賴冠文 / Kuan-Wen Lai

Teaching

Below are the courses, along with their information, that I will teach or be involved in the upcoming semester.

• Asobou! Combinatorial Games
• Calculus A (I), Section 0531
• Mission Mars (II) — a course in collaboration with a science fair, part of the "Mission Mars" event at the National Museum of Natural Science.

Research

My research area is Algebraic Geometry, with a focus on birational transformations, Fourier–Mukai transforms, and algebraic varieties over finite fields. You can find my articles below and on arXiv. Preprints on this webpage are updated more frequently than their arXiv versions prior to journal publication.

Preprints

• Nielsen realization problem for derived automorphisms of generic K3 surfaces (with Yu-Wei Fan). [PDF] [arXiv]

Publications / Accepted papers

1. Fourier–Mukai numbers of K3 categories of very general special cubic fourfolds (with Yu-Wei Fan), Israel Journal of Mathematics, accepted. [arXiv]
2. On the irrationality of moduli spaces of projective hyperkähler manifolds (with Daniele Agostini and Ignacio Barros), Épijournal de Géométrie Algébrique, Volume 9 (2025), Article No. 13.
3. Frobenius nonclassical hypersurfaces (with Shamil Asgarli and Lian Duan), Mathematische Zeitschrift 309, 18 (2025). [arXiv]
4. Transverse linear subspaces to hypersurfaces over finite fields (with Shamil Asgarli and Lian Duan), Finite Fields and Their Applications 95 (2024), Paper No. 102396. [arXiv]
5. New rational cubic fourfolds arising from Cremona transformations (with Yu-Wei Fan), Algebraic Geometry 10 (4) (2023), 432–460. [arXiv]
6. On the irrationality of moduli spaces of K3 surfaces (with Daniele Agostini and Ignacio Barros), Transactions of the American Mathematical Society 376 (2023), No. 2, 1407– 1426. [arXiv]
7. Uniform potential density for rational points on algebraic groups and elliptic K3 surfaces (with Masahiro Nakahara), International Mathematics Research Notices 2022, no. 23, 18541–18588. [arXiv]
8. Decomposition of Lagrangian classes on K3 surfaces (with Yu-Shen Lin and Luca Schaffler), Mathematical Research Letters 28 (2021), no. 6, 1739–1763. [arXiv]
9. Bijective Cremona transformations of the plane (with Shamil Asgarli, Masahiro Nakahara, and Susanna Zimmermann), Selecta Mathematica, New Series 28, 53 (2022). [arXiv]
10. Transverse lines to surfaces over finite fields (with Shamil Asgarli and Lian Duan), manuscripta mathematica, 165 (2021), 135–157. [arXiv] [erratum]
11. Cremona transformations and derived equivalences of K3 surfaces (with Brendan Hassett), Compositio Mathematica, 154 (2018), Issue. 7, 1508–1533. [arXiv] [erratum (see Lemma 3.3)]
12. New cubic fourfolds with odd degree unirational parametrizations, Algebra & Number Theory, 11 (2017), No. 7, 1597–1626. [arXiv]

Proceedings

• A tour of the rationality problem of cubic fourfolds, Proceedings of the International Congress of Chinese Mathematicians 2020. [PDF]

Recorded talks

• Estimates on the growth of irrationality for moduli spaces of K3 surfaces — A talk at the workshop: Birational Complexity of Algebraic Varieties at Simons Center during December 12–16, 2022. [video]
• Bijective Cremona transformations of the plane — An online talk at National Tsing Hua University on March 21, 2022. [video]