Research
My collaborators: Benjamin Church, François Greer, Feng Hao, Lena Ji, Olivier Martin, David Stapleton, Ruijie Yang, Junyan Zhao.
Much of my research is centered around studying rational maps between algebraic varieties, positivity of sheaves, intersection theory, and degeneration techniques. Most recently, I have been thinking about subvarieties of hypersurfaces in projective space, irrationality questions, and holomorphic forms.
Here are some videos of talks that I have given in the past:
https://scgp.stonybrook.edu/video/video.php?id=5646 -- December 2022 at the Simons Center.
https://scgp.stonybrook.edu/video_portal/video.php?id=5911 -- May 2023 at the Simons Center
Curves on complete intersections and measures of irrationality, with Benjamin Church and Junyan Zhao (an appendix by Mohan Swaminathan), preprint, arXiv:2406.12101 (2024).
The fibering genus of Fano hypersurfaces, with Benjamin Church, Lena Ji, and David Stapleton, preprint, arXiv:2308.12401 (2023).
Nowhere vanishing holomorphic one-forms and fibrations over abelian varieties, with Benjamin Church and Feng Hao, preprint, arXiv:2306.15064 (2023).
Fano hypersurfaces with no finite order birational automorphisms, with Lena Ji and David Stapleton, preprint, arXiv:2208.07396 (2022).
Rational maps from products of curves to surfaces with pg = q = 0, with Olivier Martin, Math. Z. 304, 62 (2023). [arXiv:2111.08194] [journal]
Multiplicative bounds for measures of irrationality on complete intersections, to appear in Algebraic Geometry. [arXiv:2111.05549]
Higher index Fano varieties with finitely many birational automorphisms, with David Stapleton, Compositio Math. 158 (2022), 2033 - 2045. [arXiv:2110.09568] [journal]
Rational endomorphisms of Fano hypersurfaces, with David Stapleton, to appear in Selecta Math.
Nodal elliptic curves on K3 surfaces, with François Greer and Ruijie Yang, Math. Annalen. 386 (2023), 2349 - 2370. [arXiv:2001.05104] [journal]
Fano hypersurfaces with arbitrarily large degrees of irrationality, with David Stapleton, Forum of Mathematics, Sigma 8 (2020), e.24, 12pp. [arXiv:1908.02803] [journal]
Degree of irrationality of very general abelian surfaces, Algebra & Number Theory 13 (2019), 2191 - 2198. [arXiv:1902.05645] [journal]
Measuring the irrationality of abelian surfaces and complete intersections, PhD thesis, Stony Brook University 2021. [pdf]
Unpublished: