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- MATH 422 Introduction to Geometric Topology
2023 Spring
- MATH 422 Introduction to Geometric Topology
Research: Geometric Topology
Topology of manifolds, knots and links- Related algebra, homotopy theory, and $L^2$-invariants
- Smoothing topological surfaces in smooth 4-manifolds, The 18th East Asian Conference on Geometric Topology, February 8, 2023.
- Milnor’s invariants for links and 3-manifolds, Department Colloquium, Kyungpook National University, September 22, 2022, Daegu, Korea.
- Primary decomposition in low dimensional topology, Departmental Lecture, Chungnam National University, April 07, 2022, Daejeon, Korea.
- Primary decomposition for topologically slice knots, The 15th East Asian Conference on Geometric Topology, February 12, 2020, RIMS, Kyoto, Japan.
- 공간의 현대적 수학 (Modern mathematics of spaces), 대한수학회 수학콘서트 (Mathematical Concert of the Korean Mathematical Society), October 25, 2019, Hongik University, Seoul, Korea.
- 공간의 수학 (Mathematics of spaces), IBS-CGP 수학 문화 강연 (IBS-CGP Mathematical Cultural Lecture), October 19, 2019, Pohang City Hall, Pohang, Korea.
- Primary decomposition for topologically slice knots, Four Manifolds: Confluence of High and Low Dimensions, July 11, 2019, Fields Institute, Toronto, Ontario, Canada.
- 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.
- Transfinite lower central series and Milnor invariants of 3-manifolds, Johnson homomorphisms and related topics 2019, May 14, 2019, University of Tokyo, Tokyo, Japan.
- 공간의 현대적 수학 (Modern mathematics of spaces), 무은재기념강연 (Mueunjae Memorial Lecture), April 25, 2019, POSTECH, Pohang, Korea.
- Homotopical properties and freely slicing good boundary links, Low dimensional topology and number theory XI, March 13, 2019, Osaka University, Osaka, Japan.
- 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.
- Program Committee, The 18th East Asian Conference on Geometric Topology, February 6-9, 2023, online conference hosted by Soochow University.
- Organizer, 2022 Fall PK2 Topology Workshop, Nov 1-4, 2022, Busan, Korea.
- Organizer, 2022 Spring PK2 Topology Workshop, May 29-June 1, 2022, Jeju, Korea.
- Local Organizing Committee and Program Committee, The 17th East Asian Conference on Geometric Topology, January 18-21, 2022, online conference.
- Program Committee, The 16th East Asian Conference on Geometric Topology, January 25-28, 2021, online conference hosted by University of Tokyo.
- Program Committee, The 15th East Asian Conference on Geometric Topology, February 10-13, 2020, RIMS, Kyoto University, Japan.
- Program Committee, The 14th East Asian Conference on Geometric Topology, January 21-24, 2019, Peking University, Beijing, China.
- Organizer, 2018 Mini-workshop on Low Dimensional Topology, September 14-15, 2018, POSTECH, Pohang, Korea.
- Organizer, Hyperbolic 3-manifolds and Related Topics, June 18-22, 2018, POSTECH, Pohang, Korea.
Selected Publications
- Transfinite Milnor invariants for 3-manifolds (with Kent E. Orr)
Journal of the European Mathematical Society (JEMS), to appear.
• Published (online first) • Preprint arxiv:2002.03208 - A topological approach to Cheeger-Gromov universal bounds for von Neumann ρ-invariants
Communications on Pure and Applied Mathematics 69 (2016), no. 6, 1154–1209.
• Published • Preprint arXiv:1405.1805 - Casson towers and slice links (with Mark Powell)
Inventiones Mathematicae 205 (2016), no.2, 413–457.
• Published • Preprint arXiv:1411.1621 - $L^2$-signatures, homology localization, and amenable groups (with Kent E. Orr)
Communications on Pure and Applied Mathematics 65 (2012), no. 6, 790–832.
• Published • Preprint arXiv:0910.3700 - Link concordance, homology cobordism, and Hirzebruch-type defects from iterated $p$-covers
Journal of the European Mathematical Society (JEMS) 12 (2010), no. 3, 555–610.
• Published • Preprint arXiv:0705.0088 - The structure of the rational concordance group of knots
Memoirs of the American Mathematical Society 189 (2007), no. 885, x+95pp.
• Published • Google Books • Preprint arXiv:math/0609408