CURRICULUM VITAE FOR STEPHEN P. HUMPHRIES

Education

University of Wales, 1974, B. Sc. in Pure and Applied Mathematics. University of Wales, 1978, M.Sc. in Pure Mathematics: Dissertation on Kahler mani-

folds and Hamiltonian mechanics.

University of Wales, 1983, Ph.D. ”Mapping class groups, graphs and symplectic geometry” (120 pages)

PROFESSIONAL EXPERIENCE

(1) July 1987–present, Assistant Professor, Associate Professor, Professor, Brigham Young University.

(2) July 1985-July 1987, Appointed the first Ky Fan Assistant Professorship at the University of California, Santa Barbara.

(3) July 1984–Aug. 1985, Ritt Assistant Professorship at Columbia University, New York.

PUBLICATIONS

(1) “Generators for the Mapping Class Groups,” Springer Lecture Notes in Math 722 (1979), 44–47.

(2) (with R. Brown) “Orbits Under Symplectic Transvections I,” Proc. London Math. Soc. (3) 52 (1986), 517–531.

(3) (with R. Brown) “Orbits Under Symplectic Transvection II,” Proc. London Math. Soc. (3) 52 (1986), 532–556.

(4) (with D. Johnson) “A generalization of winding number functions on surfaces,” Proceedings of London Math. Soc. (3) 58 (1989), 366–386.

(5) “Graphs and Nielsen Transformations of Symmetric, Orthogonal and Symplectic groups,” Quarterly Journal Math. Oxford (2) 36 (1985), 297–313.

(6) “On Weakly Distinguished Bases and free Generating sets of free groups,” Quarterly J. Math. Oxford (2) 36 (1985), 215–219.

(7) “Generation of Special Linear Groups by Transvections,” Journal of Algebra 99 (1986), 480–495.

(8) “Free subgroups of SL(n, Z), n > 2, generated by transvections,” Journal of Algebra, 116 (1988), 155–162.

(9) (with D. D. Long) “On the Mal’cev quotients of certain hyperbolic link groups,” Math. Proc. Cambridge Phil. Soc. 102 (1987), 475–480.

Typeset by AMS-TEX

(10) “Free Products in Mapping Class Groups generated by Dehn Twists,” Glasgow Journal of Mathematics,31 (1989), 213–218.

(11) “Some Subgroups of SL(3, Z) generated by involutions,” Glasgow Math. Journal 32 (1990), 127–136.

(12) “Split Braids,” Proc. Amer. Math. Soc. 113 (1991), 21–26.

(13) “An approach to Automorphisms of Free Groups and Braids via transvections,” Mathematische Zeitschrift 209 (1992), 131–152.

(14) “Some subgroups of SL(3, Z) generated by transvections,” Communications in Algebra 20(6) (1992), 1675–1703.

(15) “Quotients of Coxeter complexes, Fundamental Groupoids and Regular graphs,” Math. Zeitsch, 217 (1994), 247–273.

(16) “Normal Closures of Dehn Twists in Mapping Class groups,” Glasgow Math. Journal 34 (1992), 313–317.

(17) “On Reducible Braids and Composite Braids,” Glasgow Math. J., 36 (1994), 197– 199.

(18) “On representations of Artin groups and the Tits Conjecture,” Journal of Algebra, 169 (3), (1994), 847–862.

(19) “A new characterisation of braid groups and rings of invariants for symmetric automorphism groups,” Math. Zeitsch, 224 255-287 (1997).

(20) “Cogrowth and the Dedekind-Frobenius group determinant,” Philosophical Proceedings of the Cambridge Math. Soc., 121, 193-217 (1997), .

(21) “Cogrowth of Groups and a matrix of Redheffer,” Linear Algebra and Applications, 265 (1997) 101-117 .

(22) “Action of some braid groups on Hodge Algebras” Communications in Algebra. 26, (1998) 1233-1242.

(23) “Weak Cayley Table Groups,” Journal of Algebra 216 (1999) 135-158.

(24) “Braid groups, infinite Lie algebras of Cartan type and rings of invariants”, Topology and its Applications 95 (1999) 173-205 .

(25) “Some Linear Representations of Braid Groups,” Journal of Knot Theory and its Ramifications 9 (3) (2000) 341-366.

(26) “Torsion-free quotients of braid groups,” Internat. Jour. Alg. and Comp. (2001)

(27) “Intersection number operators for curves on discs and Chebychev Polynomials,” Knots, Braids and Mapping Class Groups (2001) 49-75.

(28) “Intersection number operators for curves on discs II,” (preprint) (1999) 12 pages, to appear in Geometriae Dedicata. Appeared 2001.

(29) “Action of braid groups on determinantal ideals, compact spaces and a stratification of Teichmüller space” Inventiones Mathematicae 144 (2001) 451-505.

(30) “Hurwitz action on sets of Euclidean reflections” 30 pages (2003) to appear in J. Algebra.

(31) “ Hurwitz action on Artin groups” 25 pages (2003) submitted.

(32) “Representations of Braid groups via determinantal rings” (preprint) (2001) 42 pages.

(33) “ An action of Braid groups on compact spaces with chaotic behaviour” (preprint) (2001) 34 pages, submitted.

(34) “ An action of Braid groups on a polynomial ring” (preprint) (2003) 230 pages. To be submitted to Springer Lecture Notes in Math series.

LIST OF SOME PROFESSIONAL TALKS GIVEN

University of Sussex Low Dimensional Topology conference, 1977 British Math Conference, Bristol 1984 Oxford University Colloquium, 1983 Southamptom University Colloquium, 1983 Cardiff University Colloquium, 1983 SUNY at Binghampton Colloquium, 1985 Lehigh University Colloquium, 1985 Columbia University Topology seminar 1985 Colloquia, BYU 1985 and 1987 Southern California Topology Seminar, 1986 MAA meeting at BYU, 198? AMS meeting at Logan, Ut 1986 Mal’cev Algebra Conference, Novosibirsk 1989 Colloquia at University of Wales, Bangor 1989, 1993, 1997, 1998, 2001 Groups St. Andrews at Galway, July 1993 Beijing Group theory meeting, May 1996 Canadian Math Soc meeting 1997 Sarasota Group theory meeting, Jan. 1997 Groups St. Andrews at Bath, July 1997 Cascade Topology Seminar, Nov. 1997 Birmanfest NYC 1998 Heriot-Watt July 1998 AMS Meeting at Las Vegas Apr. 1999 AMS Meeting at New York Nov. 2000 Southern England topology conference Nov 2001 Colloquium at the Univ. of Southampton Fall 2001 Topology seminar at Warwick Univ. Nov. 2001 Cannonfest June 2003

Ph. D. Students supervised

Dmitri Kouksov: “Cogrowth of groups” Ph. D. thesis (1998). From this thesis two papers have appeared so far: 1) On rationality of the cogrowth series. Proc. Amer. Math. Soc. 126 (1998), no. 10, 2845–2847. 2) Cogrowth series of free products of finite and free groups. Glasg. Math. J. 41 (1999), no. 1, 19–31.