Writings
The aim of this book is to lower the bar of entry into algebraic geometry. As such, it is written to be accessible to students with a basic understanding of rings and ideals, with a preliminary chapter reviewing the relevant ring-theoretic concepts in the context of polynomial rings. The majority of the book is focused on the interplay of algebra and geometry in the setting of affine varieties. This includes complete proofs of Noether normalization and the Nullstellensatz, as well as a chapter on dimension theory and a chapter on tangent spaces and smoothness. It also contains several chapters on projective and quasiprojective varieties.
The book was completed in June 2024, and we are currently seeking a publisher. Please feel free to send us feedback if you use the book.
Papers (student coauthor, [20xx] = year of arXiv submission, hyperlinks to arXiv)
Lorentzian fans [2023]
International Mathematical Research Notices, 22 (2023) 19697-19742
Mixed volumes of normal complexes [2023]
with Lauren Nowak and Patrick O'Melveny
Discrete and Computational Geometry (to appear)
Pseudostable Hodge Integrals [2022]
with Renzo Cavalieri, Joel Gallegos, Brandon Van Over, and Jonathan Wise
International Mathematical Research Notices, 19 (2023) 16200-16225
Tropical fans and normal complexes [2021]
with Anastasia Nathanson
Advances in Mathematics, 420 (2023)
Matroid psi classes [2021]
with Jeshu Dastidar
Selecta Mathematica, 28, 55 (2022)
Polynomiality of factorizations in reflection groups [2020]
with Elzbieta Polak
Canadian Journal of Mathematics, 75 (2023) 245-266
Topology of Z_3-equivariant Hilbert schemes [2018]
with Deborah Castro
Electronic Journal of Combinatorics, 25 (2019)
Localization and mirror symmetry [2018]
Contemporary Mathematics, 763 (2021) 43-65
Wall-crossing in genus-zero hybrid theory [2018]
with Emily Clader
Advances in Geometry, 21 (2021) 365-384
The genus-one global mirror theorem for the quintic threefold [2017]
with Shuai Guo
Compositio Mathematica, 155 (2019) 995-1024
Genus-one mirror symmetry in the Landau-Ginzburg model [2016]
with Shuai Guo
Algebraic Geometry, 6 (2019) 260-301
Sigma models and phase transitions for complete intersections [2015]
with Emily Clader
International Mathematical Research Notices, 15 (2018) 4799-4851
On GW/DT and Ruan's conjecture for Calabi-Yau 3-orbifolds [2014]
Communications in Mathematical Physics, 340 (2015) 851-864
Donaldson-Thomas theory and resolutions of toric A-singularities [2014]
Selecta Mathematica, 23 (2017) 15-37
Wall-crossing in genus-zero Landau-Ginzburg theory [2014]
with Yongbin Ruan
Crelle's Journal, 733 (2017) 183-201
Cyclic Hodge integrals and loop Schur functions [2014]
with Zhengyu Zong
Advances in Mathematics, 285 (2015) 1448-1486
Crepant resolutions and open strings [2013]
with Andrea Brini and Renzo Cavalieri
Crelle's Journal, 155 (2019) 995-1024
The gerby Gopakumar-Mariño-Vafa formula [2012]
with Zhengyu Zong
Geometry and Topology, 17 (2013) 2935-2976
The loop Murnaghan-Nakayama rule [2012]
Journal of Algebraic Combinatorics, 39 (2014) 3-15
Localization and gluing of orbifold amplitudes: the Gromov-Witten orbifold vertex [2011]
Transactions of the American Mathematical Society, 366 (2014) 1587-1620
Open Gromov-Witten theory and the crepant resolution conjecture [2011]
with Renzo Cavalieri
Michigan Mathematical Journal, 61 (2012) 807-837