- B.S. March 1978, Summa Cum Laude, University of Georgia, Athens, Georgia, Mathematics Major.
- Ph.D. in Mathematics, May 1982, Yale University, New Haven, Connecticut, Dissertation: ``Surgery on Immersions: a Geometric Approach to Stable Homotopy", Advisor Prof. Ronnie Lee.

- Oct. 5, 2010-Present: Professor, Department of Mathematics and Statistics , University of South Alabama , Mobile , Alabama.
- Jan 2003-Oct. 5, 2010: Chair, Department of Mathematics and Statistics , University of South Alabama , Mobile , Alabama.
- May 2002-Jan 2003: Interim Chair, Department of Mathematics and Statistics , University of South Alabama , Mobile , Alabama.
- Sept 1996-May 2002: Professor, Department of Mathematics and Statistics , University of South Alabama , Mobile , Alabama.
- 1993-1996: Associate Professor, Department of Mathematics and Statistics , University of South Alabama , Mobile , Alabama.
- 1989-1993: Assistant Professor, Department of Mathematics and Statistics , University of South Alabama , Mobile , Alabama.
- 1988-1989: Lecturer, Wayne State University, Department of Mathematics, Detroit, Michigan.
- 1987-1988: Lecturer, University of Texas, Austin, Texas.
- 1985-1987: Assistant Professor, Department of Mathematics and Computer Studies, Lake Forest College, Lake Forest, Illinois.
- 1982-1985: Instructor, Mathematics Department, University of Texas, Austin, Texas.

*Surgery Theory of Immersions*, Proc. Northwestern Homotopy Theory Conf. (Miller and Priddy, eds.), AMS Contemp. Math Series 19 (1983), 23-37.*Surgery on Codimension One Immersions in (n+1)-space: Removing n-tuple Points*, Trans. of the AMS 289, No. 1, (1986), 83-102.*On Generalizing Boy's Surface: Constructing a Generator of the Third Stable Stem*, Trans. of the AMS 289, No. 1 (1986), 103-121.*A Further Generalization of Boy's Surface*, Houston Journal of Mathematics 12, No. 1 (1986), 11-31.-
*Simplifying the Self Intersection Sets of Codimension One Immersions in (n+1)-space*, Houston Journal of Mathematics 13, No. 3, 353-366. -
*Surgery on the Equatorial Immersion I*, Illinois Journal of Mathematics 32, No. 4, Winter 1988, 703-715. -
*Surgery on the Equatorial Immersion in Low Dimensions*, Differential Topology Proceedings, Siegen 1987, Springer LMN 1350, U. Koschorke, ed. - with Ki Hyoung Ko
*Triple Points of Immersed Surfaces in Three Dimensional Manifolds*, Topology and Its Applications 32, (1989), 149-159. -
*Immersed Codimension One Projective Spaces in Spherical Space Forms*, Proc. of the AMS 105, No. 1, January 1989, 254-257. -
*Immersed Projective Planes in Lens Spaces*, Proc. of the AMS 106, No. 1 (May 1989), 251-260. -
*Classifying Immersed Curves*, Proc. of the AMS 111, No.1 (Jan. 1991), 281-287. -
*Extending Immersed Curves to Proper Immersions of Surface*, Topology and its Applications 40 (1991), 287-306. -
*Closed Curves that Never Extend to Proper Maps of Disks*, Proc. of the AMS 113, No. 3 (Nov 1991), 879-888. - with Masahico Saito
,
*Canceling Branch Points on Projections of Surfaces in 4-Space*, Proc. of the AMS. 116, No 1. (Sept 1992), 229-237. -
*Extending Immersed Circles in the Sphere to Immersed disks in the Ball*, Comm. Math. Helv. 67 (1992), 337-348. - with Masahico Saito
,
*Syzygies among Elementary String Interactions in Dimension 2+1*, Letters in Mathematical Physics 23 (1991), 287-300. - with Masahico Saito
,
*Planar Generalizations of the Yang Baxter Equation and Their Skeins*, Journal of Knot Theory and its Ramifications Vol 1, No. 2 (1992), 207-217. - with Masahico Saito
,
*A Diagrammatic Theory of Knotted Surfaces*, in ``Quantum Topology,'' ed. Randy Baadhio and Louis Kauffman, World Science Publishing (Singapore 1993), 91-115. -
*Solving Inequalities*, Alabama Journal of Mathematics, Vol 1, No.1 \& 2, (1992), 31-35. - with Masahico Saito
,
*Reidemeister Moves for Surface Isotopies and Their Interpretations As Moves to Movies*, Journal of Knot Theory and its Ramifications Vol 2, No 3 (1993), 251-284. - with Masahico Saito ,
*Knotted Surfaces, Braid Movies, and Beyond*, in ``Quantum Gravity,'' ed. John Baez, Oxford University Press (1994), 191-229. - with Masahico Saito
,
*New Solutions to the Permutohedron Equation*in ``Quantum Topology Kansas 1993,'' ed. David Yetter, World Science Publishing Company (1994), 51-65. - with Masahico Saito ,
*Knot Diagrams and Braid Theories in Dimension 4**Real and Complex Singularities,*ed. W. L Marar , Pitman Research Notes in Mathematics, Longman Publishing (1995). - with Masahico Saito
,
*A Seifert Algorithm for Knotted Surfaces,*Topology, Vol 36, No. 1 (1996), 179-201. - with Masahico Saito
,
*Braid and Movies*, Journal of Knot Theory and Its Ramifications, Vol 5, No. 5 (1996), 589-608. - with Masahico Saito
,
*On Formulations and Solutions of Simplex Equations,*International Journal of Modern Physics A, Vol 11, No 24, (1996), 4453-4463. - with Masahico Saito
,
*Normal Euler Classes of Knotted Surfaces and Triple Points on Their Projections*, Proc. Amer. Math. Soc., 125 (1997), no. 2, 617-623. - with Masahico Saito
, and Joachim
Rieger,
*A Combinatorial Description of Knotted Surfaces and Their Isotopies,*Advances in Mathematics, 127, No. 1, April 15 (1997), 1-51. Preprint here Sorry about quality, old ps file created with primitive unix dvi2ps! - with Masahico Saito
,
*Surfaces in 3-Space that Do Not Lift to Embeddings in 4-Space,*to appear in Conference Proceedings of the 1995 Warsaw Workshop on Knot Theory. - with Louis H.
Kauffman and Masahico
Saito ,
*Diagrammatics, Singularities, and Their Algebraic Interpretations,*10th Brazilian Topology Meeting (São Carlos, 1996). Mat. Contemp. 13 (1997), 21--115. - with Sostenes Lins
*Thin-G theory and local moves for gems*, Adv. Math. 143 (1999), no. 2, 251--283. Advances in Mathematics, 127, No. 1, April 15 (1997), 1-51. - with Masahico Saito
and Vera
Carrara
*Singularities of Surface Maps and Knots,**Pacific J. Math.***199**(2001), no. 1, 21--40. - with Masahico Saito
and
Seiichi Kamada ,
*Alexander numbering of knotted surface diagrams,*Proc. Amer. Math. Soc., 128 (2000), no. 12, 3761--3771. - with Louis H.
Kauffman and Masahico
Saito ,
*Structures and Diagrammatics of 4-Dimensional Topological Lattice Field Theories,*Advances in Math., 146, 39-100 (1999). - with Daniel Jelsovsky, Masahico Saito, Seiichi
Kamada , and Laurel Langford,
*Quandle cohomology and state-sum invariants of knotted curves and surfaces.*Trans. Amer. Math. Soc. 355 (2003), no. 10, 3947--3989. - with Daniel Jelsovsky, Masahico Saito
and
Seiichi Kamada ,
*Computations of quandle cocycle invariants of knotted curves and surfaces.*Adv. Math. 157 (2001), no. 1, 36--94. - with Daniel Jelsovsky, Masahico Saito
and
Seiichi Kamada ,
*Quandle Homology Groups, Their Betti Numbers, and Virtual Knots.*J. Pure Appl. Algebra 157 (2001), no. 2-3, 135--155. - with Daniel Jelsovsky, Masahico Saito
and
Seiichi Kamada ,
*Geometric interpretations of quandle homology.**J. Knot Theory Ramifications***10**(2001), no. 3, 345--386. - with Daniel Jelsovsky, Masahico Saito
and
Seiichi Kamada ,
*Shifting homomorphisms in quandle cohomology and skeins of cocycle knot invariants.**J. Knot Theory Ramifications***10**(2001), no. 4, 579--596. - with
Shin Satoh ,
Masahico Saito
and
Seiichi Kamada , A
theorem of Sanderson on link bordisms in
dimension 4 ,.
*Algebr. Geom. Topol.*1 (2001), 299--310. - with
Mohamed Elhamdadi , and
Masahico Saito,
Twisted quandle homology theory and cocycle knot
invariants .
*Algebr. Geom. Topol.*2 (2002), 95--135. - with Masahico Saito
and
Seiichi Kamada, Stable equivalence of
knots on surfaces and
virtual knot cobordisms.
Knots 2000 Korea, Vol. 1 (Yongpyong).
*J. Knot Theory Ramifications***11**(2002), no. 3, 311--322. - with
Shin Satoh ,
Masahico Saito
and
Seiichi Kamada, Bordism of unoriented surfaces in 4-space.
*Michigan Math. J.***50**(2002), no. 3, 575--591. - with Mohamed Elhamdadi , Angela Harris, Marina Nikiforou and Masahico Saito, Cocycle knot invariants, quandle extensions, and Alexander matrices. Low-dimensional topology of tomorrow (Japanese) (Kyoto, 2002).
- with Masahico Saito
and
Seiichi Kamada,
Diagrammatic computations for quandles and cocycle
knot invariants.
*Diagrammatic morphisms and applications (San Francisco, CA, 2000),*51--74, Contemp. Math., 318,*Amer. Math. Soc., Providence, RI,*2003. - with Masahico
Saito.
Quandle
homology theory and cocycle knot invariants.
*Topology and geometry of manifolds (Athens, GA, 2001),*249--268, Proc. Sympos. Pure Math., 71,*Amer. Math. Soc., Providence, RI,*2003. - with
Mohamed Elhamdadi and
Masahico Saito, Homology theory for the set-theoretic Yang-Baxter
equation and knot invariants from generalizations of quandles.
*Fund. Math.*184 (2004), 31--54. - with
Mohamed Elhamdadi,
Matias Grana, and
Masahico Saito, Cocycle knot invariants from quandle modules
and generalized quandle homology.
*Osaka J. Math.***42**(2005), no. 3 499--541. - with Shin Satoh and Masahico Saito, Ribbon concordance of surface knots via quandle cocycle invariants, J. Aust. Math. Soc. 80 (2006), no. 1, 131--147.
- with Mohamed Elhamdadi , Shin Satoh and Masahico Saito, A lower bound for the number fo Reidemeister moves of type III , Topology Appl. 153 (2006), no. 15, 2788--2794.
- with
Masahico Saito,
Set Theoretic Yang-Baxter Solutions via Fox Calculus. J. Knot
Theory Ramifications 15 (2006), no. 8, 949--956.

- with
Masahico Saito,
Shin Satoh
Ribbon-moves for 2-knots with 1-handles attached and Khovanov-Jacobson
numbers. Proc. Amer. Math. Soc. 134 (2006), no. 9, 2779--2783.

- with
Masahico Saito, Cohomology for self-distributivity in coalgebras.
Intelligence of low dimensional topology 2006, 9--17, Ser. Knots
Everything, 40, World Sci. Publ., Hackensack, NJ, 2007.

- with Alissa Crans ,
Mohamed Elhamdadi,
Masahico Saito, Cohomology of
the Adjoint Map of Hopf Algebras. J. Gen. Lie Theory
Appl. 2 (2008), no. 1, 19--34.

- with Alissa Crans ,
Mohamed Elhamdadi,
Masahico Saito,
Cohomology of Categorical Self-Distributivity , Journal of Homotopy
Theory and Related Structures 3 (2008), no. 1, 13-63.

- with Alissa Crans ,
Mohamed Elhamdadi,
Masahico Saito,
Cohomology of Algebraic Identities and R-Matrices,
preprint.

- with Abhijit Champanerkar , A geometric method to compute some elementary integrals, preprint.
- with Masahico Saito and Kanako Oshiro , Symmetric extensions of dihedral quandles and triple points of non-orientable surfaces. Topology Appl. 157 (2010), no. 5, 857Ð869.
- with Masahico Saito Algebraic Structures Derived from Foams, to appear J. Gen. Lie Theory Appl.
- with Masahico Saito Frobenius Modules and Essential Surface Cobordisms, preprint.
- A Survey of Quandle Ideas , preprint, to appear in conference proceedings of Trieste form May 2009.

- How Surfaces Intersect in Space: an Introduction to Topology, World Scientific Publishing, Singapore (First edition 1993), (Second edition 1995).
- The Classical and Quantum 6j-symbols (with D.E. Flath and M. Saito ), Princeton University Press (1995).
- Knotted Surfaces and Their Diagrams, with Masahico Saito American Mathematical Society.
- Surfaces
in 4-space , with Masahico
Saito and
Seiichi Kamada ,
Springer-Verlag .

- Intelligence of Low Dimensional Topology , with Seiichi Kamada , Lou Kauffman , Akio Kawauchi , and Toshitake Kohno
- An Excursion in Diagrammatic Algebra: turning a sphere from red to blue , World Science Publishing, Series on Knots and Everything, Volume 48.

- American Mathematical Society
- Phi Beta Kappa
- Managing Editor Journal of Knot Theory and Its Ramifications

*J. Scott Carter
Professor of Mathematics
Department of Mathematics
and Statistics
ILB 325
University of South Alabama
Mobile, AL
36688-0002
(251) 460-6264 / 460-7969 FAX
click here
for e-mail.
*