Research Interests

Projective algebraic geometry

higher secant varieties, higher osculating varieties, linear projections, second fundamental forms

Equations, relations, and syzygies

graded Betti numbers, Koszul cohomology groups, linear syzygies, the gonality conjecture, Green’s conjecture on canonical curves, determinantal presentation, Castelnuovo-Mumford regularity, the Eisenbud-Goto regularity conjecture

Multilinear algebra

tensors, Schur functors

Papers

[arXiv] [ResearchGate] [Google Scholar] 

Publications

1. A matryoshka structure of higher secant varieties and the generalized Bronowski’s conjecture (with Prof. Sijong Kwak), Advances in Mathematics, 406 (2022): 108526 [link] 

2. Castelnuovo–Mumford regularity of unprojections and the Eisenbud–Goto regularity conjecture, International Mathematics Research Notices, 2025.3 (2025): rnaf017 [link] 

3. Determinantal characterization of higher secant varieties of minimal degree (with Prof. Sijong Kwak), to appear [link] 

Preprint(s)

1. Syzygies of secant varieties of smooth projective curves and gonality sequences (with Prof. Sijong Kwak and Prof. Jinhyung Park) [link] 

2. A Fröberg type theorem for higher secant complexes (with Dr. Jaewoo Jung) [link] 

3. Quadratic equations of tangent varieties via four-way tensors of linear forms [link]

Ongoing project(s)

1. General tangential projections of del Pezzo varieties (with Prof. Sijong Kwak)

2. Green-Lazarsfeld index of Gaussian graphical models (with Prof. Kangjin Han)

Selected talks

1. Families of unprojections with large regularity, Workshop on ring theory and combinatorics, Thanh Hoa, Jul. 2022

2. Parallel syzygies of higher secant varieties, Geometry of secants, Warsaw, Oct. 2022

3. Partial elimination spectral sequence and its applications, Hybrid: SIAM Conference on Applied Algebraic Geometry (AG23), Eindhoven, Jul. 2023

4. (Poster) Linear syzygies of tangent varieties to Segre varieties with four factors, Modules & Rings: Recent Developments in Commutative Algebra - A conference in honor of Marilina Rossi, Genoa, Jun. 2025

5. (Poster) Determinantal type quadratic equations of tangent varieties, The 46-th Frontier Scientists Workshop, Ischia, Oct. 2025