건국대학교 수학과 교수
Professor, Department of Mathematics
Konkuk University
이메일: HeesangPark [AT] konkuk.ac.kr
2024.03.01--현재: 건국대학교 수학과 교수
2018.03.01--2024.02.29: 건국대학교 수학과 부교수
2014.03.01--2018.02.28: 건국대학교 수학과 조교수
2010.09.01--2014.02.28: 고등과학원 수학부 연구원
2012년 9월--11월: 방문연구, Renyi Institute of Mathematics, Hungary
이학박사 2010년 8월 서울대학교
4차원 사교다양체와 기하종수가 작은 일반형의 복소곡면 만들기
Construction of symplectic 4-manifolds and surfaces of general type with small geometric genus
복소곡면특이점의 사교위상수학적 수술
Symplectic surgery on complex surface singularities
$\mathbb{Q}$-Gorensteiness of rational homology disk smoothings of weighted homogeneous surface singularities
Journal of the Korean Mathematical Society 63 (2026), No. 3, pp. 509--539 (with Jaekwan Jeon, Dongsoo Shin)
The Kollár conjecture for $W_{p,q,r}$
Communications of the Korean Mathematical Society 41 (2026), No. 2, pp. 351--372 (with Dongsoo Shin)
Symplectic rational blowdown on rational 4-manifolds
Proceedings of the American Mathematical Society 152 (2024) no. 3, 1309--1318 (with Dongsoo Shin), arXiv:2111.07501
Lens spaces admitting minimal symplectic fillings with the second Betti number one
Bulletin of the Korean Mathematical Society 60 (2023) no. 1, 113--122 (with Dongsoo Shin)
Simple embeddings of rational homology balls and antiflips
Algebraic & Geometric Topology 21 (2021) 1857--1880 (with Giancarlo Urzúa, Dongsoo Shin), arXiv:1904.04927
Symplectic fillings of quotient surface singularities and minimal model program
Journal of the Korean Mathematical Society 58 (2021) no. 2, 419--437 (with Hakho Choi, Dongsoo Shin)
Complex surfaces of general type with $K^2=3,4$ and $p_g=q=0$
Comptes Rendus Mathématique 357 (2019), no. 3, 291--295 (with Dongsoo Shin, Yoonjeong Yang)
Milnor fibers and symplectic fillings of quotient surface singularities
Advances in Mathematics 329 (2018), 1156-1230 (with Jongil Park, Dongsoo Shin, Giancarlo Urzúa)
Rational homology balls in $2$-handlebodies
Bulletin of the Korean Mathematical Society 54 (2017), no. 6, 1927--1933 (with Dongsoo Shin)
Simply connected complex surfaces of general type with $p_g=0$ and $K^2=1,2$
Communications of the Korean Mathematical Society 32 (2017), no. 3, 479--494 (with Jongil Park, Dongsoo Shin, Ki-Heon Yun)
Smoothly embedded rational homology balls
Journal of the Korean Mathematical Society 53 (2016), no. 6, 1293--1308 (with Jongil Park, Dongsoo Shin)
Symplectic 4-manifolds via symplectic surgery on complex surface singularities
Bulletin of the Korean Mathematical Society 52 (2015), no. 4, 1213--1223 (with András Stipsicz)
Smoothings of singularities and symplectic surgery
Journal of Symplectic Geometry 12 (2014), no. 3, 585--597 (with András Stipsicz)
A complex surface of general type with $p_g=0$, $K^2=2$ and $H_1=\mathbb{Z}/4\mathbb{Z}$
Transactions of the American Mathematical Society 365 (2013), no. 11, 5713--5736 (with Jongil Park; Dongsoo Shin)
A simply connected numerical Campedelli surface with an involution
Mathematische Annalen 357 (2013), no. 1, 31--49 (with Dongsoo Shin, Giancarlo Urzúa)
Surfaces of general type with $p_g=1$ and $q=0$
Journal of the Korean Mathematical Society 50 (2013), no. 3, 493--507 (with Jongil Park, Dongsoo Shin)
Construction of surfaces of general type from elliptic surfaces via $\mathbb{Q}$-Gorenstein smoothing
Mathematische Zeitschrift 272 (2012), no. 3--4, 1243–-1257 (with JongHae Keum, Yongnam Lee)
A complex surface of general type with $p_g=0$, $K^2=3$ and $H_1=\mathbb{Z}/2\mathbb{Z}$
Bulletin of the Korean Mathematical Society 47 (2010), no. 6, 1269--1274 (with Jongil Park, Dongsoo Shin)
A simply connected surface of general type with $p_g=0$ and $K^2=4$
Geometry & Topology 13 (2009), no. 3, 1483--1494 (with Jongil Park, Dongsoo Shin)
A simply connected surface of general type with $p_g=0$ and $K^2=3$
Geometry & Topology 13 (2009), no. 2, 743--767 (with Jongil Park, Dongsoo Shin)
Nonlinear neighborhoods of smooth curves and arbitrarily negative Wahl defects
arXiv:2610.21093 (with Dongsoo Shin)
Positivity of Wahl defects and specialization of reflexive powers of the canonical sheaf
arXiv:2610.21092 (with Dongsoo Shin)
Normal complex surface singularities with rational homology disk smoothings
arXiv:2610.20991 (Márton Beke, Dongsoo Shin, András Stipsicz)
Deformations of weighted homogeneous surface singularities with big central node,
arXiv:2305.14738 (with Jaekwan Jeon, Dongsoo Shin)
Weighted homogeneous surface singularities admitting rational homology disk smoothings
preprint (with Dongsoo Shin)
We study rational homology disk smoothings using canonical-cover representations and specialization of reflexive canonical powers. We prove that the geometric-genus representation of the canonical covering group and its complex conjugate form a direct summand of the reduced regular representation. Vanishing canonical Riemann--Roch corrections yields explicit equations for the Seifert invariants. Together with character restrictions and numerical identities, these equations determine the three-arm families of central weight two without assuming smoothability.
Projective compactifications determine the remaining graphs, while elliptic pencils explain the four-arm attachment points and the parameter independence of their cross ratios. We construct strong \(\mathbb{Q}\)-Gorenstein rational homology disk smoothings by deforming canonical-cover equations and lifting generators of the full first syzygy module. These results recover the known dual graph and analytic classification.
The classification of taut surface singularities via representations from logarithmic vector fields
preprint (with Dongsoo Shin)
We study logarithmic vector fields on exceptional cycles through finite-dimensional representations and recover Laufer's classification of taut normal complex surface singularities. For graphs with two nodes, restriction maps define representations of a fixed quiver with uniformly bounded dimensions. We identify restriction cohomology with an extension group and use interval decomposition to reduce its vanishing to interpolation on a rational chain. The resulting conditions give the classification, including the nonrational cases.
The same obstruction calculations give a uniform criterion: a graph is taut if and only if \(H^1(5E,S_X|_{5E})=0\) for every analytic realization, where \(S_X\) is the ambient logarithmic tangent bundle. We prove that five is the smallest positive integer for which this criterion holds for all graphs.
Stable cohomology modules and universal nonlinear blowdowns
preprint (with Dongsoo Shin)
We characterize, via Fitting strata of a stable cohomology module, the base changes for which the Remmert contraction of a marked negative-definite SNC family is flat, fiberwise normal, and compatible with arbitrary analytic base change.
Intrinsic persistence of rational surface resolutions
preprint (with Dongsoo Shin)
We construct intrinsically from an unresolved deformation of a rational surface singularity the locus where its minimal good resolution persists, prove Lipman–Douady representability and arrow rigidity, and identify this locus with a target-side valuative–Rees equisingularity locus.
Integral vanishing lattices and marked $\mathbb Q$-Gorenstein degenerations of rational surfaces
preprint (with Jaekwan Jeon, Dongsoo Shin, Yoonjeong Yang)
We prove integral vanishing-lattice constraints for $\mathbb Q$-Gorenstein degenerations of rational surfaces and use them, together with marked local deformation data and explicit toric Cox pencils, to classify the Picard-number-one cases with one non-Wahl class-$T$ singularity by four Markov-type equations.
Tjurina numbers of the Okuma surface singularity family
submitted (with Dongsoo Shin)
We compute the Tjurina numbers of the Okuma surface family of isolated Cohen--Macaulay codimension-two surface singularities.