And the end of all our exploring
Will be to arrive where we started
And know the place for the first time


- from Little Gidding by T.S. Eliot

Dongryul M. Kim (🇰🇷 김동률, 🔈 [Dong-Nyool Geem] )

Ph.D. Candidate
Dept. of Mathematics, Yale University

About Me

Hi! I am a third-year Ph.D. candidate in the Dept. of Mathematics at Yale University (with candidacy since Dec. 2021). My advisor is Prof. Hee Oh.
I have been supported by the KFAS Overseas PhD Scholarship.

Previously, I was a researcher of Team for Academic Research on GEometric Topology at KAIST, under the supervision of Prof. Harry Hyungryul Baik. I received my B.S. degree in Mathematical Sciences from KAIST on Feb. 2021 with honors (Salutatorian, Department Valedictorian).

Research Interests

  Homogeneous Dynamics & Hyperbolic Geometry
   - Discrete subgroups of Lie groups
   - Kleinian groups and Anosov representations from a dynamical point of view
   - Deformations and Rigidity
  Geometric Topology & Low-dimensional Topology
   - Hyperbolic 3-manifolds
   - Mapping class groups and dynamics on Teichmüller spaces and Complexes of curves
   - Geometric group theory

Contact Details

Email: dongryul.kim (at) yale.edu
Address:
Dept. of Mathematics, Yale Universtiy
219 Prospect St, Room 705
New Haven, CT 06511
U.S.A.

Education

Yale University

  Ph.D. in Mathematics Sep. 2021 - Present
  Advisor: Prof. Hee Oh

KAIST - Korea Advanced Institute of Science and Technology

  B.S. in Mathematical Sciences (Advanced Major) Mar. 2015 - Feb. 2021
  Graduated with Honors: Summa Cum Laude, Salutatorian, Deptartment Valedictorian
  Left for mandatory military service Mar. 2017 - Dec. 2018

Kangwon Science High School

  Valedictorian, One-year early graduation Mar. 2013 - Feb. 2015

Positions

KIAS -- Korea Institute for Advanced Study

  Visiting Jul. 2022 - Aug. 2022, Jul. 2023 - Aug. 2023
  Advisor: Prof. Hee Oh

TARGET - Team for Academic Research on GEometric Topology

  Researcher Jun. 2019 - Aug. 2021
  Advisor: Prof. Harry Hyungryul Baik

University of California, Berkeley

  Summer Session Jun. 2015 - Aug. 2015
  With $10,000 funding from KAIST Presidential Fellowship

Publications

[ MathSciNet | Google Scholar | arXiv | Note: I have used my informal middle name "M." ]

[16]
Patterson-Sullivan measures of Anosov groups are Hausdorff measures

Subhadip Dey, Dongryul M. Kim, and Hee Oh
Preprint, Submitted. [arXiv]

[15]
Ergodic dichotomy for subspace flows in higher rank

Dongryul M. Kim, Hee Oh, and Yahui Wang
Preprint, Submitted. [arXiv]

[14]
Properly discontinuous actions, growth indicators and conformal measures for transverse subgroups

Dongryul M. Kim, Hee Oh, and Yahui Wang
Preprint, Submitted. [arXiv]

[13]
Non-concentration property of Patterson-Sullivan measures for Anosov subgroups

Dongryul M. Kim and Hee Oh
Preprint, Submitted. [arXiv]

[12]
Conformal measure rigidity for representations via self-joinings

Dongryul M. Kim and Hee Oh
Preprint, Submitted. [arXiv]

[11]
Rigidity of Kleinian groups via self-joinings: measure theoretic criterion

Dongryul M. Kim and Hee Oh
Preprint, Submitted. [arXiv]

[10]
Rigidity of Kleinian groups via self-joinings

Dongryul M. Kim and Hee Oh
Inventiones Mathematicae, Vol 234 (2023), no. 3, 937–948. [Journal Link]

[9]
Reducible normal generators for mapping class groups are abundant

Hyungryul Baik, Dongryul M. Kim, and Chenxi Wu
Journal of Topology and Analysis. [Journal Link]

[8]
Hausdorff dimension of directional limit sets for self-joinings of hyperbolic manifolds

Dongryul M. Kim, Yair N. Minsky, and Hee Oh
Journal of Modern Dynamics, Vol. 19 (2023), pp. 433–453.  [Journal Link]

[7]
Tent property of the growth indicator functions and applications

Dongryul M. Kim, Yair N. Minsky, and Hee Oh
Geometriae Dedicata Vol. 218, (2024), no. 1, Paper No.14, 18 pp. [Journal Link]

[6]
Minimal asymptotic translation lengths on curve complexes and homology of mapping tori

Hyungryul Baik, Dongryul M. Kim, and Chenxi Wu
To appear in Michigan Mathematical Journal. [arXiv]

[5]
Linear growth of translation lengths of random isometries on Gromov hyperbolic spaces and Teichmüller spaces

Hyungryul Baik, Inhyeok Choi, and Dongryul M. Kim
To appear in Journal of the Institute of Mathematics of Jussieu. [Journal Link]

[4]
Simple length spectra as moduli for hyperbolic surfaces and Rigidity of length identities

Hyungryul Baik, Inhyeok Choi, and Dongryul M. Kim
Preprint, Revision sent to Annales de l'Institut Fourier. [arXiv]

[3]
On the asymptotic translation lengths on the sphere complexes and the generalized fibered cone

Hyungryul Baik, Dongryul M. Kim, and Chenxi Wu
Preprint, Submitted. [arXiv]

[2]
On the surjectivity of the Symplectic representation of the mapping class group

Hyungryul Baik, Inhyeok Choi, and Dongryul M. Kim
Topology and its Applications, Vol. 322 (2022): 108334.  [Journal Link]

[1]
Topological entropy of pseudo-Anosov maps from a typical Thurston's construction

Hyungryul Baik, Inhyeok Choi, and Dongryul M. Kim
International Mathematical Research Notices (2022), no.24, 19862–19904.  [Journal Link]

Research Talks

Invited Talks

• Mar. 04, 2024 | Yale Group Actions, Geometry and Dynamics Seminar [Link]

   Title: Ergodic dichotomy for subspace flows in higher rank

• Mar. 10, 2023 | Yale Visiting day for Prospective Ph.D. students

   Title: Kleinian groups from the sphere at infinity and self-joinings

• Oct. 19, 2022 | Yale Group Actions, Geometry and Dynamics Seminar [Link]

   Title: Tent property and directional limit sets for self-joinings of hyperbolic manifolds

• Aug. 09-10, 2022 | Dynamics seminar at Seoul National University [Link 1, Link 2]

   Two series talks: Dynamics of self-joinings of hyperbolic manifolds

• Mar. 11, 2022 | Yale Visiting day for Prospective Ph.D. students [Link]

   Title: Dynamics of self-joinings of hyperbolic manifolds

• Nov. 02, 2021 | CUNY Geometry and Topology Seminar [Link]

   Title: SLLN for asymptotic translation lengths of random isometries on Gromov hyperbolic spaces and Teichmüller spaces [Link]

• Sep. 21, 2021 | Yale Geometry and Topology Seminar [Link]

   Title: SLLN for asymptotic translation lengths of random isometries on Gromov hyperbolic spaces and Teichmüller spaces [Link]

• Apr. 22, 2020 | Virtual Seminar on Geometric Topology [Link]

   Title: Topological Entropy of pseudo-Anosov mapping classes obtained from typical Thurston Construction


Contributed Talks

• Apr. 07, 2024 | Workshop on Dynamical systems and related topics at University of Maryland, College Park: in a celebration of Giovanni Forni's 60th birthday

   Title: TBD

• Jan. 27, 2023 | Graduate Student Seminar at Yale

   Title: Symplectic representations of mapping class groups restricted on (orientable) pseudo-Anosovs

• Sep. 23, 2022 | Graduate Student Seminar at Yale

   Title: Drunken climber on trees in mapping class groups

• Feb. 22, 2022 | Graduate Student Seminar at Yale

   Title: Algebraic structure of Mapping class groups via Dynamics

• Sep. 17, 2021 | Graduate Student Seminar at Yale

   Title: Simple length spectra as moduli for hyperbolic surfaces

• Oct. 30, 2020 | Lightning talk at Geometric Group Theory in East Asia [Link]

   Title: A Nexus of Probability and Geometric topology

Teaching

Yale University

 Math 115 Calculus of Functions of One Variable II

   Instructor Spring 2024

 Math 302 Vector Analysis and Integration on Manifolds

   Grader Fall 2023

 Math 435 Differential Geometry

   Grader Spring 2023

 Math 244 Discrete Mathematics

   TA Spring 2023

 Math 302 Vector Analysis and Integration on Manifolds

   Grader Fall 2022

 Math 120 Calculus of Functions of Several Variables

   Coach Fall 2022


KAIST

 MAS102 Calculus II

   Tutor for Freshmen Fall 2020

 MAS101 Calculus I

   Tutor for Freshmen Spring 2020

 MAS102 Calculus II

   Tutor for Freshmen Fall 2019

Academic Trips

Upcoming

 Workshop: Group Actions with Hyperbolicity and Measure Rigidity [Link]

   May. 27 - 31, 2024 Paris, France

 Workshop on Dynamical systems and related topics at University of Maryland, College Park: in a celebration of Giovanni Forni's 60th birthday [Link]

   Apr. 04 - 07, 2024 College Park, MD, United States


Past

 Dynamics: Classical, Modern and Quantum [Link]

   Jun. 26 - 30, 2023 Evanston, IL, United States

 Homogeneous dynamics and geometry in higher rank Lie groups [Link]

   Jun. 19 - 23, 2023 IHES, France

 Dynamics, Rigidity and Arithmetic in Hyperbolic Geometry [Link]

   May. 15 - May. 19, 2023 Providence, RI, United States

 Four Decades of the Einstein Chair Seminar in honor of Dennis Sullivan [Link]

   Jan. 17 - Jan. 19, 2023 NYC, NY, United States

 THE CIRCLE AT INFINITY: An International colloquium in honor of Curtis T. McMullen [Link]

   Jun. 15 - Jun. 17, 2022 Boston, MA, United States

 Ergodic geometry, number theory and Margulis legacy: the next generation [Link]

   Jun. 12 - Jun. 15, 2022 Chicago, IL, United States

 Flexibility and rigidity in dynamical systems [Link]

   Mar. 07 - Mar. 11, 2022 Stony Brook, NY, United States

 Institute for Advanced Study, Park City Mathematics Institute: Quantum Field Theory and Manifold Invariants

   Jun. 30 - Jul. 21, 2021 Park City, UT, United States

Collaborators (Math)

(Harry) Hyungryul Baik [ Webpage ]
  Associate Professor, KAIST
Inhyeok Choi [ Webpage ]
  June E Huh Fellow, Center for Mathematical Challenges of KIAS
Subhadip Dey [ Webpage ]
  Gibbs Assistant Professor, Yale University
Yair N. Minsky [ Webpage ]
  Einar Hille Professor of Mathematics, Yale University
Hee Oh [ Webpage ]
  Abraham Robinson Professor of Mathematics, Yale University
Yahui Wang
  Ph.D. Student, Yale University
Chenxi Wu [ Webpage ]
  Assistant Professor, The University of Wisconsin-Madison