Jae Choon Cha is a Professor of Mathematics and Mueunjae Chair Professor at POSTECH.  Also, he is an Affiliate Professor at KIAS and the Editor-in-Chief of the Bulletin of the Korean Mathematical Society.

 2019 Fall MATH 524 Algebraic Topology I
 Lecture Notes: Introduction to Geometric Topology 2018 Spring at POSTECH
Research on Geometric Topology
• Interplay 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, maintained by Charles Livingston and me.

1. Primary decomposition for topologically slice knots, Four Manifolds: Confluence of High and Low Dimensions, July 11, 2019, Fields Institute, Toronto, Ontario, Canada.
2. 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.
3. Transfinite lower central series and Milnor invariants of 3-manifolds, Johnson homomorphisms and related topics 2019, May 14, 2019, University of Tokyo, Tokyo, Japan.
4. 공간의 현대적 수학 (Modern mathematics of spaces), 무은재기념강연 (Mueunjae Lecture), April 25, 2019, POSTECH, Pohang, Korea.
5. Homotopical properties and freely slicing good boundary links, Low dimensional topology and number theory XI, March 13, 2019, Osaka University, Osaka, Japan.
6. 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.
7. Localization of groups and Milnor invariants of 3-manifolds, Workshop ⌈New Development of low-dimensional topology⌋, December 8, 2018, Hakone, Japan.
8. 4-dimensional $L^2$-acyclic bordism, Seoul-Tokyo conference, December 1, 2018, KIAS, Seoul, Korea.
9. 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.
10. Whitney towers in a rational homology 4-ball, Topology in Australia and South Korea, IBS-CGP Conference, April 26, 2018, Pohang, Korea.
11. Milnor’s question on transfinite invariants, Knotted Embeddings in Dimensions 3 and 4, February 15, 2018, CIRM, Marseille, France.
12. Milnor’s transfinite invariant problem for 3-manifolds, The 13th East Asian School of Knots and Related Topics, January 31, 2018, Daejeon, Korea.
13. $L^2$-acyclic bordism and knot concordance, December 19, 2017, University of Regensburg, Regensburg, Germany.
14. Transfinite Milnor invariants of 3-manifolds, December 8, 2017, University of Warsaw, Warsaw, Poland.
15. Transfinite Milnor invariants of 3-manifolds, December 4, 2017, Max Planck Institute for Mathematics, Bonn, Germany.
16. 4-dimensional $L^2$-acyclic bordism of 3-manifolds, November 21, 2017, University Paris Diderot (Paris 7), Paris, France.
17. Cheeger-Gromov $L^2$ rho-invariants and low dimensional topology, MFO workshop: Interactions between Low-dimensional Topology and Complex Algebraic Geometry, October 23, 2017, Oberwolfach, Germany.
18. Milnor invariants and rational Whitney towers, September 25, 2017, St. Petersburg State University, St. Petersburg, Russia.

### List of all papers

1. Two-solvable and two-bipolar knots with large four-genera (with Allison N. Miller and Mark Powell)
• Preprint arxiv:1901.02060 (31 pages)
2. A family of freely slice good boundary links (with Min Hoon Kim and Mark Powell)
Mathematische Annalen, to appear.
3. The bipolar filtration of topologically slice knots (with Min Hoon Kim)
Preprint arxiv:1710.07803 (23 pages)
4. Unknotted gropes, Whitney towers, and doubly slicing knots (with Taehee Kim)
Transactions of the American Mathematical Society 371 (2019), 2383–2429.
5. Rational Whitney tower filtration of links
Mathematische Annalen 370 (2018), no. 3, 963–992.
6. Whitney towers and abelian invariants of knots (with Mark Powell and Kent E. Orr)
Mathematische Zeitschrift, to appear.
Published • Preprint arXiv:1606.03608 (34 pages)