As seen from the 120 cell

Talks and Stuff

Many of the works here have benefitted from the support of various NSF grants

  • Here is the talk I gave at the Joint Mathematical Meetings 2016. The talk is Foams and Homology. And Here is the handout version.


  • Here is the talk that I didn't give at the 1114th meeting of the AMS. The talk is Fractal Simplices. And Here is the handout version. Bad weather delayed my flights severely.


  • Here is the talk I am giving at the 1112th meeting of the AMS. The talk is Geometrical, Categorical, and Homological Considerations of Local Crossings of Foams. And Here is the handout version.


  • Here is a draft of a paper I wrote in memory of Slavik Jablan Fractal Simplices


  • Here is a paper I wrote for Vassily Manturov's Seminar proceedings that will appear in JKTR. Geometric and Homological Considerations of Local Crossings of $n$-Foams


  • Here is a draft of notes for the Pure Math Seminar at the University of South Alabama, Braided Forests and Stuff part 2


  • Here is a draft of notes for the Pure Math Seminar at the University of South Alabama, Braided Forests and Stuff


  • Here is a more official version that I gave at MAA Mathfest 100 . Algebraic Structures Motivated by Knot Theory. An Introduction to Quandle Cohomology. The Handout version is Here.


  • Here is a paper, Some Elementary Aspects of 4-dimensional Geometry that will soon be submitted for publication. tarball


  • Here is a talk, Braided Manifolds in all dimensions presented at Fall Southeastern Sectional Meeting Meeting 1105 of the American Mathematical Society.


  • Here is a talk, Braided Manifolds presented at Knots and Low Dimensional Manifolds August, 22-24, 2014, Bexco Convention Center Pusan, Korea.


  • Here are three talks, Kyungpook Mathematics Journal Symposium, Kyungpook Topology Seminar 1, and Kyungpook Topology Seminar 2 presented at Kyungpook National University August, 2014 Daegu, Korea.


  • Here is a talk, Examples of Non-orientable surfaces in 4-dimensional space presented at the Department of Mathematics at Kyungpook National University.


  • Here is a talk, Reidemeister/Roseman moves for knotted foams that I gave at Knots in Washington XXXV, Dec. 2012 .

  • I gave a similar talk, Reidemeister/Roseman moves for knotted foams at a TQFT workshop in Lisbon, Portugal, Sept. 2012.


  • After some strange things happened, I wrote this essay about some childhood experiences and the 4th dimension.


  • Here are two versions of a manuscript that will be posted at the arXiv soon. The smaller version has the same information that the larger version does. But the quality of the figures is not as good. My plan for this page, or the math art page, is to have pdf versions of these figures readily available for those who wish to use such figures in their own work. As of this writing, I don't have the time to sort through this, but stay tuned.


  • Here are the pdfs from my recent sabbatical to Kyungpook National University where I visited the Department of Mathematics from December 25, 2011 through August 20, 2012. Not all items are available here yet. Updates to appear shortly.

  • Homology of G-Families of Quandles and Knotted Foams presented to the TAPU Knot School, Busan, 2012.
  • Reidemeister/Roseman-type Moves to Foams presented to the TAPU Knot School, Busan, 2012.
  • The Diagrammatic Theory of Knotted Surfaces and Constructing Invariants presented to the Youngnam Mathematical Society, June 2012.
  • Drawing the Hypercube presented to ICME (International Committee for Mathematics Education) in a workshop, "Can Art Save Mathematics?"
  • How to fold a manifold presented to the Korean Mathematics Society, Sookmyung Women's University, Seoul, Korea, April, 28, 2012
  • Local pictures for knotted foams and G-families of quandles presented to the Intelligence of Low Dimensional Topology, Kyoto, May 2012.
  • Local pictures for knotted foams and G-families of quandles presented to the Topology seminar at Fukuoka University, May 2012.
  • How to fold a manifold presented to the KOOK seminar, Osaka, Japan, May 2012.
  • Knotted Trivalent Graphs, n-Dimensional Foams, and G-families of Quandles presented to the 8th East Asia School of Knots Daejon, Korea, December 2012.
  • Danny the Dishwasher Presented to the Unitarian Universalists of Mobile August 14, 2011. This talk describes an unremarkable person who passed through my life and our interactions.
  • Heron's Formula from a 4-Dimensional Perspective, joint work with David Mullens presented at the University of South Alabama colloquium.
  • Heron's Formula from a 4-Dimensional Perspective, joint work with David Mullens as part of his undergraduate research project (UCUR).
  • Quandles, (co)-homology, applications, and beyond presented at the 7th East Asia School of Knots and Related Topics, Jan. 2011
  • Print version.
  • graph paper for projection.
  • graph paper green on black for projection.
  • David Mullen's talk MAA meeting at University of West Florida, Nov. 19, 2010.
  • Categorical Quandles and Knots, III --- Relations to the Fundamental Group presented at the 1063rd meeting of the American Mathematical Society. Oct. 2010. Print version.
  • Classical knots, quandles, categorical quandles, and invariants presented at TAPU-KOOK Seminar July 2010. Handout version.
  • Choose your Heroes (and Villians) Wisely Unitarian Universalist Fellowship of Mobile Sermon, June 27, 2010.
  • Categorical Quandles and Knots Knots in Washington XXX (That is 30) Print version.
  • Categorical Quandles and Knots April 10, 2010, AMS Regional meeting 1058, Saint Paul, Minnesota. Print version.
  • You are not the boss of me Mar. 28, 2010, Unitarian Universalist Fellowship of Mobile.
  • Introducing Dan Silver November 10, 2009, University of South Alabama, College of Arts and Sciences Dean's Lecture.
  • Riverside, CA November 7-8, 2009, Sectional Meeting of the AMS 1054.
  • Boca Raton, FL October 30-November 1, 2009, Sectional Meeting of the AMS 1053.
  • Unitarian Universalist Fellowship of Mobile Sermon, August 30, 2009.
  • Summer workshop on Math and Science Circles June 17, 2009 .
  • Projecting from 4-dimensional to 2-dimensions slides for DIMACS Algorithmic Mathematical Art Best downloaded and viewed with acroread. See also the the youtube link
  • The sphere eversion book, "Turning a Sphere from Red to Blue. Here the complete eversion is given. If you see any typos, please let me know. here is a gzipped tarred version of the same file but it is still 52.9 MB.
  • The sphere eversion slides for Champaign Urbana AMS Conference Regional Meeting # 1047.
  • Flier for the a Mobile Mathematics Society talk.
  • Slides for the Mobile Mathematics Society talk, Wednesday, Oct. 8, 2008; same slides used at Knots in Washington # 27.
  • Slides for a different Mobile Mathematics Society talk, Spring 2007.
  • Text of a talk at the Unitarian Universalist of Mobile, Sunday, Oct. 5, 2008.
  • Baton Rouge many years ago.
  • Baltimore many years ago.
  • College Park, Md. many years ago.
  • Knots in Washington, November, 2006.
  • Miami of Ohio.
  • A defintion of mathematics I gave this in Polimetria.
  • I think this was Columbus, Ohio.
  • Some notes and the slides .
  • The Binomial Theorem.
  • Osaka
  • Shodo-Shima
  • A compendium of drawings inspired by Tony Robbin.
  • An etude on the central projection of the hypercube.
  • Another article for Polimetria.
  • Another Knots in Washington talk. Here I give the braid movie for the 2-twist spun trefoil and arrange it to be readable by robots.
  • A little picture to depict quandle coloring.
  • Intelligence of Low Dimensional Topology, Hiroshima.
  • Hanoi 2007 beamer presentation.
  • Dallas 2007 beamer presentation.
  • Columbia University 2007 beamer presentation.
  • Gdansk 2008 beamer presentation.
  • Tampa 2007 beamer presentation with Tony Robbin.
  • Oberwolfach 2008 beamer presentation.
  • Baton Rouge 2008 beamer presentation.
  • An essay about mathematics education my opinion only at the time of the writing.
  • Summary of quandle ideas. Some notes about the Joyce/Matveev Theorem and other quandle matters.
  • Remarks on the dedication to Tubular #19.  Casey Downing's piece dedicated to the memory of members of the Eichold family.
  • Number Shapes Notes written to a 2nd grader on count-bys, squares, and triangles.
  • Problem book sketch Notes written to a high schooler: Drill problems in various areas. Incomplete.
  • Book sketch for High School teachers Incomplete, and material in the next link is also needed for understanding.
  • Fractals in Higher Dimensions Complete book manuscript, but images of the fractals are supposed to run in the margins as a flip book.

  • J. Scott Carter
    Professor of Mathematics
    Department of Mathematics and Statistics
    ILB 325
    University of South Alabama
    Mobile, AL 36688-0002

    (334) 460-6264 / 460-7969 FAX
    click here for e-mail.


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    The views and opinions expressed in these web page(s) are strictly those of the author. The contents of these page(s) have not been reviewed or approved by the University of South Alabama. I am not responsible for content in linked material. Come to think of it, I am not repsonsible for much!