arXiv subjects

Youngmin Lee

Publications and source records attributed to Youngmin Lee.

7 recordsLinked to original sources

arXiv2026

H2G: Hierarchy-Aware Hyperbolic Grouping for 3D Scenes

Hierarchical 3D grouping aims to recover scene groups across multiple granularities, from fine object parts to complete objects, without relying on semantic labels or a fixed vocabulary. The main challenge is to transform 2D foundation-model cues into coherent hierarchy supervision and embed that hierarchy in a 3D representation. We propose H2G, a hyperbolic affinity field for hierarchical 3D grouping. Our method derives semantically organized tree supervision by interpreting foundation-model affinities through Dasgupta's objective for similarity-based hierarchical clustering. This supervision is distilled into a single Lorentz hyperbolic feature field, whose geometry is well suited for tree-like branching structures. A hierarchy-aware objective aligns the field with fine-level assignments, coarse object structure, compact feature clusters, and LCA (Lowest Common Ancestor) ordering. This formulation represents multiple grouping levels in one feature space, enabling semantic hierarchical grouping grounded in 2D foundation-model knowledge.

cs.CV↗

arXiv2026

Quantum ergodicity of Eisenstein series for Bianchi groups

We prove the quantum ergodicity of Eisenstein series on the arithmetic hyperbolic 3-manifold $\operatorname{PSL}_2(\mathcal{O}_F)\backslash \mathbb{H}^3$, where $F$ is an imaginary quadratic field with ring of integers $\mathcal{O}_F$ and class number $h_F\geq 1$. This extends the work of Koyama, who proved the result in the case $h_F=1$, and establishes the first instance of quantum ergodicity of Eisenstein series over number fields with nontrivial class groups.

math.NT↗

arXiv2026

On the structure of prime-detecting quasimodular forms in higher levels

Craig, van Ittersum, and Ono conjectured that every prime-detecting quasimodular form of level $1$ is a quasimodular Eisenstein series. This conjecture was proved by Kane--Krishnamoorthy--Lau and by van Ittersum--Mauth--Ono--Singh independently. However, in higher levels, prime-detecting quasimodular forms need not be Eisenstein. Recently, Kane, Krishnamoorthy, and Lau formulated a natural higher level analogue of the above conjecture and proved it by analytic methods. In a similar direction, but via an alternative approach based on the independence of characters of $\ell$-adic Galois representations, we prove that any prime-detecting quasimodular form on $\Gamma_{0}(N)$ belongs to the direct sum of the spaces of quasimodular Eisenstein series and quasimodular oldforms. Moreover, for a quasimodular form $f$ that is not prime-detecting, we give an upper bound for the number of primes $p$ less than $X$ for which the $p$-th Fourier coefficient of a quasimodular form vanishes.

math.NT↗

arXiv2026

Rankin-Cohen Bracket for Vector-Valued Modular Forms

In this paper, we explore the relationship between Rankin-Cohen brackets for vector-valued modular forms and Petersson's inner products, deriving an explicit description of the adjoint map for the bracket operator. The study extends to the cases of Jacobi forms and skew-holomorphic Jacobi forms, establishing connections between their respective Rankin-Cohen brackets and those defined for vector-valued modular forms through an isomorphism. Adjoint maps for these extended bracket operators are also examined.

math.NT↗

arXiv2024

The number of automorphic representations of $\mathrm{GL}_2$ with exceptional eigenvalues

We obtain an upper bound for the dimension of the cuspidal automorphic forms for $\mathrm{GL}_2$ over a number field, whose archimedean local representations are not tempered. More precisely, we prove the following result. Let $F$ be a number field and $\mathbb{A}_{F}$ be the ring of adeles of $F$. Let $\mathcal{O}_{F}$ be the ring of integers of $F$. Let $\mathfrak{X}_{F,\mathrm{ex}}$ be the set of irreducible cuspidal automorphic representations $π$ of $\mathrm{GL}_2(\mathbb{A}_{F})$ with the trivial central character such that for each archimedean place $v$ of $F$, the local representation of $π$ at $v$ is an unramified principal series and is not tempered. For an ideal $J$ of $\mathcal{O}_{F}$, let $\mathrm{K}_{0}(J)$ be the subgroup of $\mathrm{GL}_2(\mathbb{A}_{F})$ corresponding to $Γ_0(J) \subset \mathrm{SL}_2(\mathcal{O}_F)$. Let $r_1$ be the number of real embeddings of $F$ and $r_2$ be the number of conjugate pairs of complex embeddings of $F$. Using the Arthur-Selberg trace formula, we have \begin{equation*} \sum_{π\in \mathfrak{X}_{F,\mathrm{ex}}} \dim π^{\mathrm{K}_0(J)} \ll_{F} \frac{[\mathrm{SL}_2(\mathcal{O}_{F}) : Γ_0(J)]}{(\log (N_{F/\mathbb{Q}}(J)))^{2r_1+3r_2}} \quad \text{ as } \quad |N_{F/\mathbb{Q}}(J)|\to \infty. \end{equation*} From this result, we obtain the result on an upper bound for the number of Hecke-Maass cusp forms of weight $0$ on $Γ_0(N)$ which do not satisfy the Selberg eigenvalue conjecture.

math.NT↗

arXiv2022

Newman's conjecture for the partition function modulo integers with at least two distinct prime divisors

Let $M$ be a positive integer and $p(n)$ be the number of partitions of a positive integer $n$. Newman's Conjecture asserts that for each integer $r$, there are infinitely many positive integers $n$ such that \[ p(n)\equiv r \pmod{M}. \] For a positive integer $d$, let $B_{d}$ be the set of positive integers $M$ such that the number of prime divisors of $M$ is $d$. In this paper, we prove that for each positive integer $d$, the density of the set of positive integers $M$ for which Newman's Conjecture holds in $B_{d}$ is $1$. Furthermore, we study an analogue of Newman's Conjecture for weakly holomorphic modular forms on $\Gamma_0(N)$ with nebentypus, and this applies to $t$-core partitions and generalized Frobenius partitions with $h$-colors.

math.NT↗

arXiv2013

Exchange Bias Effect in Au-Fe3O4 Nanocomposites

We report exchange bias (EB) effect in the Au-Fe3O4 composite nanoparticle system, where one or more Fe3O4 nanoparticles are attached to an Au seed particle forming dimer and cluster morphologies, with the clusters showing much stronger EB in comparison with the dimers. The EB effect develops due to the presence of stress in the Au-Fe3O4 interface which leads to the generation of highly disordered, anisotropic surface spins in the Fe3O4 particle. The EB effect is lost with the removal of the interfacial stress. Our atomistic Monte-Carlo studies are in excellent agreement with the experimental results. These results show a new path towards tuning EB in nanostructures, namely controllably creating interfacial stress, and open up the possibility of tuning the anisotropic properties of biocompatible nanoparticles via a controllable exchange coupling mechanism.

cond-mat.mtrl-sci↗