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Joonhyung Kim

Publications and source records attributed to Joonhyung Kim.

11 recordsLinked to original sources
arXiv2026

On the sub-Riemannian geometry of the quaternionic Heisenberg group

Utilizing the framework of quaternionic contact geometry, we define a sequence of Riemannian metrics $\{g_L\}$ on the quaternionic Heisenberg group $\mathfrak{H}_{\mathbb{H}}$ by rescaling the vertical directions. By analyzing the limit of this sequence, we characterize the Carnot-Carathéodory geodesics and provide the explicit description of the Carnot-Carathéodory distance and spheres in $\mathfrak{H}_{\mathbb{H}}$ . Furthermore, we derive a general formula for the horizontal mean curvature of hypersurfaces.

math.DG↗
arXiv2023

PCR-Kähler equivalent metrics in the Siegel domain

Let $\mathfrak{H}$ be the Heisenberg group. From the standard CR structure $\mathcal{H}$ of $\mathfrak{H}$ we construct the complex hyperbolic structure of the Siegel domain. Additionally, using the same minimal data for $\mathfrak{H}$, that is, its Sasakian structure, we provide the Siegel domain with yet another Kähler structure: this structure is of unbounded negative sectional curvature, and its complex structure does not commute with the standard complex structure. However, we show that those two Kähler structures are {\rm PCR} Kähler equivalent, that is to say, essentially the same when restricted to $\mathcal{H}$.

math.DG↗
arXiv2022

A Charge Domain P-8T SRAM Compute-In-Memory with Low-Cost DAC/ADC Operation for 4-bit Input Processing

This paper presents a low cost PMOS-based 8T (P-8T) SRAM Compute-In-Memory (CIM) architecture that efficiently per-forms the multiply-accumulate (MAC) operations between 4-bit input activations and 8-bit weights. First, bit-line (BL) charge-sharing technique is employed to design the low-cost and reliable digital-to-analog conversion of 4-bit input activations in the pro-posed SRAM CIM, where the charge domain analog computing provides variation tolerant and linear MAC outputs. The 16 local arrays are also effectively exploited to implement the analog mul-tiplication unit (AMU) that simultaneously produces 16 multipli-cation results between 4-bit input activations and 1-bit weights. For the hardware cost reduction of analog-to-digital converter (ADC) without sacrificing DNN accuracy, hardware aware sys-tem simulations are performed to decide the ADC bit-resolutions and the number of activated rows in the proposed CIM macro. In addition, for the ADC operation, the AMU-based reference col-umns are utilized for generating ADC reference voltages, with which low-cost 4-bit coarse-fine flash ADC has been designed. The 256X80 P-8T SRAM CIM macro implementation using 28nm CMOS process shows that the proposed CIM shows the accuracies of 91.46% and 66.67% with CIFAR-10 and CIFAR-100 dataset, respectively, with the energy efficiency of 50.07-TOPS/W.

cs.AR↗
arXiv2015

Complex and Quaternionic hyperbolic Kleinian groups with real trace fields

Let $Γ$ be a nonelementary discrete subgroup of SU(n,1) or Sp(n,1). We show that if the trace field of $Γ$ is contained in $\mathbb R$, $Γ$ preserves a totally geodesic submanifold of constant negative sectional curvature. Furthermore if $Γ$ is irreducible, $Γ$ is a Zariski dense irreducible discrete subgroup of SO(n,1) up to conjugation. This is an analog of a theorem of Maskit for general semisimple Lie groups of rank $1$.

math.GT↗
arXiv2012

McShane's Identity in Rank One Symmetric Spaces

In this paper we study McShane's identity in real and complex hyperbolic spaces and obtain various generalizations of the identity for representations of surface groups into the isometry groups of rank one symmetric spaces. Our methods unify most of the existing methods used in the existing literature for proving this class of identities.

math.GT↗