soliton resolution, we exclude bubble trees by modulation analysis, deriving a contradiction from the relative dynamics of the two innermost scales. This energy method does not rely on maximum principle and, in particular, applies without restriction on the bubble signs.

math.AP↗

arXiv2026

RustGo: Fairly Directed Greybox Fuzzing for Enforcing Rust Memory Safety

Rust is a popular systems programming language that provides strong memory safety and introduces low-performance overhead. While Rust guarantees memory safety through strict security policies, such as ownership, memory bugs can still occur in unsafe-related Rust codes where these policies are not fully enforced. Although such unsafe Rust code accounts for only a small portion of the entire code (e.g., 10%), existing approaches fuzz the entire code-including safe Rust, whose memory safety is already enforced by the Rust compiler-resulting in inefficient use of fuzzing resources. In this paper, we propose RustGo, the new Rust-directed greybox fuzzer that effectively and fairly focuses on code regions potentially containing memory bugs. For this, RustGo automatically identifies potential memory bug targets and accurately prunes the paths irrelevant to each target by leveraging Rust-specific static analysis. For each identified target, RustGo includes a new fuzzing approach that maintains an independent state and applies dynamic pruning to maximize balanced and focused fuzzing. We evaluate RustGo on various real-world Rust applications. On average, RustGo prunes 78.49% of irrelevant paths, reaches targets x 2.09 to x 5.08 faster than existing fuzzers, and identifies 13 unknown bugs (six assigned RUSTSEC IDs and one assigned CVE ID).

cs.CR↗

arXiv2026

A log-log upper bound on blow-up rates for the mass-critical half-wave equation

We study finite-time blow-up for the one-dimensional focusing mass-critical half-wave equation \begin{equation*} i\partial_tu=|D|u-|u|^2u. \end{equation*} For even initial data with negative energy and mass slightly above the ground-state mass, we prove the log-log upper bound \begin{equation*} \|u(t)\|_{\dot H^{1/2}}\lesssim \left(\frac{\log|\log(T-t)|}{T-t}\right)^{1/2} \quad \text{as}\quad t\uparrow T. \end{equation*} This gives, for the half-wave equation, the same log-log law upper bound as in the mass-critical nonlinear Schr\"odinger equation. The proof follows a similar strategy developed by Merle and Rapha\"el, but requires a new construction of the blow-up profile. Main difficulty arises from the nonlocal operator $|D|$ and the absence of pseudo-conformal symmetry. We construct an almost self-similar profile with exponentially small error by combining tail computations carried out to arbitrary order, depending on a dynamical parameter, with Borel integral summation in $\Lambda$-analytic spaces. Then, in the modulation analysis, we use a local-virial spectral property proved in the companion paper \cite{Park2026arXiv}.

math.AP↗

arXiv2026

Learning to Recover Task Experts from a Multi-Task Merged Model

Multi-task model merging aims to consolidate several task-specific experts into a unified model, yet static merging consistently suffers from parameter interference. While dynamic merging models aim to bridge this gap, many works rely on the costly storage and loading of redundant expert components at inference. In this work, from the perspective of task expert, we view parameter interference as parameter perturbation introduced to each expert during merging process. We show that such parameter perturbations can be modeled as affine transformation, which can be approximated as additive offsets. Motivated by these, we propose Recover Task eXpert (ReTeX), a framework that predicts those offsets, in order to undo parameter interference and recover task-expert performance from a single merged checkpoint. To recover the appropriate expert when task identity is unknown, we introduce a router-free task identifier based on SVD subspace signatures computed offline before inference. At inference, the identifier selects the task whose subspace yields the smallest projection residual for a given input. As a result, ReTeX recovers over 95% of individual-expert performance in both vision and NLP domains, while significantly improving generalization to unseen tasks. Crucially, we also show that the parameter offset prediction leads to emergent adaptive interpolation of expert knowledge for out-of-distribution (OOD) tasks. ReTeX adaptively interpolates seen expert knowledge to handle unseen tasks. Our code is available at https://github.com/BAIKLAB/ReTeX

cs.AI↗

arXiv2026

Quantized blow-up dynamics for Calogero--Moser derivative nonlinear Schrödinger equation

We consider the Calogero--Moser derivative nonlinear Schrödinger equation (CM-DNLS), an $L^2$-critical nonlinear Schrödinger type equation enjoying a number of numerous structures, such as nonlocal nonlinearity, self-duality, pseudo-conformal symmetry, and complete integrability. In this paper, we construct smooth finite-time blow-up solutions to (CM-DNLS) that exhibit a sequence of discrete blow-up rates, so-called \emph{quantized blow-up rates}. Our strategy is a forward construction of the blow-up dynamics based on modulation analysis. Our main novelty is to utilize the \emph{nonlinear adapted derivative} suited to the \textit{Lax pair structure} and to rely on the \emph{hierarchy of conservation laws} inherent in this structure to control higher-order energies. This approach replaces a repulsivity-based energy method in the bootstrap argument, which significantly simplifies the analysis compared to earlier works. Our result highlights that the integrable structure remains a powerful tool, even in the presence of blow-up solutions. In (CM-DNLS), one of the distinctive features is \emph{chirality}. However, our constructed solutions are not chiral, since we assume the radial (even) symmetry in the gauge transformed equation. This radial assumption simplifies the modulation analysis.

math.AP↗

arXiv2026

Soliton resolution for Calogero--Moser derivative nonlinear Schrödinger equation

We consider soliton resolution for the Calogero--Moser derivative nonlinear Schrödinger equation (CM-DNLS). A rigorous PDE analysis of (CM-DNLS) was recently initiated by Gérard and Lenzmann, who demonstrated its Lax pair structure. Additionally, (CM-DNLS) exhibits several symmetries, such as mass-criticality with pseudo-conformal symmetry and a self-dual Hamiltonian. Despite its integrability, finite-time blow-up solutions have been constructed. The purpose of this paper is to establish soliton resolution for both finite-time blow-up solutions and global solutions in a fully general setting, \emph{without imposing radial symmetry or size constraints}. To our knowledge, this is the first non-integrable proof of full soliton resolution for Schrödinger-type equations. A key aspect of our proof is the control of the energy of the outer radiation after extracting a soliton, referred to as the \emph{energy bubbling} estimate. This benefits from two levels of convervation laws, mass and energy, and self-duality. This approach allows us to directly prove continuous-in-time soliton resolution, bypassing time-sequential soliton resolution. Importantly, our proof does not rely on the integrability of the equation, potentially offering insights applicable to other non-integrable models.

math.AP↗

arXiv2026

Classification of single-bubble blow-up solutions for Calogero--Moser derivative nonlinear Schrödinger equation

We study the Calogero--Moser derivative nonlinear Schrödinger equation (CM-DNLS), a mass-critical and completely integrable dispersive model. Recent works established finite-time blow-up constructions and soliton resolution, describing the asymptotic behaviors of blow-up solutions. In this paper, we go beyond soliton resolution and provide a sharp classification of finite-time blow-up dynamics in the \textit{single-bubble} regime. Assuming that a solution blows up at time $0<T<\infty$ with a single-soliton profile, we determine all possible blow-up rates. For initial data in $H^{2L+1}(\mathbb{R})$ with $L\ge1$, we prove a dichotomy: either the solution lies in a \emph{quantized regime}, where the scaling parameter satisfies \[ λ(t)\sim (T-t)^{2k},\qquad 1\le k\le L, \] with convergent phase and translation parameters, or it lies in an \emph{exotic regime}, where the blow-up rate satisfies $λ(t)\lesssim (T-t)^{2L+\frac 32}$. To our knowledge, this is the first classification result for quantized blow-up dynamics in the class of dispersive models. We provide a framework for identifying the quantized blow-up rates in classification problems. The proof relies on a modulation analysis combined with the hierarchy of conservation laws provided by the complete integrability of (CM-DNLS). However, it does not use \emph{more refined integrability-based techniques}, such as the inverse scattering method, the method of commuting flows, or the explicit formula. As a result, our analysis applies beyond the chiral solutions.

math.AP↗

arXiv2025

LiteRSan: Lightweight Memory Safety Via Rust-specific Program Analysis and Selective Instrumentation

Rust is a memory-safe language, and its strong safety guarantees combined with high performance have been attracting widespread adoption in systems programming and security-critical applications. However, Rust permits the use of unsafe code, which bypasses compiler-enforced safety checks and can introduce memory vulnerabilities. A widely adopted approach for detecting memory safety bugs in Rust is Address Sanitizer (ASan). Optimized versions, such as ERASan and RustSan, have been proposed to selectively apply security checks in order to reduce performance overhead. However, these tools still incur significant performance and memory overhead and fail to detect many classes of memory safety vulnerabilities due to the inherent limitations of ASan. In this paper, we present LiteRSan, a novel memory safety sanitizer that addresses the limitations of prior approaches. By leveraging Rust's unique ownership model, LiteRSan performs Rust-specific static analysis that is aware of pointer lifetimes to identify risky pointers. It then selectively instruments risky pointers to enforce only the necessary spatial or temporal memory safety checks. Consequently, LiteRSan introduces significantly lower runtime overhead (18.84% versus 152.05% and 183.50%) and negligible memory overhead (0.81% versus 739.27% and 861.98%) compared with existing ASan-based sanitizers while being capable of detecting memory safety bugs that prior techniques miss.

cs.CR↗

arXiv2025

Construction of smooth chiral finite-time blow-up solutions to Calogero--Moser derivative nonlinear Schrödinger equation

We consider the Calogero--Moser derivative nonlinear Schrödinger equation (CM-DNLS), which is an $L^{2}$-critical nonlinear Schrödinger equation with explicit solitons, self-duality, and pseudo-conformal symmetry. More importantly, this equation is known to be completely integrable in the Hardy space $L_{+}^{2}$ and the solutions in this class are referred to as \emph{chiral} solutions. A rigorous PDE analysis of this equation with complete integrability was recently initiated by Gérard and Lenzmann. Our main result constructs smooth, chiral, and finite energy finite-time blow-up solutions with mass arbitrarily close to that of a soliton, answering the global regularity question for chiral solutions raised by Gérard and Lenzmann. The blow-up rate obtained for these solutions is different from the pseudo-conformal rate. Our proof also gives a construction of a codimension one set of smooth finite energy initial data (but without addressing chirality) leading to the same blow-up dynamics. Our blow-up construction in the Hardy space might also be contrasted with the global well-posedness of the derivative nonlinear Schrödinger equation (DNLS), which is another integrable $L^{2}$-critical Schrödinger equation. The overall scheme of our proof is the forward construction of blow-up dynamics with modulation analysis. We begin with developing a linear theory for the near-soliton dynamics. We discover a nontrivial conjugation identity, which unveils a surprising connection from the linearized (CM-DNLS) to the 1D free Schrödinger equation, which is a crucial ingredient for overcoming the difficulties from the nonlocal nonlinearity. Another principal challenge in this work, the slow decay of the soliton, is overcome by introducing a trick of decomposing solutions depending on topologies, which we believe is of independent interest.

math.AP↗

arXiv2025

Blow-up construction and instability for mass-critical half-wave equation with slightly superthreshold mass

We study the blow-up dynamics for the $L^2$-critical focusing half-wave equation on the real line, a nonlocal dispersive PDE arising in various physical models. As in other mass-critical models, the ground state solution becomes a threshold between the global well-posedness and the existence of a blow-up. The first blow-up construction is due to Krieger, Lenzmann and Rapha\"el, in which they constructed the minimal mass blow-up solution at the threshold mass. In this paper, we construct finite-time blow-up solutions with mass slightly exceeding the threshold. This is inspired by similar results in the mass-critical NLS by Bourgain and Wang, and their instability by Merle, Rapha\"el and Szeftel. We exhibit a blow-up profile driven by the rescaled ground state, with a decoupled dispersive radiation component. We rigorously describe the asymptotic behavior of such solutions near the blow-up time, including sharp modulation dynamics. Furthermore, we demonstrate the instability of these solutions by constructing non-blow-up solutions that are arbitrarily close to the blow-up solutions. The main contribution of this work is to overcome the nonlocal setting of half-wave and to extend insights from the mass-critical NLS to a setting lacking pseudo-conformal symmetry.

math.AP↗

arXiv2023

The stability of degenerate solitons for derivative nonlinear Schrodinger equations

In this paper, we consider the following nonlinear Schr\"odinger equation with derivative: \begin{align*} i\partial_tu+\partial_{xx}u+i|u|^{2}\partial_xu+b|u|^4u=0, \quad (t,x) \in \mathbb{R}\times\mathbb{R}, \quad b\geq 0. \end{align*} For the case $b=0$, the original DNLS, Kwon and Wu \cite{KwonWu2018} proved the conditional orbital stability of degenerate solitons including scaling, phase rotation, and spatial translation with a non-smallness condition, $\|u(t)\|_{L^6}^6> \sqrt{\delta}$. In this paper, we remove this condition for the non-positive initial energy and momentum, and we extend the stability result for $b\geq0$.

math.AP↗

arXiv2022

Junctions of mass-deformed nonlinear sigma models on $SO(2N)/U(N)$ and $Sp(N)/U(N)$ I

We construct on-shell ${\mathcal{N}}=2$ nonlinear sigma models on $SO(2N)/U(N)$ and $Sp(N)/U(N)$ by holomorphically embedding the models in the hyper-Kähler nonlinear sigma model on the cotangent bundle of the Grassmann manifold $T^\ast G_{2N,N}$ in the ${\mathcal{N}}=1$ superspace formalism. We apply the moduli matrix formalism to the mass-deformed nonlinear sigma models on the quadrics to study three-pronged junctions by using a recently proposed diagram method.

hep-th↗

arXiv2020

A Vanishingly Small Vector Mass from Anisotropy of Higher Dimensional Spacetime

We consider five-dimensional massive vector-gravity theory which is based on the foliation preserving diffeomorphism and anisotropic conformal invariance. It does not have an intrinsic scale and the only relevant parameter is the anisotropic factor $z$ which characterizes the degree of anisotropy between the four-dimensional spacetime and the extra dimension. We assume that physical scale $M_*$ emerges as a consequence of spontaneous conformal symmetry breaking of vacuum solution. It is demonstrated that a very small mass for the vector particle compared to $M_*$ can be achieved with a relatively mild adjustment of the parameter $z$. At the same time, it is also observed that the motion along the extra dimension can be highly suppressed and the five-dimensional theory can be effectively reduced to four-dimensional spacetime.

hep-th↗

arXiv2020

Junctions of mass-deformed nonlinear sigma models on $SO(2N)/U(N)$ and $Sp(N)/U(N)$ II

We study vacua, walls and three-pronged junctions of mass-deformed nonlinear sigma models on $SO(2N)/U(N)$ and $Sp(N)/U(N)$ for generic $N$. We review and discuss the on-shell component Lagrangians of the ${\mathcal{N}}=2$ nonlinear sigma model on the Grassmann manifold, which are obtained in the ${\mathcal{N}}=1$ superspace formalism and in the harmonic superspace formalism. We also show that the Kähler potential of the ${\mathcal{N}}=2$ nonlinear sigma model on the complex projective space, which is obtained in the projective superspace formalism, is equivalent to the Kähler potential of the ${\mathcal{N}}=2$ nonlinear sigma model with the Fayet-Iliopoulos parameters $c^a=(0,0,c=1)$ on the complex projective space, which is obtained in the ${\mathcal{N}}=1$ superspace formalism.

hep-th↗

arXiv2018

Hamiltonian Formalism of Topologically Massive Electrodynamics

We consider the four dimensional topologically massive electrodynamics in which a gauge field is interacting with 2nd rank antisymmetric tensor field through a topological interaction. The photon becomes massive by eating the 2nd rank tensor field, which is dual to the Higgs mechanism. We explicitly demonstrate the nature of the mechanism by performing a canonical analysis of the theory and discuss various aspects of it.

hep-th↗