Research

Papers and Preprints:

• Cubic fourfolds with birational Fano varieties of lines
  With Corey Brooke, and Lisa Marquand.
  
• Birational geometry of Fano varieties of lines on cubic fourfolds containing pairs of cubic scrolls
  With Corey Brooke, Lisa Marquand, and Xuqiang Qin.
  Submitted.
• Conic bundle threefolds differing by a constant Brauer class and connections to rationality
  With Lena Ji, Soumya Sankar, Bianca Viray, and Isabel Vogt.
  Submitted.
• On decompositions for Fano schemes of intersections of two quadrics
  With Pieter Belmans, Jishnu Bose, Benjamin Gould, James Hotchkiss, Alicia Lamarche, Jack Petok, Cristian Rodriguez Avila, and Saket Shah.
  Submitted.
• Rationality of threefolds over non-closed fields
  These are survey notes written for a lecture series I gave at the Notre Dame 2023 Thematic Program on Rationality and Hyperbolicity.
  
• On abelian varieties whose torsion is not self-dual
  With Katrina Honigs, and John Voight.
  Submitted.
• A threefold violating a local-to-global principle for rationality
  With Lena Ji.
  Res. Number Theory, 10(2): 39, 2024.
• Groups of symplectic involutions on symplectic varieties of Kummer type and their fixed loci
  With Katrina Honigs.
  Forum Math. Sigma, 11:e40 1-35, 2023.
• Curve classes on conic bundle threefolds and applications to rationality
  With Lena Ji, Soumya Sankar, Bianca Viray, and Isabel Vogt.
  Algebr. Geom., 11(3): 421-459, 2024.
• Reduction of Brauer classes on K3 surfaces, rationality, and derived equivalence
  With Brendan Hassett, and Anthony Várilly-Alvarado.
  J. reine angew. Math. (Crelle), 792: 289–305, 2022.
• Rational points and derived equivalence
  With Nicolas Addington, Benjamin Antieau, and Katrina Honigs.
  Compositio Math., 157(5): 1036–1050, 2021.
• Moduli spaces of sheaves on K3 surfaces and Galois representations
  Selecta Math. (N.S.), 26(1): 1-16, 2020.
• The a-number of hyperelliptic curves
  Women in Numbers Europe II, Springer, 107-116, 2018.

Other Writing:

• University of Oregon AWM Chapter: Creation and Evolution.
  With Elisa Bellah, Leanne Merrill, and Kelly Pohland.
  Fifty Years of Women in Mathematics: Reminiscences, History, and Visions for the Future of AWM, to appear.

Theses:

• Moduli spaces of sheaves on K3 surfaces and Galois representations
  My Ph.D. thesis, advised by Nicolas Addington. A longer version of the paper above by the same name, with background.
• The a-number of hyperelliptic curves
  My Master's thesis, advised by Rachel Pries. A longer version of the paper above by the same name, with background.

Other:

• In Oct 2021 I spoke at the AGNES Showcase on the Reduction of Brauer classes on K3 surfaces. You can find a recording of my talk on the AGNES website (although the first couple of minutes of the talk did not get recorded).
• In Aug 2021 I spoke at the PRIMA 2021 Summer School on Brauer classes in moduli problems and arithmetic. You can find lecture videos (given by me and Nicolas Addington) and exercises there.
• In Nov 2019 I spoke at BIRS on Rational points and derived equivalence. You can find the recording of my talk on the workshop page.
• Here are slides from a talk I gave at the Arithmetic of Algebraic Curves Conference at the University of Wisconsin, Madison.
• Here is a poster I presented at the Fall 2017 Western Algebraic Geometry Symposium in Los Angeles, CA.