Hyunsuk Kim (김현석)

Hi, I am a graduate student in the University of Michigan mainly interested in algebraic and complex geometry. My advisor is Mircea Mustaţă.

Curriculum Vitae

Research Interests

• Birational Geometry and Minimal model program (Canonical Bundle Formula, Invariants of Singularities in MMP etc.)
• Hodge theory applications to birational geometry (Hodge modules, Period maps, Variation of Hodge structures etc.)
• Analytic methods in algebraic geometry (L2 methods, ∂-bar equations, singularities of plurisubharmonic functions etc.)
• Periods and Degenerations of K-trivial varieties
• Zeta functions
• Toric geometry

(Pre)Publications

• The intersection cohomology Hodge module of toric varieties (with Sridhar Venkatesh), available at arXiv (See Abstract)

  We study the Hodge filtration of the intersection cohomology Hodge module for toric varieties. More precisely, we study the cohomology sheaves of the graded de Rham complex of the intersection cohomology Hodge module and give a precise formula relating it with the stalks of the intersection cohomology as a constructible complex. The main idea is to use the Ishida complex in order to compute the higher direct images of the sheaf of reflexive differentials.

• L2 approach to the Saito vanishing theorem, available at arXiv (See Abstract)

  We give an analytic approach to the Saito vanishing theorem going back to the original idea for the proof of the Kodaira-Nakano vanishing theorem. The key ingredient is the curvature formula for Hodge bundles and the Higgs field estimates for degenerations of Hodge structures.

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