Complete Publications List
Research projects sponsored by the National Security Agency under Grant Number H98230-15-1-0264, the Simons Foundation under Award Number 429929, and the National Science Foundation under Grant Number 2001565.
Pure Mathematics
Extending the Torelli map to alternative compactifications of the moduli space of curves
Submitted. 41 pages (May 8, 2024)
A relative orientation for the moduli space of stable maps to a del Pezzo surface
Submitted. 80 pages (July 4, 2023)
A quadratically enriched count of rational curves
Submitted. 47 pages (July 4, 2023)
Counting rational points on the Hilbert scheme of pairs of points in the plane
Submitted. 19 pages (May 7, 2023)
An Example of Wild Ramification in an Enriched Riemann-Hurwitz Formula
in Motivic Homotopy Theory and Refined Enumerative Geometry (AMS 2020) 69–82
An arithmetic count of lines on a smooth cubic surface
Compositio Mathematica, 157(4), 677–709 (2021)
A classical proof that the algebraic homotopy class of a rational function is the residue pairing
Linear Algebra Appl. 595 (2020), 157–181
The stability space of compactified universal Jacobians
Trans. Amer. Math. Soc. 372 (2019), no. 7, 4851–4887
The class of Eisenbud-Khimshiashvili-Levine is the local A¹-Brouwer degree
Duke Math. J. 168 (2019), no. 3, 429–469
How can a line bundle on a curve degenerate
Oberwolfach Report on workshop Flat Surfaces and Algebraic Curves (November 5, 2018)
An étale realization function which does not exist
in New Directions in Homotopy Theory (AMS 2018) 11–30
Extending the Double Ramification Cycle using Jacobians
European Journal of Mathematics (2018) 1–13
Extensions of the universal theta divisor
Advances in Mathematics 321(1) (2017) 221–268
Autoduality holds for a degenerating abelian variety
Research in the Mathematical Sciences 4:27 (2017), 11 pp.
The singularities and birational geometry of the universal compactified Jacobian
Algebraic Geometry 4(3) (2017) 353–393
A¹-Milnor number
Oberwolfach Report 35(2016) 2047–2052
Moduli of generalized line bundles on a ribbon
J. Pure Appl. Algebra 220(2) (2016) 822–844
The compactified Jacobian can be nonreduced
Bull. London Math. Soc. 47(4) (2015) 686–692
The local structure of compactified Jacobians
Proc. Lond. Math Soc. 110(2) (2015) 510–542
An Abel map to the compactified Picard scheme realizes Poincaré duality
Algebraic & Geometric Topology 15.1 (2015) 319–369
An explicit semi-factorial model of the Néron model
Comptes Rendus Mathematique 352.9 (2014) 667–671
Singular curves and their compactified Jacobians
in A celebration of algebraic geometry -- in honor of Joe Harris's 60th birthday (AMS 2013) 391–429
The geometry and combinatorics of cographic toric face rings
Algebra & Number Theory 7.8 (2013) 1781–1815
An explicit non-smoothable component of the compactified Jacobian
Journal of Algebra 370 (2012), 326–343
Two ways to degenerate the Jacobian are the same
Algebra & Number Theory 7.2 (2012) 379–404
A Riemann singularity theorem for integral curves
American Journal of Mathematics 134.5 (2012) 1143–1165
Good Completions of Néron Models
PhD Thesis (2009)
History
Joseph Carter Corbin: Arkansas's "Profound Mathematician"
Notices Amer. Math. Soc. 70 (2023), no. 2, 293–300
The arXiv version has a lengthier bibliography and an additional section "Added after publication" that addresses some historical points.
South Carolina's effort to cancel professor tenure echoes the 1950s
The Washington Post, Made by History Series (February 18, 2022)
David L. Hunter and the desegregation of MAA meetings
MAA Focus (August-September 2021) 18–21
This article is cited in the Wikipedia entry for Dr. Hunter.
The library at UNC Charlotte has a recorded interview with Hunter that is available
here.
James L. Solomon and the end of segregation at the University of South Carolina
Notices Amer. Math. Soc. 67 (2020), no. 2, 192–200
Additional material here.
Essays
Some Advice on Filing a Harassment Complaint
Notices Amer. Math. Soc. 68 (2021), no. 11, 1925–1926
Letters
Untitled
Letter to the Editor. Notices Amer. Math. Soc. 70 (2023), no. 10, 1581
Untitled
Letter to the Editor. Notices Amer. Math. Soc. 68 (2020), no. 2, 175–176
This letter thanked the AMS President and others for their response to my suggestion that the AMS issue an apology
for the historical mistreatment of African-Americans. The AMS responded to my request by forming a 7-person committee
that issued a 76-page report ("Towards a Fully Inclusive Mathematics Profession")
and creating a new named fellowship (the AMS Claytor-Gilmer Fellowship).
When Did Reconstruction End?
Letter to the Editor. New York Review of Books (March 12, 2020), p. 45
Expository Notes
Studying Euclid in the Arkansas Delta: the Branch Normal College
Slides for the presentation at the NEH workshop Reconstructing the Black Archive (Summer 2023)
Early Career Advice: Advice about harassment reporting
Prepublication draft. The published version appeared as "Some Advice on Filing a Harassment Complaint," Notices Amer. Math. Soc. 68 (2021), no. 11, 1925–1926.
Questions in equivariant homotopy theory
Questions posted by my collaborator Kirsten Wickelgren (Summer 2016)
How many possible Burger Tavern 77 orders?
A student project from SCHC 212 "The Magic of Numbers". The restaurant Burger Tavern 77 advertises over "200,000 different possible orders".
Students Taylor Belinski, Mae Bradford, and Georgia Higgins analyzed their claim. Thanks to Frank Thorne for suggesting this problem. (Fall 2015)
Degenerating the Jacobian
A poster I presented at the conference The View from Joe's Office (August 28, 2011)
Local Structure of Compactified Jacobians
Slides from a talk I gave at the 2011 Joint Meetings (January 7, 2011. Updated April 15, 2011)
The Chow Ring of a Blow-up
A short note explaining how to compute the Chow Ring of a simple blow-up (Winter 2010)
A Non-Reduced Picard Scheme
A note describing Igusa's example of a surface with non-reduced Picard scheme (March 2008)
Notes on Néron Models
Notes on Néron models for a talk that I gave in a student seminar (Fall 2007)
Notes on Compactified Jacobians
Notes on compactified Jacobians for a talk that I gave in a student seminar (Fall 2007)
Notes on Abelian Schemes
Notes on abelian schemes (Summer 2005)
Notes on Dieudonne modules
Notes on Dieudonne modules (Summer 2005)