Publications

 

Essays and Opinion

Ideas in the Ascendant. The Chronicle Review, forthcoming.

Mathematical Community. Notices of the American Mathematical Society 58: 365 (2011). Notices page

Proving Yourself: How to Develop an Interview Lecture. Notices of the American Mathematical Society 56: 948--951 (2009). Notices page

Beautiful Numbers. The American Scholar 64:4 (Autumn 1995), 572--578.

Textbook

Exploratory Galois theory (Book). New York: Cambridge University Press, 2004. MR 2005h:12002, Zbl 1056.12005. EGT on the web

Expositions and Reviews

Hilbert 90 for biquadratic extensions (with R. Dwilewicz, J. Mináč, and A. Schultz). American Mathematical Monthly 114:7 (August-September 2007), 577--587. MR 2008f:12008, Zbl 1137.12004. Arxiv.org page

Reality Conditions by Alex Kasman. Notices of the American Mathematical Society 53: 761--763 (2006). Notices page

Cohomological invariants in Galois cohomology by Skip Garibaldi, Alexander Merkurjev, and Jean-Pierre Serre (Book review). Bulletin of the American Mathematical Society 42: 93--98 (2005). BAMS page

Research

Galois module structure of square classes of units of biquadratic extensions (with F. Chemotti* and J. Mináč).

*Undergraduate at Davidson during some of the research

Galois module structure of eigenspaces of Milnor k-theory (with N. Lemire and J. Mináč).

Cyclic algebras, Schur indices, norms, and Galois modules (with J. Mináč and A. Schultz). Annales des sciences mathématiques du Québec 35 (2011), no. 1, 123--136, special issue dedicated to Paulo Ribenboim. Arxiv.org page ASMQ page

Galois module structure of Galois cohomology for embeddable cyclic extensions of degree p^n (with N. Lemire, J. Mináč, and A. Schultz). Journal of the London Mathematical Society 81 (3): 525-543 (2010). Arxiv.org page JLMS page

Hilbert 90 for Galois cohomology (with N. Lemire, J. Mináč, and A. Schultz). Communications in Algebra 38: 361--372 (2010). Arxiv.org page

Automatic realizations of Galois groups with cyclic quotient of order p^n (with J. Mináč and A. Schultz). Journal de Théorie des Nombres de Bordeaux 20: 419--430 (2008). Arxiv.org page

Galois module structure of Milnor K-theory mod p^s in characteristic p (with J. Mináč and A. Schultz). New York Journal of Mathematics 14: 225--233 (2008). MR 2009d:19006, Zbl 1148.19002. NYJM page

Galois module structure of Milnor K-theory in characteristic p (with G. Bhandari, N. Lemire, and J. Mináč). New York Journal of Mathematics 14: 215--224 (2008). MR 2009d:19005, Zbl 1148.19001. NYJM page

Detecting pro-p-groups that are not absolute Galois groups (with D. Benson, N. Lemire, and J. Mináč). Journal für die reine und angewandte Mathematik (Crelle's Journal) 613: 175-191 (2007). MR 2009h:11184. Arxiv.org page

Note: an expanded version, not intended for publication, is also available Arxiv.org page

Galois module structure of Galois cohomology and partial Euler-Poincaré characteristics (with N. Lemire and J. Mináč). Journal für die reine und angewandte Mathematik (Crelle's Journal) 613: 147--173 (2007). Arxiv.org page

Cohomological dimension and Schreier's formula in Galois cohomology (with J. Labute, N. Lemire, and J. Mináč). Canadian Mathematical Bulletin 50, no. 4: 588--593 (2007). MR 2008i:12011. Arxiv.org page

Demuškin groups, Galois modules, and the elementary type conjecture (with J. Labute, N. Lemire, and J. Mináč). Journal of Algebra 304: 1130--1146 (2006). MR 2007h:12004. Arxiv.org page

Galois module structure of pth-power classes of cyclic extensions of degree p^n (with J. Mináč and A. Schultz*). Proceedings of the London Mathematical Society 92: 307--341 (2006). MR 2006j:12006, Zbl 1157.12002. Arxiv.org page

*Undergraduate at Davidson during some of the research; Doob Assistant Professor at Illinois; now assistant professor at Wellesley

Galois modules appearing as pth-power classes of units of extensions of degree p (with J. Mináč). Mathematische Zeitschrift 250: 907--914 (2005). MR 2006f:12002, Zbl 1128:12005. MZ page Arxiv.org page

When is Galois cohomology free or trivial? (with N. Lemire and J. Mináč). New York Journal of Mathematics 11: 291--302 (2005). MR 2006e:12011, Zbl 1159.12312. NYJM page

Brauer groups of genus zero extensions of number fields (with J. Sonn). Transactions of the American Mathematical Society 357: 2723--2738 (2005). MR 2006b:16030, Zbl 1069.16019. TAMS page

Galois embedding problems with cyclic quotient of order p (with J. Mináč). Israel Journal of Mathematics 145: 93--112 (2005). MR 2006e:12008, Zbl 1069.12002. Arxiv.org page

Galois module structure of pth-power classes of extensions of degree p (with J. Mináč). Israel Journal of Mathematics 138: 29--42 (2003). MR 2004m:12008, Zbl 1040.12006. Arxiv.org page

Quadratic corestriction, C$$₂ -embedding problems, and explicit construction (with N. Thiem*). $$Communications in Algebra 30: 3227--3258 (2002). MR 2003i:12007, Zbl 1019.12001. $$

*Undergraduate in summer research program in 1998; Szegö Assistant Professor at Stanford; now assistant professor at Colorado

Quadratic descent for quaternion algebras. Communications in Algebra 29: 4523--4544 (2001). MR 2002j:12002, Zbl 1004.12001.

Relative embedding problems (with E. Black). Transactions of the American Mathematical Society 353: 2347-2370 (2001). MR 2001m:12007, Zbl 0991.12003. TAMS page

Central p-extensions of (p,p,...,p)-type Galois groups. Journal of Algebra 186: 277--298 (1996). MR 97m:12004, Zbl 870:12005.

Explicit construction of PSL(2,7) fields over $Q(t)$ embeddable in SL(2,7) fields. Communications in Algebra 24: 3787--3796 (1996). MR 97e:12006, Zbl 863:12007.

Solutions to embedding problems are constructible. Journal of Algebra 184: 1041--1051 (1996). MR 97e:12007, Zbl 862:12004.

Groups of order 16 as Galois groups (with H. Grundman and T. Smith). Expositiones Mathematicae 13: 289--319 (1995). MR 96h:12005, Zbl 838:12004.

Embedding problems and the $C$₁₆ -->C₈ obstruction. In Recent Developments in the Inverse Galois Problem $$(Michael D. Fried, coord. ed.), vol. 186 of Contemporary Mathematics $$(Providence, RI: American Mathematical Society), 1995. 75--90. MR 96j:12010, Zbl 828:12005. $$

On constructing fields corresponding to the Ã_n's of Mestre for odd $n$. $$Proceedings of the American Mathematical Society $$122: 85--89 (1994). $$ MR 95i:12002, Zbl 812:12001.$$

L. Manivel. Symmetric functions, Schubert polynomials and degeneracy loci. Trans. J. Swallow. SMF/AMS Texts and Monographs 6. Providence, RI: American Mathematical Society, 2001. MR 2002h:05161.

High-performance sorting algorithms for the Cray T3D parallel computer (with B. Dixon). Journal of Supercomputing 10: 371--395 (1997).