About

Michelle Chu is an Assistant Professor and McKnight Land-Grant Professor at the University of Minnesota – Twin Cities. She completed her PhD at the University of Texas at Austin in 2018 under the supervision of Alan W. Reid. Prior to joining UMN, she was an NSF Postdoctoral Fellow at the University of Illinois at Chicago and the University of California Santa Barbara. Her research focuses on topics in geometry and topology, particularly related to hyperbolic manifolds, arithmetic groups, and low-dimensional topology. She has contributed to the understanding of arithmetic hyperbolic manifolds, virtual properties of Bianchi groups, and embeddings of hyperbolic manifolds, among other areas. Chu is actively involved in teaching both undergraduate and graduate courses, including Elementary Linear Algebra and Graduate Differential Topology. She is partially supported by NSF grant DMS-2441043 and maintains an active research presence at UMN.

Research topics

• Mathematical analysis
• Pure mathematics
• Computer Science
• Mathematics
• Artificial Intelligence
• Engineering
• Physics

Selected publications

• Counting Salem numbers arising from arithmetic hyperbolic orbifolds

  ArXiv.org · 2025-08-11

  preprintOpen access1st authorCorresponding

  The relationship between Salem numbers and short geodesics has been fruitful in quantitative studies of arithmetic hyperbolic orbifolds, particularly in dimensions 2 and 3. In this article, we push these connections even further. The primary goals are: (1) to bound the proportion of Salem numbers of degree up to $n+1$ in the commensurability class of classical arithmetic lattices in any odd dimension $n$; (2) to improve lower bounds for the strong exponential growth of averages of multiplicities in the geodesic length spectrum of non-compact arithmetic orbifolds. In order to accomplish these goals, we bound, for a fixed square-free integer $D$, the count of Salem numbers with minimal polynomial $f$ satisfying $f(1)f(-1)=-D$ in $\mathbb{Q}^{\times}/\mathbb{Q}^{\times 2}$. To do this, we make use of results on the distribution of Salem numbers, as well as classical methods for counting Pythagorean triples and Gauss' lattice-counting argument. To this end, we give a generalization of the count of Pythagorean triples and provide an elementary proof which may be of independent interest.

  PublisherOA PDFDOI

• Salem numbers and commensurability classes of arithmetic hyperbolic manifolds

  ArXiv.org · 2025-06-25

  preprintOpen access1st authorCorresponding

  In this article we show that given a Salem number $λ$, a totally real number field $k\subseteq\mathbb{Q}(λ+λ^{-1})$, and a positive integer $n\geq\mathrm{deg}_k(λ)-1$, there exist infinitely many commensurability classes of arithmetic hyperbolic $n$-manifolds defined over $k$ which contain a geodesic of length $\logλ$.

  PublisherOA PDFDOI

• Mixed-platonic 3-manifolds

  arXiv (Cornell University) · 2024-07-01

  preprintOpen access

  We introduce a class of cusped hyperbolic $3$-manifolds that we call mixed-platonic, composed of regular ideal hyperbolic polyhedra of more than one type, which includes certain previously-known examples. We establish basic facts about mixed-platonic manifolds which allow us to conclude, among other things, that there is no mixed-platonic hyperbolic knot complement with hidden symmetries.

  PublisherOA PDFDOI

• Totally geodesic hyperbolic 3-manifolds inhyperbolic link complements of tori in S4

  Pacific Journal of Mathematics · 2023-11-03

  articleOpen access1st authorCorresponding

  We prove that certain hyperbolic link complements of 2-tori in S 4 do not contain closed embedded totally geodesic hyperbolic 3-manifolds.

  PublisherOA PDFDOI

• PRESCRIBED VIRTUAL HOMOLOGICAL TORSION OF 3-MANIFOLDS

  Journal of the Institute of Mathematics of Jussieu · 2022-06-08

  article1st authorCorresponding

  Abstract Let M be an irreducible $3$ -manifold M with empty or toroidal boundary which has at least one hyperbolic piece in its geometric decomposition, and let A be a finite abelian group. Generalizing work of Sun [20] and of Friedl–Herrmann [7], we prove that there exists a finite cover $M' \to M$ so that A is a direct factor in $H_1(M',{\mathbb Z})$ .

  PublisherDOI

• Embedding closed hyperbolic 3–manifolds insmall volume hyperbolic 4–manifolds

  arXiv (Cornell University) · 2021 · 3 citations

  1st authorCorresponding
  • Computer Science
  • Mathematics
  • Pure mathematics

  In this paper we study existence and lack thereof of closed embedded orientable co-dimension one totally geodesic submanifolds of minimal volume cusped orientable hyperbolic manifolds.

  PublisherOA PDF

• Totally geodesic hyperbolic 3-manifolds in hyperbolic link complements of tori in $S^4$

  arXiv (Cornell University) · 2021-09-03

  preprintOpen access1st authorCorresponding

  In this paper we prove that certain hyperbolic link complements of $2$-tori in $S^4$ do not contain closed embedded totally geodesic hyperbolic $3$-manifolds.

  PublisherOA PDFDOI

• Ancillary files for “A hyperbolic counterpart to Rokhlin's cobordism theorem”

  Harvard Dataverse · 2020-06-01

  datasetOpen access1st authorCorresponding

  SageMath worksheets & Wolfram Mathematica notebooks

  PublisherDOI

• Prescribed virtual homological torsion of 3-manifolds

  arXiv (Cornell University) · 2020-10-08

  preprintOpen access1st authorCorresponding

  We prove that given any finite abelian group $A$ and any irreducible $3$-manifold $M$ with empty or toroidal boundary which is not a graph manifold there exists a finite cover $M' \to M$ so that $A$ is a direct factor in $H_1(M',\mathbb{Z})$. This generalizes results of Sun and of Friedl-Herrmann.

  PublisherOA PDFDOI

• Cusped_polytopes_dim_4-13.nb

  Harvard Dataverse · 2020-01-01

  datasetOpen access1st authorCorresponding

  :unav

  PublisherDOI

Recent grants

• PostDoctoral Research Fellowship

  NSF · $150k · 2018–2022

Frequent coauthors

• Alexander Kolpakov

  All-Russian Research Institute for Optical and Physical Measurements

  9 shared

• Alan W. Reid

  Rice University

  7 shared

• Daniel Groves

  University of Illinois Chicago

  2 shared

• Stephanie Jensen

  Wake Forest University

  1 shared

• Kyler Siegel

  1 shared

• Priyadip Mondal

  1 shared

• Colin Adams

  Areté Associates (United States)

  1 shared

• Neil Hoffman

  1 shared

Labs

• Michelle Chu's LabPI

  Research in arithmetic hyperbolic manifolds, 3-manifolds, and low-dimensional topology.

Education

• PhD, Mathematics

  The University of Texas at Austin

  2018

• BS

  Emory University

  2011

Awards & honors

• CSE awards
• Outstanding Achievement
• Distinguished Leadership