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Jinwon Choi

Publications and source records attributed to Jinwon Choi.

At least 19 recordsLinked to original sources
arXiv2026

Cohomology of moduli spaces of pointed curves

In this paper, after reviewing recent progress on the cohomology of $\overline{{\cal M}}_{0,n}$, we further our investigation on the cohomology of moduli spaces of pointed curves in continuation of [2,4,5,6,7,8]. In particular, we prove that the Betti number distribution of the Fulton-MacPherson compactification $C[n]$ of the space of $n$ ordered distinct points on any smooth projective curve $C$ is asymptotically Gaussian as $n$ goes to infinity.

math.AG↗
arXiv2026

Asymptotic distribution of the Betti numbers of $\overline{\mathcal{M}}_{0,n}$

Asymptotic normality is frequently observed in large combinatorial structures, rigorously established for many quantities such as cycles or inversions in random permutations, the number of prime factors of random integers, and various parameters of random graphs. In this paper, we investigate whether this normal limit behavior extends to the topological invariants of geometric spaces. We show that the Betti numbers of the moduli space of rational curves with $n$ marked points $\overline{\mathcal{M}}_{0,n}$ and the Fulton-MacPherson configuration space $\mathbb{P}^1[n]$ are asymptotically normally distributed. Based on numerical evidence and established log-concavity, we conjecture that the Betti numbers of the quotients of these spaces by the symmetric group $\mathbb{S}_n$ are also asymptotically normally distributed. In contrast, we provide examples of geometric spaces that do not follow this Gaussian law.

math.AG↗
arXiv2025

Characteristic polynomial of $\overline{\mathcal{M}}_{0,n}$ and log-concavity

Motivated by Stanley's generalization of the chromatic polynomial of a graph to the chromatic symmetric function, we introduce the characteristic polynomial of a representation of the symmetric group, or more generally, of a symmetric function. When the representation arises from geometry, the coefficients of its characteristic polynomial tend to form a log-concave sequence. To illustrate, we investigate explicit examples, including the $n$-fold products of the projective spaces, the GIT moduli spaces of points on $\mathbb{P}^1$ and Hessenberg varieties. Our main focus lies on the cohomology of the moduli space of pointed rational curves, for which we prove asymptotic formulas of its characteristic polynomial and establish asymptotic log-concavity.

math.AG↗
arXiv2024

Recursive algorithm and log-concavity of representations on the cohomology of $\overline{\mathcal M}_{0,n}$

We provide a programmable recursive algorithm for the $\mathbb{S}_n$-representations on the cohomology of the moduli spaces $\overline{\mathcal M}_{0,n}$ of $n$-pointed stable curves of genus 0. As an application, we find explicit inductive and asymptotic formulas for the invariant part $H^*(\overline{\mathcal M}_{0,n}/\mathbb{S}_n)$ and prove that its Poincar\'e polynomial is asymptotically log-concave. Based on numerical computations with our algorithm, we further conjecture that the sequence $\{H^{2k}(\overline{\mathcal M}_{0,n})\}$ of $\mathbb{S}_n$-modules is equivariantly log-concave.

math.AG↗
arXiv2023

Threshold-aware Learning to Generate Feasible Solutions for Mixed Integer Programs

Finding a high-quality feasible solution to a combinatorial optimization (CO) problem in a limited time is challenging due to its discrete nature. Recently, there has been an increasing number of machine learning (ML) methods for addressing CO problems. Neural diving (ND) is one of the learning-based approaches to generating partial discrete variable assignments in Mixed Integer Programs (MIP), a framework for modeling CO problems. However, a major drawback of ND is a large discrepancy between the ML and MIP objectives, i.e., variable value classification accuracy over primal bound. Our study investigates that a specific range of variable assignment rates (coverage) yields high-quality feasible solutions, where we suggest optimizing the coverage bridges the gap between the learning and MIP objectives. Consequently, we introduce a post-hoc method and a learning-based approach for optimizing the coverage. A key idea of our approach is to jointly learn to restrict the coverage search space and to predict the coverage in the learned search space. Experimental results demonstrate that learning a deep neural network to estimate the coverage for finding high-quality feasible solutions achieves state-of-the-art performance in NeurIPS ML4CO datasets. In particular, our method shows outstanding performance in the workload apportionment dataset, achieving the optimality gap of 0.45%, a ten-fold improvement over SCIP within the one-minute time limit.

math.OC↗
arXiv2022

Evaluating Out-of-Distribution Detectors Through Adversarial Generation of Outliers

A reliable evaluation method is essential for building a robust out-of-distribution (OOD) detector. Current robustness evaluation protocols for OOD detectors rely on injecting perturbations to outlier data. However, the perturbations are unlikely to occur naturally or not relevant to the content of data, providing a limited assessment of robustness. In this paper, we propose Evaluation-via-Generation for OOD detectors (EvG), a new protocol for investigating the robustness of OOD detectors under more realistic modes of variation in outliers. EvG utilizes a generative model to synthesize plausible outliers, and employs MCMC sampling to find outliers misclassified as in-distribution with the highest confidence by a detector. We perform a comprehensive benchmark comparison of the performance of state-of-the-art OOD detectors using EvG, uncovering previously overlooked weaknesses.

cs.CR↗
arXiv2022

JORLDY: a fully customizable open source framework for reinforcement learning

Recently, Reinforcement Learning (RL) has been actively researched in both academic and industrial fields. However, there exist only a few RL frameworks which are developed for researchers or students who want to study RL. In response, we propose an open-source RL framework "Join Our Reinforcement Learning framework for Developing Yours" (JORLDY). JORLDY provides more than 20 widely used RL algorithms which are implemented with Pytorch. Also, JORLDY supports multiple RL environments which include OpenAI gym, Unity ML-Agents, Mujoco, Super Mario Bros and Procgen. Moreover, the algorithmic components such as agent, network, environment can be freely customized, so that the users can easily modify and append algorithmic components. We expect that JORLDY will support various RL research and contribute further advance the field of RL. The source code of JORLDY is provided on the following Github: https://github.com/kakaoenterprise/JORLDY

cs.LG↗
arXiv2022

Representations on the cohomology of $\overline{\mathcal{M}}_{0,n}$

The moduli space $\overline{\mathcal{M}}_{0,n}$ of $n$ pointed stable curves of genus $0$ admits an action of the symmetric group $S_n$ by permuting the marked points. We provide a closed formula for the character of the $S_n$-action on the cohomology of $\overline{\mathcal{M}}_{0,n}$. This is achieved by studying wall crossings of the moduli spaces of quasimaps which provide us with a new inductive construction of $\overline{\mathcal{M}}_{0,n}$, equivariant with respect to the symmetric group action. Moreover we prove that $H^{2k}(\overline{\mathcal{M}}_{0,n})$ for $k\le 3$ and $H^{2k}(\overline{\mathcal{M}}_{0,n})\oplus H^{2k-2}(\overline{\mathcal{M}}_{0,n})$ for any $k$ are permutation representations. Our method works for related moduli spaces as well and we provide a closed formula for the character of the $S_n$-representation on the cohomology of the Fulton-MacPherson compactification $\mathbb{P}^1[n]$ of the configuration space of $n$ points on $\mathbb{P}^1$ and more generally on the cohomology of the moduli space $\overline{\mathcal{M}}_{0,n}(\mathbb{P}^{m-1},1)$ of stable maps.

math.AG↗
arXiv2021

Classification of graphs by Laplacian eigenvalue distribution and independence number

Let $m_GI$ denote the number of Laplacian eigenvalues of a graph $G$ in an interval $I$ and let $α(G)$ denote the independence number of $G$. In this paper, we determine the classes of graphs that satisfy the condition $m_G[0,n-α(G)]=α(G)$ when $α(G)= 2$ and $α(G)= n-2$, where $n$ is the order of $G$. When $α(G)=2$, $G \cong K_1 \nabla K_{n-m} \nabla K_{m-1}$ for some $m \geq 2$. When $α(G)=n-2$, there are two types of graphs $B(p,q,r)$ and $B'(p,q,r)$ of order $n=p+q+r+2$, which we call the binary star graphs. Also, we show that the binary star graphs with $p=r$ are determined by their Laplacian spectra.

math.CO↗
arXiv2021

Sheaves of maximal intersection and multiplicities of stable log maps

A great number of theoretical results are known about log Gromov-Witten invariants, but few calculations are worked out. In this paper we restrict to surfaces and to genus 0 stable log maps of maximal tangency. We ask how various natural components of the moduli space contribute to the log Gromov-Witten invariants. The first such calculation by Gross-Pandharipande-Siebert deals with multiple covers over rigid curves in the log Calabi-Yau setting. As a natural continuation, in this paper we compute the contributions of non-rigid irreducible curves in the log Calabi-Yau setting and that of the union of two rigid curves in general position. For the former, we construct and study a moduli space of "logarithmic" 1-dimensional sheaves and compare the resulting multiplicity with tropical multiplicity. For the latter, we explicitly describe the components of the moduli space and work out the logarithmic deformation theory in full, which we then compare with the deformation theory of the analogous relative stable maps.

math.AG↗
arXiv2020

Log BPS numbers of log Calabi-Yau surfaces

Let $(S,E)$ be a log Calabi-Yau surface pair with $E$ a smooth divisor. We define new conjecturally integer-valued counts of $\mathbb{A}^1$-curves in $(S,E)$. These log BPS numbers are derived from genus 0 log Gromov-Witten invariants of maximal tangency along $E$ via a formula analogous to the multiple cover formula for disk counts. A conjectural relationship to genus 0 local BPS numbers is described and verified for del Pezzo surfaces and curve classes of arithmetic genus up to 2. We state a number of conjectures and provide computational evidence.

math.AG↗
arXiv2020

Entangled edge states of corank one with positive partial transposes

We construct a parameterized family of $n\otimes n$ PPT (positive partial transpose) states of corank one for each $n\ge 3$. With a suitable choice of parameters, we show that they are $n\otimes n$ PPT entangled edge states of corank one for $3\le n\le 1000$. They violate the range criterion for separability in the most extreme way. Note that corank one is the smallest possible corank for such states. The corank of the partial transpose is given by $2n-3$, which is also the smallest possible corank for the partial transposes of PPT entangled edge states of corank one. They provide the first explicit examples of such states for $n\ge 4$.

quant-ph↗
arXiv2019

A new method toward the Landau-Ginzburg/Calabi-Yau correspondence via quasi-maps

The Landau-Ginzburg/Calabi-Yau correspondence claims that the Gromov-Witten invariant of the quintic Calabi-Yau 3-fold should be related to the Fan-Jarvis-Ruan-Witten invariant of the associated Landau-Ginzburg model via wall crossings. In this paper, we consider the stack of quasi-maps with a cosection and introduce sequences of stability conditions which enable us to interpolate between the moduli stack for Gromov-Witten invariants and the moduli stack for Fan-Jarvis-Ruan-Witten invariants.

math.AG↗
arXiv2018

Local BPS Invariants: Enumerative Aspects and Wall-Crossing

We study the BPS invariants for local del Pezzo surfaces, which can be obtained as the signed Euler characteristic of the moduli spaces of stable one-dimensional sheaves on the surface $S$. We calculate the Poincare polynomials of the moduli spaces for the curve classes $β$ having arithmetic genus at most 2. We formulate a conjecture that these Poincare polynomials are divisible by the Poincare polynomials of $((-K_S).β-1)$-dimensional projective space. This conjecture motivates upcoming work on log BPS numbers.

math.AG↗
arXiv2015

Moduli of sheaves supported on quartic space curves

As a continuation of the work of Freiermuth and Trautmann, we study the geometry of the moduli space of stable sheaves on $\mathbb{P}^3$ with Hilbert polynomial $4m+1$. The moduli space has three irreducible components whose generic elements are, respectively, sheaves supported on rational quartic curves, on elliptic quartic curves, or on planar quartic curves. The main idea of the proof is to relate the moduli space with the Hilbert scheme of curves by wall crossing. We present all stable sheaves contained in the intersections of the three irreducible components. We also classify stable sheaves by means of their free resolutions.

math.AG↗
arXiv2015

Moduli Spaces of $α$-stable Pairs and Wall-Crossing on $\mathbb{P}^2$

We study the wall-crossing of the moduli spaces $\mathbf{M}^α(d,1)$ of $α$-stable pairs with linear Hilbert polynomial $dm+1$ on the projective plane $\mathbb{P}^2$ as we alter the parameter $α$. When $d$ is 4 and 5, at each wall, the moduli spaces are related by a smooth blow-up morphism followed by a smooth blow-down morphism, where one can describe the blow-up centers geometrically. As a byproduct, we obtain the Poincaré polynomials of the moduli space $\mathbf{M}(d,1)$ of stable sheaves. We also discuss the wall-crossing when the number of stable components in Jordan-Hölder filtrations is three.

math.AG↗
arXiv2014

The geometry of the moduli space of one-dimensional sheaves

Let $\mathbf{M}_d$ be the moduli space of stable sheaves on $\mathbb{P}^2$ with Hilbert polynomial $dm+1$. In this paper, we determine the effective and the nef cone of the space $\mathbf{M}_d$ by natural geometric divisors. Main idea is to use the wall-crossing on the space of Bridgeland stability conditions and to compute the intersection numbers of divisors with curves by using the Grothendieck-Riemann-Roch theorem. We also present the stable base locus decomposition of the space $\mathbf{M}_6$. As a byproduct, we obtain the Betti numbers of the moduli spaces, which confirm the prediction in physics.

math.AG↗