Elena Kim

activity

20192026

collaborators

12 papers

math.SP2026

Discrete Mixed Quantization for Cat Maps

Elena Kim, Qiaochu Ma

In this paper, we develop a mixed quantization technique for graph vector bundles that combines semiclassical analysis and quantum cat maps. We apply it to study the Kesten--McKay…

math.SP2026

Polynomial bounds for eigenfunctions and eigenvalues on random covers of hyperbolic surfaces

Elena Kim, Zhongkai Tao

Let $X$ be a compact connected orientable hyperbolic surface and let $X_{n}$ be a degree $n$ cover, taken uniformly at random. We show that, with high probability, the $L^{\infty}$ nor…

math.AP2025

Semiclassical Measures on Hyperbolic Manifolds

Elena Kim, Nicholas Miller

We examine semiclassical measures for Laplace eigenfunctions on compact hyperbolic $(n + 1)$ -manifolds. We prove their support must contain the cosphere bundle of a compact immersed…

math.AP2024

Characterizing the support of semiclassical measures for higher-dimensional cat maps

Elena Kim, Theresa C. Anderson, Robert J. Lemke Oliver

Quantum cat maps are toy models in quantum chaos associated to hyperbolic symplectic matrices $A \in Sp (2 n, Z)$ . The macroscopic limits of sequences of eigenf…

math.SP2023

Bounds on Eigenfunctions of Quantum Cat Maps

Elena Kim, Robert Koirala

We study $ℓ^{\infty}$ norms of $ℓ^{2}$ -normalized eigenfunctions of quantum cat maps. For maps with short quantum periods (constructed by Bonechi and de Bièvre), we show that the…

math.OA2023

The strongly Leibniz property and the Gromov--Hausdorff propinquity

Konrad Aguilar, Stephan Ramon Garcia, Elena Kim +1

We construct a new version of the dual Gromov--Hausdorff propinquity that is sensitive to the strongly Leibniz property. In particular, this new distance is complete on the class o…

math.DG2022

Spectral Analysis of the Kohn Laplacian on Lens Spaces

Colin Fan, Elena Kim, Ian Shors +3

We obtain an analog of Weyl's law for the Kohn Laplacian on lens spaces. We also show that two 3-dimensional lens spaces with fundamental groups of equal prime order are isospectra…

math.OA2021

Frobenius-Rieffel norms on finite-dimensional C*-algebras

Konrad Aguilar, Stephan Ramon Garcia, Elena Kim

In 2014, Rieffel introduced norms on certain unital C*-algebras built from conditional expectations onto unital C*-subalgebras. We begin by showing that these norms generalize the…

math.CV2021

A Tauberian Approach to an Analog of Weyl's law for the Kohn Laplacian on Compact Heisenberg Manifolds

Colin Fan, Elena Kim, Yunus E. Zeytuncu

Let $M = Γ ∖ H_{d}$ be a compact quotient of the $d$ -dimensional Heisenberg group $H_{d}$ by a lattice subgroup $Γ$ . We show that the eigenvalue counting functi…

math.NT2020

Constructions of Generalized MSTD Sets in Higher Dimensions

Elena Kim, Steven J. Miller

Let $A$ be a set of finite integers, define $A + A = {a_{1} + a_{2} : a_{1}, a_{2} \in A}, A - A = {a_{1} - a_{2} : a_{1}, a_{2} \in A},$ and for non-negative integers $s$ and $d$ define $…

math.NT2020

Tinkering with Lattices: A New Take on the Erdős Distance Problem

Elzbieta Boldyriew, Elena Kim, Steven J. Miller +4

The Erdős distance problem concerns the least number of distinct distances that can be determined by $N$ points in the plane. The integer lattice with $N$ points is known as \texti…

math.SP2019

Sobolev and Schatten Estimates for the Complex Green Operator on Spheres

Elena Kim, W. Jacob Ogden, Tommie Reerink +1

The complex Green operator $G$ on CR manifolds is the inverse of the Kohn-Laplacian $□_{b}$ on the orthogonal complement of its kernel. In this note, we prove Schatte…