Youngjin Bae
My research interest covers symplectic geometry, contact topology, and their applications to dynamics, graph and knot theory. Nowadays, I am trying to extend my research area toward the relation between Legendrian theory and cluster theory.
Preprints and Publications
Legendrian links and cluster structures
[3] Lagrangian cobordism of positroid links. arXiv:2305.16232. (with Johan Asplund, Orsola Capovilla-Searle, Marco Castronovo, Caitlin Leverson, Angela Wu)
[2] Lagrangian fillings for Legendrian links of affine type. arXiv:2107.04283. (with Byung Hee An and Eunjeong Lee)
[1] Lagrangian fillings for Legendrian links of finite type. arXiv:2101.01943. (with Byung Hee An and Eunjeong Lee)
Legendrian graphs related
[5] Augmentations are sheaves for Legendrian graphs. J. Symplectic Geom. 20 (2022), no 2, 259–416. arXiv:1912.10782. (with Byung Hee An and Tao Su)
[4] Augmentations and ruling polynomials for Legendrian graphs. Algebr. Geom. Topol. 22 (2022), 2079–2185. arXiv:1911.11563. (with Byung Hee An and Tao Su)
[3] Ruling invariants for Legendrian graphs. J. Symplectic Geom. 20 (2022), no 1, 49–98. arXiv:1911.08668. (with Byung Hee An and Tamás Kálmán)
[2] A Chekanov-Eliashberg algebra for Legendrian graphs. J. Topol. 13 (2020), no 2, 777-869, arXiv:1803.05717. (with Byung Hee An)
[1] Legendrian singular links and singular connected sums. J. Symplectic Geom. 16 (2018), no 4, 885–930. arXiv:1503.00818. (with Byung Hee and Seonhwa Kim)
Knot theory related
[2] Formality of Floer complex of the ideal boundary of hyperbolic knot complement. Asian J. Math. 25 (2021), no 1, 117–176. arXiv:1901.02258. (with Seonhwa Kim and Yong-Geun Oh)
[1] A wrapped Fukaya category of knot complement. Math. Z. 304 (2023), no 29, 885–930. arXiv:1901.02239. (with Seonhwa Kim and Yong-Geun Oh)
Hamiltonian dynamics related
[4] Periodic orbits in virtually contact structures. J. Topol. Anal. 12, (2020) No. 2, 371-418. arXiv:1705.02208. (with Kevin Weigand and Kai Zehmisch)
[3] On the growth sequence for symplectically hyperbolic manifolds. Israel J. Math. 204 (2014), no. 1, 417–430. arXiv:1211.2523.
[2] On magnetic leaf-wise intersections. J. Topol. Anal. 4 (2012), no. 3, 361–411. arXiv:1111.5115.
[1] Continuation homomorphism in Rabinowitz Floer homology for symplectic deformations. Math. Proc. Cambridge Philos. Soc. 151 (2011), no 3, 471–502. arXiv:1010.1649. (with Urs Frauenfelder)
Other activities
Honors and awards
[2] Research Grant(우수신진연구, 202200480002), Legendrian, N-graphs, and their applications, March 2022 – February 2025, KRW 175Million, National Research Foundation, Korea.
[1] Research Grant(중견연구, 2020R1A2C1A01003201), Legendrian, Fukaya Category and Mirror Symmetry, March 2020 – February 2023, KRW 450Million, National Research Foundation, Korea. (with Byung Hee An at at Department of Mathematics Education of Kyungpook National University.)
Conferences co-organized
[10] Workshop for Young Symplectic Geometers VI, Pusan National University, June 9-11 2023.
[9] Workshop for Young Symplectic Geometers V, Sungkyunkwan University, February 24-26 2023.
[8] Workshop for Young Symplectic Geometers IV, Incheon National University, August 16-18 2022.
[7] Workshop for Young Symplectic Geometers III, Yeonsei University, February 18-20 2022.
[6] Workshop for Young Symplectic Geometers II, Ramada Plaza Jeju Hotel, Jeju, October 29-31 2021
[5] Workshop for Young Symplectic Geometers I, Kyungpook National University, June 18-20 2021.
[4] Legendirans, Cluster Algebras, and Mirror symmetry, On-line, Korea, January 11∼15 2021.
[3] CIMPA-NIMS Research School on symplectic embeddings, systolic inequalities and celestial mechanics, NIMS, Korea, June 11∼20 2018.
[2] Pohang Math Workshop, IBS-CGP, Korea, November 24∼27 2016.
[1] CIMPA-NIMS Research School on dynamical systems: Examples, billiards, and the 3-body problem, NIMS, Korea, May 25∼June 3 2015.