Personal Information

First name: Jong In

Last name: Han

Name in Korean: 한종인

Email: jihan09 at kias dot re dot kr

Nationality: South Korea

Current affiliation: KIAS

Education

B.S., Mathematical Sciences, KAIST, 2015

M.S., Mathematical Sciences, KAIST, 2018 (Thesis advisor: Sijong Kwak)

Ph.D., Mathematical Sciences, KAIST, 2025 (Thesis advisor: Sijong Kwak)

Positions

KIAS (Korea Institute for Advanced Study), Research Fellow, 2025.03-

Research Interest

In short: algebraic geometry (syzygies and tensors)

In detail: both pure and applied algebraic geometry

• syzygies (especially, Castelnuovo-Mumford regularity, Eisenbud-Goto conjecture, distribution of graded Betti numbers)

• secant and tangent varieties

• tensors (especially, determinants and permanents)

• geometric complexity theory

• sum of squares

Papers and Preprints

1. The rank of the 5×5 permanent tensor is sixteen, with Jeyoung Song,
   submitted. [arXiv]
   R(perm₅) = 16

2. The Eisenbud-Goto conjecture for projectively normal varieties with mild singularities,
   submitted. [arXiv]
   The Eisenbud-Goto conjecture holds for 2-very ample projectively normal varieties with mild singularities.

3. Hierarchical structure of graded Betti numbers in the quadratic strand, with Sijong Kwak and Wanseok Lee,
   submitted. [arXiv][Latest preprint (will be updated on arXiv later)]
   The known sharp upper bounds on βₚ,₁ were the first glimpse of a vast hierarchy stratifying the quadratic strand.

4. The border rank of the 4×4 determinant tensor is twelve, with Jeong-Hoon Ju and Yeongrak Kim,
   submitted. [arXiv]
   R(det₄) = 12

5. On quadratic persistence and Pythagoras numbers of totally real projective varieties, with Jaewoo Jung and Euisung Park,
   submitted. [arXiv]
   Classified totally real varieties with next-to-minimal Pythagoras number when codim = 3 or codim ≥ 4 with deg ≥ 2codim + 3.

6. Recursive Koszul flattenings of determinant and permanent tensors, with Jeong-Hoon Ju and Yeongrak Kim,
   submitted. [arXiv]
   (1) Determinant tensors and permanent tensors are completely separated by their tensor ranks: R(detₙ) > R(permₙ) for all n ≥ 3.
   (2) R(det₄) = 12     and     R(det₄) ≥ 11
   (3) R(perm₄) = R(perm₄) = 8,     R(perm₅) ≥ 15,     R(perm₆) ≥ 29,     and     R(perm₇) ≥ 55

7. Surface counterexamples to the Eisenbud-Goto regularity conjecture, with Sijong Kwak,
   Trans. Amer. Math. Soc. 377 (2024), 5561-5581. [arXiv] [journal]
   Unexpectedly, there exist surface counterexamples to the Eisenbud-Goto conjecture.

8. Characterization of projective varieties beyond varieties of minimal degree and del Pezzo varieties, with Sijong Kwak and Euisung Park,
   J. Algebra 636 (2023), 732-756. [arXiv] [journal]
   In the syzygetic view, the next simplest varieties after varieties of minimal degree and del Pezzo varieties are
   (1) varieties of almost minimal degree with depth = dim and Green-Lazarsfeld index 0
   (2) ACM varieties with deg = codim + 3.

Ongoing Works

1. Jong In Han and Sijong Kwak, On the locus of multisecant lines to projective varieties, ongoing work.

2. Junho Choe, Jong In Han, and Sijong Kwak, Higher secant varieties of minimal degree from toric varieties, ongoing work.

3. Jong In Han and Jeong-Hoon Ju, On the partially skew-symmetric rank, ongoing work.

Talks

1. Hierarchical structure of graded Betti numbers in the quadratic strand, International Conference for the 80th Anniversary of the Korean Mathematical Society, Seoul, South Korea, 2026.06.23.

2. The Eisenbud-Goto conjecture for projectively normal varieties with mild singularities, BRL-AGSTA One-day Workshop, Daegu, South Korea, 2026. 06. 17.

3. The Eisenbud-Goto conjecture for projectively normal varieties with mild singularities, Algebraic Geometry Seminar in Korea University, Seoul, South Korea, 2026. 03. 31.

4. Positive and negative results on the Eisenbud-Goto conjecture, Gangneung, South Korea, 2026.02.09.

5. Castelnuovo theory of syzygies, 2025 Symposium in Algebraic Geometry, Busan, South Korea, 2025.12.21.

6. Border rank of the 4 x 4 determinant tensor is twelve, Special Session, 2025 KMS Annual Meeting, Seoul, South Korea, 2025.10.24.

7. On quadratic persistence and Pythagoras numbers of totally real projective varieties, One-day Algebraic Geometry workshop in DGIST, Daegu, South Korea, 2025.06.24.

8. Recursive Koszul flattenings of determinant and permanent tensors, KIAS HCMC Algebraic Geometry Seminar, Seoul, South Korea, 2025.05.07.

9. Hierarchy on graded Betti numbers and Castelnuovo theory of syzygies, 2025 WORKSHOP on Projective Algebraic Geometry and Commutative Algebra, Busan, South Korea, 2025.04.11.

10. Some open problems in syzygies and related topics, PNU Geometry and Topology seminar, Busan, South Korea, 2025.04.07.

11. Higher secant varieties of curves of minimal degree and del Pezzo curves, Algebraic Geometry Seminar in Kumamoto, Kumamoto, Japan, 2024.08.08.

12. Surface counterexamples to the Eisenbud-Goto conjecture, Algebraic Geometry Seminar in Kumamoto, Kumamoto, Japan, 2024.08.06.

13. Recursive Koszul flattenings of determinant and permanent tensors, JM Invariant@60: A Conference on Tensor Invariants in Geometry and Complexity Theory, Auburn, AL, USA, 2024.05.14.

14. Methods to decompose tensors, Mini-Workshop on Algebra, Geometry and Applications - After SIAM-AG 2023, Daejeon, South Korea, 2023.10.05.

15. Characterization of projective varieties beyond varieties of minimal degree and del Pezzo varieties, Exploring Algebraic Geometry and Topology, Yangpyeong, South Korea, 2023.05.31.

16. Projective surfaces in ℙ⁴ that are counterexamples to the Eisenbud-Goto regularity conjecture, Current Developments in Algebra and Topology 2022 - Joint Workshop between Korea and Vietnam, Buyeo, South Korea, 2022.10.28.

17. Upper bounds of graded Betti numbers of projective varieties and characterizations of extremal cases, Algebraic Geometry (Castelnuovo Theory and Related Fields) Seminar, Busan, South Korea, 2022.04.13.

Posters

1. Hierarchy on graded Betti numbers and Castelnuovo theory of syzygies, 2025 Algebraic Geometry Conference in Jeonju Hanok Village - on the occasion of Professor Youngook Choi's 60th birthday, Jeonju, South Korea, 2025.06.12.

2. Surface counterexamples to the Eisenbud-Goto conjecture, 2024 KMS Spring Meeting, Daejeon, South Korea, 2024.04.19.

3. Counterexamples of surfaces to the Eisenbud-Goto regularity conjecture, Budding Workshop in Algebraic Geometry, Hwaseong, South Korea, 2023.03.30.

Honors and Awards

1. 2024 KAIST graduate student excellent paper award

2. 2024 KMS spring meeting, excellent poster award

3. 2008 KMO, high school session, main test, silver prize

4. 2007 KMO, high school session, main test, silver prize

5. 2006 KMO, middle school session, main test, gold prize

Activities

1. Certificate of Completion: 2026 KMS-NIMS-KRIMS AI Winter School (Incheon/Gyeonggi/Gangwon Chapter)

2. Organizing 2026 KIAS Algebraic Geometry Seminar Series

Teaching Assistant Experience (at KAIST)

1. 2021 Fall, Modern Algebra II

2. 2021 Spring, Modern Algebra I

3. 2021 Spring, Calculus I

4. 2020 Fall, Linear Algebra

5. 2020 Fall, Calculus II

6. 2020 Spring, Introduction to Number Theory

7. 2020 Spring, Introduction to Linear Algebra

8. 2019 Fall, Linear Algebra

9. 2019 Fall, Calculus II

10. 2019 Spring, Modern Algebra I

11. 2019 Spring, Calculus I

12. 2018 Fall, Modern Algebra II

13. 2018 Spring, Modern Algebra I

14. 2018 Spring, Introduction to Linear Algebra

15. 2017 Fall, Introduction to Linear Algebra

16. 2017 Spring, Complex Variables I

17. 2017 Spring, Introduction to Linear Algebra

Links to my academic profiles

1. arXiv

2. ORCID

3. MathSciNet

4. zbMATH

5. Google scholar

6. ResearchGate