Nathan Chen is a Research

Research Interests

Focus Areas

A large part of my research is devoted to studying rational maps between algebraic varieties. These appear in various guises, such as birational invariants called measures of irrationality, (birational) automorphisms and self-maps, and moduli spaces of curves on a given variety.

Recently, I have been thinking about subvarieties of hypersurfaces in projective space.

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Publications

Preprints

A primer on measures of irrationality,
joint with Olivier Martin.
preprint (2025)·arXiv:2509.03783
Curves on complete intersections and measures of irrationality,
joint with Benjamin Church and Junyan Zhao (an appendix by Mohan Swaminathan).
preprint (2024)·arXiv:2406.12101

Published Papers

The fibering genus of Fano hypersurfaces,
joint with Benjamin Church, Lena Ji, and David Stapleton.
Algebraic Geometry & Physics (to appear)·arXiv:2308.12401
Group actions and irrationality in surface families,
joint with Louis Esser.
Selecta Mathematica (N.S.) (to appear)·arXiv:2410.18427
Nowhere vanishing holomorphic one-forms and fibrations over abelian varieties,
joint with Benjamin Church and Feng Hao.
Advances in Mathematics (2025)·arXiv:2306.15064·journal
Fano hypersurfaces with no finite order birational automorphisms,
joint with Lena Ji and David Stapleton.
American Journal of Mathematics (to appear)·arXiv:2208.07396
Multiplicative bounds for measures of irrationality on complete intersections,
Algebraic Geometry (2024)·arXiv:2111.05549·journal
Rational maps from products of curves to surfaces with pg = q = 0,
joint with Olivier Martin.
Mathematische Zeitschrift (2023)·arXiv:2111.08194·journal
Higher index Fano varieties with finitely many birational automorphisms,
joint with David Stapleton.
Compositio Mathematica (2022)·arXiv:2110.09568·journal
Rational endomorphisms of Fano hypersurfaces,
joint with David Stapleton.
Selecta Mathematica (N.S.) (2024)·arXiv:2103.12207·journal
Nodal elliptic curves on K3 surfaces,
joint with François Greer and Ruijie Yang.
Mathematische Annalen (2023)·arXiv:2001.05104·journal
Fano hypersurfaces with arbitrarily large degrees of irrationality,
joint with David Stapleton.
Forum of Mathematics, Sigma (2020)·arXiv:1908.02803·journal
Degree of irrationality of very general abelian surfaces,
Algebra & Number Theory (2019)·arXiv:1902.05645·journal

Other

Measuring the irrationality of abelian surfaces and complete intersections,
PhD thesis, Stony Brook University (2021)·pdf
Curves on surfaces blown up at three points·pdf

Recent Talks

Videos

Higher index Fano varieties in positive characteristic with Bir(X) = 1
May 2023, Simons Center, Stony Brook·video
Rational endomorphisms on Fano hypersurfaces
February 2023, Birational Geometry Seminar, Virtual·video
Curves on very general hypersurfaces
December 2022, Simons Center, Stony Brook·video

Invited Talks and Presentations

Algebraic Geometry Northeastern Series (AGNES)
November 2024, Dartmouth College
conference page
Thematic Program on Rationality and Hyperbolicity
June 2023, University of Notre Dame
conference page
Higher Dimensional Geometry
May 2023, Simons Foundation Conference
conference page
Birational Complexity of Algebraic Varieties
December 2022, Stony Brook University
AMS-EMS-SMF Joint Congress of Mathematics
July 2022, Special session on algebraic geometry, Université Grenoble Alpes
AMS Spring Eastern Sectional Meeting
October 2020, Special session on moduli spaces in algebraic and tropical geometry, Tufts University (virtual)
AMS Fall Eastern Sectional Meeting
October 2020, Special session on geometry and arithmetic of algebraic varieties, Pennsylvania State University (virtual)
American Graduate Student Algebraic Geometry Seminar
September 2020
Algebraic Geometry Seminar Talks
2025:
  • Florida State University (September)
  • Università di Pavia (June)
  • Stony Brook University (April)
  • Tufts University (February)

2024:
  • University of California, Los Angeles Colloquium (December)
  • University of California, Santa Barbara (December)
  • Washington University in St. Louis (December)
  • Cornell University (October)
  • City University of New York (algebra and algebraic geometry, October)
  • University of Washington (May)
  • University of Maryland (April)
  • Stony Brook University (March)
  • Stanford University (March)
  • City University of New York (number theory, March)
  • Brown University (February)

2023:
  • University of Washington (November)
  • University of Illinois Chicago (October)
  • New York University (September)
  • Purdue University (April)
  • Princeton University (April)
  • Washington University in St. Louis (March)
  • Stanford University (March)
  • Columbia University (January)

2022:
  • University of Michigan (October)
  • Michigan State University (October)
  • Northwestern University (October)
  • Università di Pavia (July)
  • University of Massachusetts at Amherst (April)

2021:
  • Harvard University/MIT (joint seminar, September)
  • University of Utah (March)

2020:
  • Princeton University (December)
  • Institut de Mathématiques de Jussieu - Paris Rive Gauche (June)

Collaborators

Current

My collaborators: