Research on Geometric Topology
  • Figure eight on my caffè latteInterplay between topology of dimension 3 and 4
  • Knot theory: placement problems of manifold pairs
  • Related algebra, homotopy theory, and $L^2$-invariants

KnotInfo: a table of invariants of classical knots, created by Charles Livingston and me.

  1. Milnor’s invariants for links and 3-manifolds, Department Colloquium, Kyungpook National University, September 22, 2022, Daegu, Korea.
  2. Primary decomposition in low dimensional topology, Departmental Lecture, Chungnam National University, April 07, 2022, Daejeon, Korea.
  3. Primary decomposition for topologically slice knots, The 15th East Asian Conference on Geometric Topology, February 12, 2020, RIMS, Kyoto, Japan.
  4. 공간의 현대적 수학 (Modern mathematics of spaces), 대한수학회 수학콘서트 (Mathematical Concert of the Korean Mathematical Society), October 25, 2019, Hongik University, Seoul, Korea.
  5. 공간의 수학 (Mathematics of spaces), IBS-CGP 수학 문화 강연 (IBS-CGP Mathematical Cultural Lecture), October 19, 2019, Pohang City Hall, Pohang, Korea.
  6. Primary decomposition for topologically slice knots, Four Manifolds: Confluence of High and Low Dimensions, July 11, 2019, Fields Institute, Toronto, Ontario, Canada.
  7. Filtering and decomposing the smooth concordance group of topologically slice knots, AIM workshop: smooth concordance classes of topologically slice knots, June 3, 2019, American Institute of Mathematics, San Jose, California, USA.
  8. Transfinite lower central series and Milnor invariants of 3-manifolds, Johnson homomorphisms and related topics 2019, May 14, 2019, University of Tokyo, Tokyo, Japan.
  9. 공간의 현대적 수학 (Modern mathematics of spaces), 무은재기념강연 (Mueunjae Memorial Lecture), April 25, 2019, POSTECH, Pohang, Korea.
  10. Homotopical properties and freely slicing good boundary links, Low dimensional topology and number theory XI, March 13, 2019, Osaka University, Osaka, Japan.
  11. Freely slicing good boundary links with a homotopy trivial plus property, Topology of Manifolds: Interactions between high and low dimensional topology, January 18, 2019, MATRIX Research Institute, Creswick, Victoria, Australia.
  12. Localization of groups and Milnor invariants of 3-manifolds, Workshop ⌈New Development of low-dimensional topology⌋, December 8, 2018, Hakone, Japan.
  13. 4-dimensional $L^2$-acyclic bordism, Seoul-Tokyo conference, December 1, 2018, KIAS, Seoul, Korea.
  14. Hirzebruch-type $L^2$-signature defects and topology of dimension 3 and 4, 2018 Joint Meeting of Korean Mathematical Society and German Mathematical Society, October 4, 2018, Seoul, Korea.

Selected Papers

List of all papers

  1. Transfinite Milnor invariants for 3-manifolds (with Kent E. Orr)
    Journal of the European Mathematical Society (JEMS), to appear.
    • Preprint arxiv:2002.03208 (55 pages)
  2. Primary decomposition in the smooth concordance group of topologically slice knots
    Forum of Mathematics, Sigma 9 (2021), E57.
    Published • Preprint arxiv:1910.14629
  3. Two-solvable and two-bipolar knots with large four-genera (with Allison N. Miller and Mark Powell)
    Mathematical Research Letters 28 (2021), no. 2, 331–382.
    Published • Preprint arxiv:1901.02060
  4. A family of freely slice good boundary links (with Min Hoon Kim and Mark Powell)
    Mathematische Annalen 376 (2020), 1009–1030.
    • Published • Preprint arxiv:1807.05474
  5. The bipolar filtration of topologically slice knots (with Min Hoon Kim)
    Advances in Mathematics 388 (2021), 107868.
    • Published • Preprint arxiv:1710.07803