Hongtaek JUNG (정홍택)
Hongtaek JUNG (정홍택)
Research Fellow at KIAS
85 Hoegiro, Dongdaemun-gu, Seoul 02455, Republic of Korea.
Contact: htjung at kias.re.kr
Research Fellow at KIAS
85 Hoegiro, Dongdaemun-gu, Seoul 02455, Republic of Korea.
Contact: htjung at kias.re.kr
I earned my Ph.D. in 2019 at KAIST under the supervision of Suhyoung Choi.
Now I am working on geometric topology; geometric structures on manifolds, higher Teichmuller spaces, and Anosov representations.
(with Suhyoung Choi and Hong Chan Kim) Symplectic coordinates on PSL(3,R)-Hitchin components, Pure and applied mathematics quarterly, Vol. 16, No. 5 (2020) .
(with Suhyoung Choi) Symplectic coordinates on the deformation space of convex projective structures on 2-orbifolds ( Mathematica files ), Transformation Groups, Vol. 28, 639-693 (2023).
(with Sungkyung Kang and Seungwon Kim) Concordance invariants and the Turaev genus , IMRN, Vol. 2022 , No.19, 15410–15420 (2022).
(with Sungkyung Kang and Seungwon Kim) Stabilization and satellite construction of doubly slice links , Submitted.
(with Hyungryul Baik and KyeongRo Kim) Groups action on veering pairs and Kleinian groups, J. Lond. Math. Soc. vol 111, Paper No. e70052 (2025).
(with Suhyoung Choi) The volumes of the Hitchin-Riemann moduli spaces are infinite, Submitted.
Generic properties of Hitchin representations, Submitted.
Convergence of cataclysms and its applications, Work in progress. Draft available upon request.
Abstract: We show that if a sequence of twisted transverse cocycles converges weakly, the sequence of associated cataclysm deformations on the space of Anosov representations converges uniformly on compact sets. This leads to a generalization of the Goldman product formula. We also show that, for a split real form G whose Weyl group contains -1, the set of strongly dense G-Hitchin representations is not open.
(with students at SKKU) Volumes of thick Hitchin Riemann moduli spaces are infinite. Work in progress.
Abstract: We show that, for G=PSL(n,R), the thick parts of the G-Hitchin-Riemann moduli spaces have infinite total Atiyah-Bott-Goldman volume. This gives a partial answer to one of questions in my previous paper with Suhyoung Choi regarding volumes of Hitchin-Riemann moduli spaces.
(with Hyungryul Baik and KyeongRo Kim) Cannon-Thurston maps from veering pairs. Work in progress.
Abstract: We show that a group acting on a circle with an invariant veering pair admits a convergence action on a 2-sphere. If we further assume that the action on the circle is cofinite, we obtain a geometrically finite action on a 2-sphere, allowing us to find the Cannon-Thurston map from the Bowditch boundary to the 2-sphere.
Differential geometry lecture note based on do Carmo's "differential geometry of curves and surfaces" (in progress)
Introduction to Higher Teichmuller Spaces. 2025 HCMC Fall workshop (Jeongseon, South Korea), November 2025.
Generic properties of Hitchin representations. Teichmuller Theory and Beyond (Seoul National University, South Korea), February 2025.
Generic properties of Hitchin representations. The 20th East Asian Conference on Geometric Topology (Tokyo University, Japan), February 2025.
Hamiltonian flows on Hitchin components and their applications. JNU / SNU / KAIST Geometric Topology Workshop (KAIST, South Korea), August 2024.
Hitchin components and their symplectic structure. KIAS summer school in Geometry and Physics (KIAS, South Korea), July 2024.
Symplectic structure on Hitchin components. The 7th Workshop for Young Symplectic Geometers (Daegu, South Korea), February 2024.