賴冠文 / Kuan-Wen Lai

Teaching

Below are the courses, along with their information, that I am teaching or involved in this semester. Course materials are available on iLearn.

• Calculus A (I), Section 0536
• Calculus A (I), Section 0767
• Special Topic on Creative Science (I): a course in collaboration with a science fair, part of the "Mission Mars" event at the National Museum of Natural Science, during November 9–10, 2024.

Research

My research focuses on Algebraic Geometry, with particular interest in birational transformations, derived categories, and algebraic varieties over finite fields. Recently, I am focusing on problems related to the arithmetic and topology of Shimura varieties arising from K3 categories, such as the derived categories of K3 surfaces.

Papers

Below is a list of my papers in reverse chronological order. They are also available on the arXiv. Please note that the versions on this site are updated more frequently than those on the arXiv prior to journal publication.

Preprints

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

Published / Accepted

1. On the irrationality of moduli spaces of projective hyperkähler manifolds (with Daniele Agostini and Ignacio Barros), Épijournal de Géométrie Algébrique, accepted. [PDF] [arXiv]
2. Frobenius nonclassical hypersurfaces (with Shamil Asgarli and Lian Duan), Mathematische Zeitschrift 309, 18 (2025). [PDF] [arXiv]
3. Fourier–Mukai numbers of K3 categories of very general special cubic fourfolds (with Yu-Wei Fan), Israel Journal of Mathematics, accepted. [PDF] [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. [PDF] [arXiv]
5. New rational cubic fourfolds arising from Cremona transformations (with Yu-Wei Fan), Algebraic Geometry 10 (4) (2023), 432–460. [PDF] [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. [PDF] [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. [PDF] [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. [PDF] [arXiv]
9. Bijective Cremona transformations of the plane (with Shamil Asgarli, Masahiro Nakahara, and Susanna Zimmermann), Selecta Mathematica, New Series 28, 53 (2022). [PDF] [arXiv]
10. Transverse lines to surfaces over finite fields (with Shamil Asgarli and Lian Duan), manuscripta mathematica, 165 (2021), 135–157. [PDF] [arXiv] [erratum]
11. Cremona transformations and derived equivalences of K3 surfaces (with Brendan Hassett), Compositio Mathematica, 154 (2018), Issue. 7, 1508–1533. [PDF] [arXiv]
12. New cubic fourfolds with odd degree unirational parametrizations, Algebra & Number Theory, 11 (2017), No. 7, 1597–1626. [PDF] [arXiv]

Other writings

• A tour of the rationality problem of cubic fourfolds — An expository article written for a series of lectures given at Academia Sinica during July 28–August 3, 2021. [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]