Research
Research
Research
Research
415+ open-access research outputs.
The Karch-Randall braneworld concerns the physics of an AdS$_{d}$ brane embedded in an ambient gravitational AdS$_{d+1}$ spacetime. The gravitational theory induced on the AdS$_{d}$ brane has a very l…
Let $O$ be a discrete valuation ring and $A := O[X_{m \times n}]/I_{m}(X)$ the determinantal ring of maximal minors. We consider algebra maps $\lambda \colon A \to O$, which is tantamount to choosing …
In this expository paper, we discuss a unified framework for proving various geometric inequalities, based on the so-called Alexandrov-Bakelman-Pucci technique. Examples include Cabr\'e's proof of the…
Recent progress in learning-based image compression has demonstrated that end-to-end optimization can substantially outperform traditional codecs by jointly learning compact latent representations and…
Weight-space merging aims to combine multiple fine-tuned LLMs into a single model without retraining, yet most existing approaches remain fundamentally parameter-space heuristics. This creates three p…
We study the equation of state (EoS) of QCD matter in a bottom-up holographic setup that combines an Einstein-Maxwell-dilaton (EMD) sector with an improved Karch-Katz-Son-Stephanov (KKSS) flavor actio…
We propose a definition of the Riemannian median $M(\mathbb{A})$ of a tuple of positive-definite matrices $\mathbb{A}:=(A_{1}, \cdots, A_{n})$. We will define it as a positive-definite matrix using La…
Black holes exactly incorporating quantum matter backreaction effects, namely, quantum black holes, are notoriously difficult to construct, let alone study their horizon thermodynamics. Here, we deriv…
This paper develops a systematic and geometric theory of optimal quantization on the unit sphere $\mathbb S^2$, focusing on finite uniform probability distributions supported on the spherical surface …
We consider general bilinear products defined by positive semidefinite matrices. Typically non-commutative, non-associative, and non-unital, these products preserve positivity and include the classica…
In this paper, we study the overdetermined problem for the p-Laplacian equation on a compact Riemannian manifold with positive Ricci curvature. By introducing a new P-function which is related to the …
In this paper, we study the behavior of some locally constrained inverse curvature flow in de Sitter space, with initial value any closed spacelike $k$-convex hypersurface satisfying some pinching con…
Large language models (LLMs) are known to inherit and even amplify societal biases present in their pre-training corpora, threatening fairness and social trust. To address this issue, recent work has …
We address the correspondence-free alignment of two rotation sets on \(SO(3)\), a core task in calibration and registration that is often impeded by missing time alignment, outliers, and unknown axis …
In this paper, we first prove that any interior point of an open interval of the real line can be interpreted as Fr\'echet means with respect to corresponding metric distances, thus extending the resu…
Large language models (LLMs) are increasingly used in scientific domains. While they can produce reasoning-like content via methods such as chain-of-thought prompting, these outputs are typically unst…
This thesis advances the spectral theory of structured matrix-sequences within the framework of Generalized Locally Toeplitz (GLT) $*$-algebras, focusing on the geometric mean of Hermitian positive de…
In this article, we investigate the proposed duality between the island and the defect extremal surface (DES) prescriptions using the fine-grained entanglement entropy in Karch-Randall (KR) brane-worl…
We present two generalizations for the celebrated works of Ferus-Karcher-M\"unzner \cite{FKM81} and Wang \cite{W94}. We first show that an isoparametric foliation on $\mathbb{S}^{2n+1}$ constructed by…
We construct an analogue of Gerasimov-Kharchev-Lebedev-Oblezin (GKLO) representations for twisted Yangians of type $\mathsf{AI}$, using the recently found current presentation of these algebras due to…
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