Michael D. Fried
Michael David Fried | |
|---|---|
| Nationality | American |
| Alma mater | University of Michigan |
| Known for | inverse Galois problem modular tower program monodromy method branch cycle lemma Nielsen class Galois stratification proofs of Schur's conjecture and Davenport's problem |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Stony Brook University University of California, Irvine University of Florida Hebrew University of Jerusalem |
| Doctoral advisor | Donald John Lewis |
| Doctoral students | Chidambaram Alimoolam Ronald Biggers Castillo Del Paul Bailey Darren Semmen |
Michael David Fried is an American mathematician working in the geometry and arithmetic of families of nonsingular projective curve covers. He uses group representation theory to avoid solving equations (the monodromy method).
Fried's mathematical articles can be roughly divided into four groups: Arithmetic of Covers and Regular Inverse Galois Problem,[1][2] [3] [4] [5] Hilbert's Irreducibility Theorem,[6] [7] Finite fields and Diophantine problems, [8] [9] [10][11][12] and Modular Towers and Strong Torsion Conjecture [13] [14] [15] .[16]
Career
Fried got his PhD from University of Michigan in Mathematics (1964–1967); from 1959–1961 he got his undergraduate degree from Michigan State University in electrical engineering. Between those degrees he worked for three years as an aerospace electrical engineer. This included work on the Lunar Excursion Module and the Nautilus submarine . He chose the two years of postdoctoral at the Institute for Advanced Study in Princeton (1967–1969). Before living in Montana in 2004, he was a Professor at Stony Brook University (8 years), University of California at Irvine (26 years), University of Florida (3 years) and Hebrew University (2 years). He has been a visiting professor at MIT, MSRI, University of Michigan, University of Florida, Hebrew University and Tel Aviv University. He has been an editor on several mathematics journals including the Research Announcements of the Bulletin of the American Mathematical Society, and the Journal of Finite Fields and its Applications. He was included in the inaugural (2013) class of Fellows of the AMS. Frieds fellowships include Alfred P. Sloan Foundation (1972–1974), Lady Davis Fellow at Hebrew University (1987–1988), Fulbright spent at Helsinki University (1982–1983), Alexander von Humboldt Research Fellowship (1994–1996), and the two periods at the Institute for Advanced Study (Fall, 1967 to Spring 1969 and Spring 1974).
Arithmetic of covers and regular inverse Galois problem
Hilbert's irreducibility theorem
Finite fields and Diophantine problems
Modular towers and strong torsion conjecture
Other work
See also
References
- ^ Fried, M. (1977). "Fields of Definition of Function Fields and Hurwitz Families – Groups as Galois Groups". Communications in Algebra. 5 (1): 17–82. doi:10.1080/00927877708822158.
- ^ Fried, Michael (1978). "Galois groups and complex multiplication" (PDF). Trans. Amer. Math. Soc. 235: 141–163. doi:10.1090/S0002-9947-1978-0472917-6.
- ^ Fried, Michael D.; Völklein, Helmut (1991). "The inverse Galois problem and rational points on moduli spaces". Math. Ann. 290: 771–800.
{{cite journal}}: Cite has empty unknown parameter:|1=(help) - ^ Fried, Michael D.; Völklein, Helmut (1992). "The embedding problem over an Hilbertian-PAC field". Annals of Mathematics. 136 (3): 469–481. doi:10.2307/2946573. JSTOR 2946573.
- ^ Fried, Michael D. (2010). "Alternating groups and moduli space lifting Invariants". Israel J. Math. 179: 57–125. doi:10.1007/s11856-010-0073-2.
- ^ Fried, Michael (1974). "On Hilbert's irreducibility theorem". Journal of Number Theory. 6 (3): 211–232. doi:10.1016/0022-314X(74)90015-8.
- ^ Fried, M. (1985). "On the Sprindzuk-Weissauer approach to universal Hilbert subsets". Israel Journal of Mathematics. 51 (4): 347–363. doi:10.1007/BF02764725.
- ^ Fried, Michael (1970). "On a Conjecture of Schur". Michigan Math. J. 17 (1): 41–55. doi:10.1307/mmj/1029000374.
- ^ Fried, Michael (1973). "The field of definition of function fields and a problem in the reducibility of polynomials in two variables". Illinois J. Math. 17 (1): 128–146.
- ^ Fried, M.; Sacerdote, G. (1976). "Solving diophantine problems over all residue classes of a number fields and all finite fields". Annals of Mathematics. 104 (2): 203–233. doi:10.2307/1971045.
- ^ Fried, Michael D. (2005). "The place of exceptional covers among all diophantine relations". Finite fields and their applications. 11 (3): 367–433. doi:10.1016/j.ffa.2005.06.005.
- ^ Fried, Michael D. (2012). "Variables separated equations: Strikingly different roles for the Branch Cycle Lemma and the Finite Simple Group Classification". Science China Mathematics. 55 (1): 1–72. doi:10.1007/s11425-011-4324-4.
- ^ Michael D. Fried, Introduction to Modular Towers: Generalizing dihedral group–modular curve connections, Recent Developments in the Inverse Galois Problem (Seattle, WA, 1993), 111–171, Contemp. Math. , 186, Amer. Math. Soc., Providence, RI, 1995, ISBN 978-0-8218-0299-1
- ^ Michael D. Fried and Yaacov Kopeliovich, Applying Modular Towers to the Inverse Galois Problem, Geometric Galois Actions, 2, 151–175, London Math. Soc. Lecture Note Ser., 243,Cambridge Univ. Press, Cambridge, 1997, ISBN 978-0-521-59641-1.
- ^ Paul Bailey and Michael D. Fried, Hurwitz monodromy, spin separation and higher levels of a Modular Tower, Arithmetic fundamental groups and noncommutative algebra (Berkeley, CA, 1999), 79–220, Proc. Sympos. Pure Math., 70, Amer. Math. Soc., Providence, RI, 2002, ISBN 978-0-8218-2036-0.
- ^ Michael D. Fried, The Main Conjecture of Modular Towers and its higher rank generalization, Groupes de Galois arithmétique et différentiels, 165–233, Sémin. Congr., 13, Soc. Math. France, Paris, 2006, ISBN 978-2-85629-222-8.
External links
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