Research Papers

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. The United States Government is authorized to reproduce and distribute reprints of the projects sponsored by the NSA notwithstanding any copyright notation herein.

• Counting rational points on the Hilbert scheme of pairs of points in the plane (with F. Thorne)
  Submitted. 19 pages. (May 7, 2023)
• Joseph Carter Corbin: Arkansas's "Profound Mathematician."
  Notices Amer. Math. Soc. 70 (2023), no. 2, 293–300.
• 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.
• An Example of Wild Ramification in an Enriched Riemann-Hurwitz Formula (with C. Bethea and K. Wickelgren)
  in Motivic Homotopy Theory and Refined Enumerative Geometry (AMS 2020) 69–82.
• An arithmetic count of lines on a smooth cubic surface (with K. Wickelgren)
  Compositio Mathematica, 157(4), 677–709.
• A classical proof that the algebraic homotopy class of a rational function is the residue pairing (with K. Wickelgren)
  Linear Algebra Appl. 595 (2020), 157–181.
• James L. Solomon and the end of segregation at the University of South Carolina (with contributions from N. Knox, H. M. Treadwell, and C. L. Solomon)
  Notices Amer. Math. Soc. 67 (2020), no. 2, 192–200. Additional material here.
• The stability space of compactified universal Jacobians (with N. Pagani)
  Trans. Amer. Math. Soc. 372 (2019), no. 7, 4851–4887.
• The class of Eisenbud-Khimshiashvili-Levine is the local A-Brouwer degree (with K. Wickelgren)
  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 (with K. Wickelgren)
  in New Directions in Homotopy Theory (AMS 2018) 11–30.
• Extending the Double Ramification Cycle using Jacobians (with D. Holmes and N. Pagani)
  European Journal of Mathematics (2018) 1–13.
• Extensions of the universal theta divisor (with N. Pagani)
  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 (with S. Casalaina-Martin and F. Viviani)
  Algebraic Geometry 4(3) (2017) 353–393.
• A1-Milnor number (with K. Wickelgren)
  Oberwolfach Report 35(2016) 2047–2052.
• Moduli of generalized line bundles on a ribbon (with D. Chen)
  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 (with S. Casalaina-Martin and F. Viviani)
  Proc. Lond. Math Soc. 110(2) (2015) 510–542.
• An Abel map to the compactified Picard scheme realizes Poincaré duality (with K. Wickelgren)
  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 (with S. Casalaina-Martin and F. Viviani)
  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 (with S. Casalaina-Martin)
  American Journal of Mathematics 134.5 (2012) 1143–1165.
• Good Completions of Néron Models
  PhD Thesis. (2009)

One of the first African-American students who desegregated the University of South Carolina in 1963 was mathematics graduate student James L. Solomon. You can find more information about him here: James L. Solomon Archive.

I keep a blog Blind Math with a Math Degree. The blog primarily records my thoughts and ideas about the racial desegregation of higher education, especially the role played by mathematicians. The blog started as a place to record thought about James Solomon that did not make it into my article.

Course website is here.

If you are an undergraduate thinking of asking me for a letter of recommendation, please read Keith Conrad’s page.

Interesting in having me sit on your thesis committee? I require a draft of your thesis 45 days in advance of your defense.

Students who have attended my classes have gone to have successful careers in law, medicine, science, and professional football.

When I was a graduate student, I had the honor of being a course assistant for the 7th most ridiculous-sounding math class offered at a liberal-arts college. The movie trailer for the class can be found here.

• Candace Bethea, PhD 2020.
• Mohammed Alabbood, PhD 2019.
• Tyler Lewis, PhD 2017.
• David Galban, Undergraduate honors thesis 2016.
• Marvin Jones, MA 2014.

Interested in working with me? Check out the advice pages of Jordan Ellenberg, Kiran Kedlaya, Bjorn Poonen, Hal Schenk, and David Zureick-Brown.

Current Santa Cruz graduate students are advised to read this FAQ about graduation requirements.

Seminars

• Algebra and Number Theory Seminar: Current.
• The Department Colloquium: Current.
• Motives Seminar: Spring 2018.
• Model Categories Seminar: Spring 2016.
• Seminar on Vector Bundles on Abelian Varieties: Summer 2014.
• Seminar on Moduli of Abelian Varieties: Summer 2013, Fall 2013.

• Motivic Euler numbers and an arithmetic count of lines on a cubic surface. Kirsten Wickelgren speaking about our joint work.
• Motivic Euler numbers and an arithmetic count of lines on a cubic surface. Kirsten Wickelgren giving another talk on our joint work.
• Two ways of degenerating a Jacobian are the same.

Events Organized

• Celebrating history: A commemoration of the University of South Carolina's first African-American mathematics students, James L. Solomon, Jr. 2019. Press: Carolina Panorama, UofSC Today, College of Arts and Science News, Post and Courier.
• Georgia Summer Workshop in Algebraic Geometry 2016.
• Special Session on Interactions Between Algebraic and Tropical Geometry 2016.
• The Commutative Algebra-Algebraic Geometry Meeting at South Carolina 2013.

Letters to the Editor

• 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 ).
• with reply by J. Oakes, "When Did Reconstruction End?" Letter to the Editor. New York Review of Books, March 12, 2020, p. 45.

Other publications

• "South Carolina’s effort to cancel professor tenure echoes the 1950s," The Washington Post, Made by History Series. February 18, 2022.
• "Some Advice on Filing a Harassment Complaint," Notices Amer. Math. Soc. 68 (2021), no. 11, 1925–1926.

Press

• Sarah Brown, "U. of South Carolina Wants to Rename Buildings. State Politics Will Stop It," The Chronicle of Higher Education, July 16, 2021. (See also her follow-up article "The Name-Change Charade: How a racial-justice effort at the U. of South Carolina became a smokescreen for inaction.")
• Kevin Hartnett, "A Path Less Taken to the Peak of the Math World," Quanta Magazine, June 27, 2017.

• 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
  
• 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. (28 Aug, 2011)
• Local Structure of Compactified Jacobians
  Slides from a talk I gave at the 2011 Joint Meetings. (7 Jan, 2011. Updated 15 April, 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. Related exercises can be found at the botton of this webpage. (Summer 2005)
• Notes on Dieudonne modules
  Notes on Dieudonne modules. (Summer 2005)

Me in Hannover next to the gravestone of Raphael Levi.

Me next to an announcement of the James Solomon Commemoration.