Last update: May 23, 2024.

I will make papers available on this page when they are in a complete form, and post a note when they are substantively updated.

Research Publications by Adam Coffman

A. Coffman, Y. Pan, and Y. Zhang, Unique continuation for a gradient inequality with Ln potential, Preprint, 23 pages. Last update Feb. 28, 2024.
A. Coffman, A non-unital generalized trace and linear complex structures, Operators and Matrices (2) 15 (2021), 525-569.
A. Coffman and Y. Zhang, Vector fields with continuous curl but discontinuous partial derivatives, The American Mathematical Monthly (10) 127 (2020), 911-917.
A. Coffman and J. Lebl, Removing isolated zeroes by homotopy, Topological Methods in Nonlinear Analysis (1) 54 (2019), 275-296.
A. Coffman, Y. Pan, and Y. Zhang, Continuous solutions of nonlinear Cauchy-Riemann equations and pseudoholomorphic curves in normal coordinates, Transactions of the AMS (7) 369 (2017), 4865-4887.
A. Coffman, Real linear maps preserving some complex subspaces, Beiträge zur Algebra und Geometrie (1) 56 (2015), 159-173.
A. Coffman, Weighted projective spaces and a generalization of Eves' Theorem, Journal of Mathematical Imaging and Vision (3) 48 (2014), 432-450.
A. Coffman and Y. Pan, Smooth counterexamples to strong unique continuation for a Beltrami system in C2, Communications in Partial Differential Equations (12) 37 (2012), 2228-2244.
A. Coffman and Y. Pan, Glaeser's inequality on an interval, Real Analysis Exchange (2) 36 (2010/2011), 483-490.
A. Coffman and Y. Pan, Some nonlinear differential inequalities and an application to Hölder continuous almost complex structures, Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire (2) 28 (2011), 149-157.
A. Coffman, CR singularities of real fourfolds in C3, Illinois Journal of Mathematics (3) 53 (2009), 939-981.
A. Coffman, Unfolding CR Singularities, Memoirs of the AMS (962) 205 (2010), vii+90 pages.
A. Coffman and Y. Pan, Proper holomorphic maps from domains in C2 with transverse circle action, Chinese Annals of Mathematics (English Series B) (5) 28 (2007), 533-542.
A. Coffman, Analytic stability of the CR cross-cap, Pacific Journal of Mathematics (2) 226 (2006), 221-258.
A. Coffman, CR singularities of real threefolds in C4, Advances in Geometry (1) 6 (2006), 109-137.
A. Coffman, Real equivalence of complex matrix pencils and complex projections of real Segre varieties, Electronic Journal of Linear Algebra 17 (2008), 651-698.
A. Coffman, D. Legg, and Y. Pan, A Taylor series condition for harmonic extension, Real Analysis Exchange (1) 28 (2002-2003), 235-253.
A. Coffman and M. Frantz, Möbius transformations and ellipses, The Pi Mu Epsilon Journal (6) 12 (2007), 339-345.
  • abstract.txt
  • Without figures: DVI
  • With 3 figures: PS PDF
  • Article page at JSTOR
  • An abstract for a talk based on this paper appeared in the Spring 2003 Newsletter of the Indiana Section of the MAA. The notes for this talk form a significantly longer, unpublished version of this paper, with several different proofs of the main result, more pictures, and a longer list of references: see Ellipses in the inversive plane, listed under Lecture Notes (below).
  • For related images, see the link on the "hippopede of Proclus" on my graphics gallery page.
  • Google Scholar citations
  • CiteSeer record
A. Coffman, Real congruence of complex matrix pencils and complex projections of real Veronese varieties, Linear Algebra and its Applications 370 (September 2003), 41-83.
A. Coffman, CR singular immersions of complex projective spaces, Beiträge zur Algebra und Geometrie (2) 43 (2002), 451-477.
A. Coffman, Analytic normal form for CR singular surfaces in C3, Houston Journal of Mathematics (4) 30 (2004), 969-996.
A. Coffman, The attraction of surfaces of revolution, The College Mathematics Journal (5) 32 (November 2001), 372-375.
A. Coffman, A. J. Schwartz, and C. M. Stanton, The algebra and geometry of Steiner and other quadratically parametrizable surfaces, Computer Aided Geometric Design (3) 13 (April 1996), 257-286.

Thesis excerpts

A. Coffman, Enumeration and Normal Forms of Singularities in Cauchy-Riemann Structures, Ph.D. dissertation, University of Chicago. Defended June 9, 1997.
  • Available in The University of Chicago Library system.
    • #QA999.C64 in the University of Chicago Library Catalog
    • WorldCat entry: the entire thesis may be viewable online via ProQuest and UMI.
  • Chapter I, Introduction, 3 pages
    • DVI PS
    • with cover page and citation information: PDF
  • Chapter II, Degeneracy loci in CR geometry, and comprehensive bibliography, 20 pages. (1 figure omitted)
  • Chapters III and V, condensed into: Formal stability of the CR cross-cap, 26 pages.
  • Chapter IV, condensed into: Complexification of the CR cross-cap, see my Lecture Notes (below), and also Example 8.5 in my ...real Veronese varieties paper (above).
  • Listed in the Feb. 1999 AMS Notices, p. 251. PS .PDF
  • MathSciNet entry: 2716702PDF
  • Google Scholar citations
A. Coffman, A Classification of Quadratically Parametrized Maps of the Real Projective Plane, B.S. Honors Thesis, University of Michigan, Ann Arbor, 1991.
  • Re-typeset, added update sections, and posted online in 2018: .PDF 37 pages + 10 Figures.


These are some notes © by Adam Coffman, unpublished and not in any final form, and falling into three somewhat indistinct categories.

Research Notes

These are notes on fairly well-known topics, but I have found it convenient to collect some related results in one place, with consistent notation and elementary proofs.

Course Notes

These are compiled from my classroom handouts, for Purdue Fort Wayne courses since 2018 and IPFW courses 1997-2018.

Lecture Notes

These notes are based on talks I've given about my research. See also my Grants and Talks page for more information about my talks and poster sessions.

Other stuff by Adam Coffman

Archives and Reviews

Related Papers available on the Web

These papers (with which I had no involvement) are related to my research interests and current projects.

What is CR geometry? Here are some survey articles:

More papers related to my research in geometry:

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