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. abstract.txt arXiv.org: 2402.15503 - version 1 from 23 Feb. 2024. zbMath pre-review

A. Coffman, A non-unital generalized trace and linear complex structures, Operators and Matrices (2) 15 (2021), 525-569. abstract.txt (42 page format) Article page at Ele-Math Related conference poster: MathSciNet review: 4280043 Zbl. Math review: 1484.15028 For errata, updates, and a few details omitted from this paper, see my Notes on Abstract Linear Algebra (below).

A. Coffman and Y. Zhang, Vector fields with continuous curl but discontinuous partial derivatives, The American Mathematical Monthly (10) 127 (2020), 911-917. abstract.txt Article page at Taylor & Francis See the Lecture Notes, below, for slides from a talk on Green's Theorem, which sketches a version of the construction mentioned in the article's last paragraph. MathSciNet review: 4185988 Zbl. Math review: 1454.26013

A. Coffman and J. Lebl, Removing isolated zeroes by homotopy, Topological Methods in Nonlinear Analysis (1) 54 (2019), 275-296. abstract.txt (17 page format) Article page at TMNA web site Article page at Project Euclid arXiv.org: 1712.01787 - version 2 from Oct. 2018. An abstract for a talk based on this paper appears in the Abstracts of Papers Presented to the AMS (3) 38 (2017), p. 1008. MathSciNet review: 4018281 Zbl. Math review: 1436.57040

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. abstract.txt (28 page format) Article page at AMS web site Article page at JSTOR Errata & post-publication comments, updated May 15, 2023. arXiv.org: 1410.1582 - version 3 from Oct. 2, 2015. An abstract for a talk based on this paper appears in the Abstracts of Papers Presented to the AMS (2) 36 (2015), p. 671. MathSciNet review: 3632553 Zbl. Math review: 1375.35152

A. Coffman, Real linear maps preserving some complex subspaces, Beiträge zur Algebra und Geometrie (1) 56 (2015), 159-173. abstract.txt (13 page format) Article page at Springer An abstract for a talk based on this paper appears in the Abstracts of Papers Presented to the AMS (1) 35 (2014), p. 100. MathSciNet review: 3305441 Zbl. Math review: 1316.15035

A. Coffman, Weighted projective spaces and a generalization of Eves' Theorem, Journal of Mathematical Imaging and Vision (3) 48 (2014), 432-450. abstract.txt 46 pages with 8 figures in color. Article page at Springer Addendum, 3 pages. Updated March 4, 2022. (a 2-page version of this Addendum appears on the Springer web site.) An abstract for a talk based on this paper appears in the Abstracts of Papers Presented to the AMS (3) 34 (2013), p. 865. arXiv.org: 1204.1686 MathSciNet review: 3171423 Zbl. Math review: 1296.51034 ACM Digital Library page

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. abstract.txt (18 page format) Article page at Taylor & Francis arXiv.org: 1102.2462 MathSciNet review: 3005542 Zbl. Math review: 1261.35032 Google Scholar citations

A. Coffman and Y. Pan, Glaeser's inequality on an interval, Real Analysis Exchange (2) 36 (2010/2011), 483-490. abstract.txt (6 page format) Article page at Project Euclid (with full-text open access) Article page at JSTOR An abstract for a talk based on this paper appeared in the Spring 2010 Newsletter of the Indiana Section of the MAA. (See the Lecture Notes, below.) MathSciNet review: 3016732 Zbl. Math review: 1259.26022

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. abstract.txt (12 page format) Article page at ScienceDirect arXiv.org: 0907.3307 - an older version, 18 pages. An abstract for a talk based on this paper appears in the Abstracts of Papers Presented to the AMS (2) 31 (2010), p. 416. MathSciNet review: 2784067 (2012c:35492) Zbl. Math review: 1213.35409 Google Scholar citations

A. Coffman, CR singularities of real fourfolds in C3, Illinois Journal of Mathematics (3) 53 (2009), 939-981. abstract.txt (46 page format) Article page at Project Euclid (with full-text open access) An abstract for a talk based on this paper appears in the Abstracts of Papers Presented to the AMS (2) 30 (2009), p. 436. arXiv.org: 0904.2794 MathSciNet review: 2727363 (2011m:32067) Zbl. Math review: 1233.32027 Google Scholar citations

A. Coffman, Unfolding CR Singularities, Memoirs of the AMS (962) 205 (2010), vii+90 pages. abstract.txt and temporary Errata Without figures: 0.5 MB With 14 figures: 21 MB 1.1 MB (vii+115 pages: larger font than AMS published version.) eBook page at AMS Here's a graphics page with some related illustrations, animations, and comments. An abstract for a talk based on this paper appears in the Abstracts of Papers Presented to the AMS (2) 27 (2006), p. 409. MathSciNet review: 2650710 (2011f:32077) Zbl. Math review: 1194.32016 Google Scholar citations AMS bookstore page ISBN-10: 0-8218-4657-4, ISBN-13: 978-0-8218-4657-5 AMS Notices announcement Amazon.com, Barnes & Noble

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. abstract.txt Article page at Springer Addendum, 26 pages. Updated Feb. 23, 2023. MathSciNet review: 2358939 (2008i:32021) Zbl. Math review: 1143.32011

A. Coffman, Analytic stability of the CR cross-cap, Pacific Journal of Mathematics (2) 226 (2006), 221-258. abstract.txt full-text open access at PJM: Article page at Pacific Journal of Mathematics Post-publication comments, updated June 7, 2023. MathSciNet review: 2247863 (2007j:32038) Zbl. Math review: 1123.32018

A. Coffman, CR singularities of real threefolds in C4, Advances in Geometry (1) 6 (2006), 109-137. abstract.txt Article page at de Gruyter Addendum, 12 pages. Updated May 27, 2018. An abstract for a talk based on this paper appears in the Abstracts of Papers Presented to the AMS (3) 25 (2004), p. 459. MathSciNet review: 2242865 (2007d:32033) Zbl. Math review: 1120.32024

A. Coffman, Real equivalence of complex matrix pencils and complex projections of real Segre varieties, Electronic Journal of Linear Algebra 17 (2008), 651-698. abstract.txt Without figures: With 7 figures: full-text open access at EJLA: Article page at EJLA MathSciNet review: 2470963 (2010c:14003) Zbl. Math review: 1173:15003 EuDML page

A. Coffman, D. Legg, and Y. Pan, A Taylor series condition for harmonic extension, Real Analysis Exchange (1) 28 (2002-2003), 235-253. abstract.txt (19 page format) Article page at Project Euclid (with full-text open access, page numbering 229-248) Article page at JSTOR For an illustration related to this paper, see my graphics gallery page. An abstract for a talk based on this paper appears in Abstracts of Short Communications and Poster Sessions, International Congress of Mathematicians, Beijing 2002 (Higher Education Press, Beijing, 2002). MathSciNet review: 1973984 (2004c:31006) Zbl. Math review: 1055.31003 Russian language abstract (p. 721/722 of large PDF file). Google Scholar citations

A. Coffman and M. Frantz, Möbius transformations and ellipses, The Pi Mu Epsilon Journal (6) 12 (2007), 339-345. abstract.txt Without figures: With 3 figures: 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. abstract.txt Article page at ScienceDirect Errata & post-publication comments, updated July 7, 2021. An abstract for a talk based on this paper appears in the Abstracts of Papers Presented to the AMS (3) 22 (2001), p. 466. MathSciNet review: 1994320 (2004f:14026) Zbl. Math review: 1049.14042 CiteSeer record

A. Coffman, CR singular immersions of complex projective spaces, Beiträge zur Algebra und Geometrie (2) 43 (2002), 451-477. abstract.txt full-text open access at BzA&G: Article page at BzA&G Addendum, 17 pages. Updated Feb. 28, 2023. For an illustration related to this paper, see the "deflating ellipsoid" on my graphics gallery page. MathSciNet review: 1957752 (2003k:32052) Zbl. Math review: 1029.32020 EuDML page CiteSeer record

A. Coffman, Analytic normal form for CR singular surfaces in C3, Houston Journal of Mathematics (4) 30 (2004), 969-996. abstract.txt MathSciNet review: 2110245 (2006d:32048) Zbl. Math review: 1074.32013 Google Scholar citations

A. Coffman, The attraction of surfaces of revolution, The College Mathematics Journal (5) 32 (November 2001), 372-375. abstract.txt Without figures: 4 pages, 207KB 102KB With 1 figure: 5 pages, 232KB 107KB Article page at JSTOR Zbl. Math review: 0995.26003

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. abstract.txt Article page at ScienceDirect (and full-text link for subscribers) Article page at academia.edu For related links, images, animation, and code, see my Steiner Surfaces web page. Errata & post-publication comments, updated June 19, 2023. MathSciNet review: 1390390 (97g:53012) Zbl. Math review: 0875.68860 ACM Digital Library page

Notes

• Notes on abstract linear algebra. Two parts planned, Part 1 (Chapters 0-4) completed, Part 2 (starting with Chapter 5) in progress, v+244 pages. Updated April 1, 2024.
  • abstract.txt
  • Here are chapters 0-5:
• Notes on differential equations and differential inequalities, related to joint work with Y. Pan and Y. Zhang. 15 pages. Updated March 23, 2021.
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• Notes on differential topology and almost complex structures, related to joint work with Yifei Pan. 68 pages. Updated July 28, 2014.
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• Notes on series in several variables. 26 pages. Updated January 12, 2002.
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• Notes on the elementary geometry of real involutions of complex projective spaces. 16 pages. Updated June 10, 2003.
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• A Pi Day handout, for March 14. Distributed in Calculus II and also at a Pi Day demonstration at a local children's science museum. 4 pages. Updated March 2007.
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• Notes on first semester calculus, for MA 165: Calculus I. 29 pages. Updated April 8, 2021.
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• Notes on sequences and series in the calculus of one variable, for MA 166: Calculus II. 17 pages. Updated July 20, 2007.
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• Notes on elementary linear algebra, for MA 351: Elementary Linear Algebra, MA 511: Linear Algebra and Applications, and MA 554: Linear Algebra. 35 pages. Updated Nov. 3, 2013.
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• Notes on abstract algebra, for MA 453: Algebra I and MA 553: Introduction to Abstract Algebra. 19 pages. Updated Dec. 15, 2013.
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  • I have also prepared a "teacher's edition," with solutions to selected problems.
• Notes from a first course on complex analysis, for MA 525: Introduction to Complex Analysis. 20 pages. Updated May 17, 2022.
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  • I have also prepared a "teacher's edition," with solutions to selected problems.
• Notes on axiomatic geometry, for MA 560: Fundamental Concepts of Geometry. 43 pages. Updated May 27, 2018 (previous update August 8, 2001).
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  • I have also prepared a "teacher's edition," with solutions to selected problems, and sample quiz and test questions.
• Notes for the Physics-Based Calculus workshop. 10 pages, no pictures. Updated May 1, 2021.
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  • These notes originated in a Summer Workshop for Teachers, on incorporating Fourier analysis in a calculus curriculum, as part of an Indiana University initiative supported by an NSF grant, from 2001 to 2004.
  • I also use some of this material in MA 363: Differential Equations.

Lecture Notes

• J-holomorphic curves in rough almost complex structures, based on joint work with Y. Pan and Y. Zhang
  • I presented this talk in the General Contributed Paper Session in Analysis at the July 2017 MAA MathFest in Chicago.
  • Slides:
• An example for Green's Theorem with discontinuous partial derivatives, joint work with Y. Zhang, related to our "Vector fields..." paper (listed above).
  • I presented this talk at the August 2015 MAA MathFest in Washington, DC, again at the Fall 2015 Indiana MAA meeting, and an expanded version in the Analysis and Geometry Seminar at Central Michigan University, Dec. 2017.
  • Slides:
• Lecture Notes on: Glaeser's inequality on an interval, joint work with Y. Pan. The following document is a longer, illustrated version of our published article with the same title (listed above), related to talks given at MAA meetings in Indiana, Kentucky, and the 2010 MathFest.
  • 8 pages with 3 figures:
• I gave a talk, CR singularities and their unfoldings, at the conference on Rigidity in Dynamics and Geometry, at CIRM in Luminy, near Marseille, France, May 21-25, 2007.
  • Slides:
• Ellipses in the inversive plane, joint work with M. Frantz: a shorter article on the same topic appeared in 2007 (listed above). These notes are related to a talk at the Spring 2003 MAA Indiana Section meeting, an Oct. 2001 talk at the Midwest SCV conference at the University of Michigan, and a few later talks.
  • Without figures, 25 pages: 232KB
  • With figures, 26 pages: 399KB
  • CiteSeer record
• Complexification of the CR cross-cap, based on my dissertation and a Dec. 1997 talk in the Several Complex Variables Seminar, University of Michigan. 8 pages. Updated Dec. 30, 1998.
  • abstract.txt
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• Invariants for pairs of almost complex structures, based on a Feb. 1996 talk in the Geometry and Topology Seminar, University of Chicago. 20 pages. Updated May 20, 1997.
  • abstract.txt
  • Without figures: 238KB 250KB
  • With 4 figures: 1071KB 370KB

Other stuff by Adam Coffman

• One of my old automobile license plates appeared in the "Back Page" Section of the AMS Notices (10) 65 (Nov. 2018), page 1300.
• I was quoted in an interview with a local newspaper, No forks needed to enjoy slice of Pi Day, The Journal Gazette, Thursday, March 12, 2015.
• My technical assistance with the cover illustration of The College Mathematics Journal (4) 38 (September 2007) issue is acknowledged in the inside front cover.
• Illustrations for: A. Gurevich, Boundary regularity for free boundary problems, Comm. Pure Appl. Math. (3) 52 (1999), 363-403.
  • MathSciNet review: 1656068 (99m:35272)
  • Zbl. Math review: 928.35213
• Some of my amateur photographs have been published by various local media, including these:
  • My digital photo of the IPFW Mastodon sculpture appeared in Indiana Alumni Magazine, (2) 67 (2004), p. 12.
  • Some of my digital photos taken on the IPFW campus were selected to appear in the Sunday Snapshots feature on the WANE-TV news, March 14, 2004. They showed both this flower picture and this hawk picture.
  • Department of Mathematical Sciences Alumni Newsletter archive
• I am a contributor to Mathematical Reviews and Zentralblatt Math.
• I am participating in the GIMPS, a distributed computing project searching for Mersenne prime numbers.
• Published abstracts of Conference talks.
• I occasionally contribute articles (listed above), solutions to problems, letters to the editor, photos, and referee reports to the MAA journals.
  Links from JSTOR: Solutions from Problem Sections:
  • Amer. Math. Monthly 10202, 10249, 10317, 10322, 10348, 10368, 10378, 10519, 10930, 11028, 11040, 11095
  • CMJ 531, 537, 546, 570, 574, 606, 629, 646, 650, 651, 753, 759, 776
  • Mathematics Magazine 1468, 1476, 1661, 1700, 1723, 1766, 1767, 2061

Archives and Reviews

• Front End for the Mathematics arXiv at Cornell Univ.
• MathSciNet
• European Mathematical Information Service, Zentralblatt Math / zbMATH
• CiteSeer^x Digital Library
• ResearchGate

Related Papers available on the Web