arXiv subjects

Jiwan Jung

Publications and source records attributed to Jiwan Jung.

4 recordsLinked to original sources

arXiv2026

Ulrich bundles on intersections of two quadrics

We construct Ulrich bundles on smooth intersections of two quadrics. We determine all possible ranks and prove the existence of indecomposable Ulrich bundles of every allowable rank. To our knowledge, this gives the first such construction for a family of nonhomogeneous varieties of arbitrarily large dimension. We also study the moduli spaces of these bundles and relate them to moduli spaces of vector bundles on curves. For intersections of two even-dimensional quadrics, our results prove a conjecture of Eisenbud and Schreyer.

math.AG↗

arXiv2026

Sharp threshold for universality of cokernels of classical random matrix models over the $p$-adic integers

We prove that $\frac{\log n}{n}$ is the sharp threshold for universality of the distribution of cokernels of random matrices over $\mathbb{Z}_p$. More precisely, let $α_n = \frac{c\log n}{n}$ for a constant $c>0$ and let $A(n)$ be an $α_n$-balanced random matrix over $\mathbb{Z}_p$. For non-symmetric, symmetric, and alternating matrix models, we prove that if $c>1$, then the limiting distribution of the cokernel of $A(n)$ coincides with the universal distribution of the corresponding symmetry type, whereas universality fails at the critical scale $c=1$. This improves earlier universality results, which required $α_n \gg \frac{\log n}{n}$, to the optimal threshold. As an application, we generalize the universality result for Sylow $p$-subgroups of sandpile groups of Erdős-Rényi random graphs to a broader class of Erdős-Rényi graph sequences. Our approach is based on a unified framework that simultaneously treats all symmetry types of random matrices as well as the random graph model, rather than handling each case separately.

math.CO↗

arXiv2024

Carbon Intensity-Aware Adaptive Inference of DNNs

DNN inference, known for its significant energy consumption and the resulting high carbon footprint, can be made more sustainable by adapting model size and accuracy to the varying carbon intensity throughout the day. Our heuristic algorithm uses larger, high-accuracy models during low-intensity periods and smaller, lower-accuracy ones during high-intensity periods. We also introduce a metric, carbon-emission efficiency, which quantitatively measures the efficacy of adaptive model selection in terms of carbon footprint. The evaluation showed that the proposed approach could improve the carbon emission efficiency in improving the accuracy of vision recognition services by up to 80%.

cs.LG↗

arXiv2024

Joint distribution of the cokernels of random $p$-adic matrices II

In this paper, we study the combinatorial relations between the cokernels $\text{cok}(A_n+px_iI_n)$ ($1 \le i \le m$) where $A_n$ is an $n \times n$ matrix over the ring of $p$-adic integers $\mathbb{Z}_p$, $I_n$ is the $n \times n$ identity matrix and $x_1, \cdots, x_m$ are elements of $ \mathbb{Z}_p$ whose reductions modulo $p$ are distinct. For a positive integer $m \le 4$ and given $x_1, \cdots, x_m \in \mathbb{Z}_p$, we determine the set of $m$-tuples of finitely generated $\mathbb{Z}_p$-modules $(H_1, \cdots, H_m)$ for which $(\text{cok}(A_n+px_1I_n), \cdots, \text{cok}(A_n+px_mI_n)) = (H_1, \cdots, H_m)$ for some matrix $A_n$. We also prove that if $A_n$ is an $n \times n$ Haar random matrix over $\mathbb{Z}_p$ for each positive integer $n$, then the joint distribution of $\text{cok}(A_n+px_iI_n)$ ($1 \le i \le m$) converges as $n \rightarrow \infty$.

math.CO↗