|Office: || ||Duke 204 C|
|Phone:|| ||(336) 278-6299|
|Address: || ||Department of Mathematics and Statistics|
| || ||Campus Box 2320|
| || ||Elon University|
| || ||Elon, NC 27244|
Dr. Awtrey joined Elon University in 2010 after completing his graduate work at Arizona State University. His main research interests lie in algebraic number theory, p-adic fields, and computational Galois theory.
A passionate proponent of undergraduate research, Dr. Awtrey regularly engages undergraduates in problems related to his research program, and he fosters a commitment in his students to disseminate their work through publications and national/regional presentations. From 2013-2015, his work in mentoring undergraduate research was supported by a grant from the Center for Undergraduate Research in Mathematics. In recognition of his success in mentoring undergraduate research, Dr. Awtrey received the 2014 Early Career Mentoring Award from the Division of Mathematics and Computer Science within the Council on Undergraduate Research (CUR). In 2015, Elon University awarded Dr. Awtrey the A.L. Hook Endowed Professorship.
A dedicated teacher-scholar, Dr. Awtrey received the Dean's Distinguished Teaching Award while at Arizona State in 2008, and he was chosen as a 2010 national Project NExT fellow. From 2012-2014, Dr. Awtrey's SoTL research on Writing to Learn and Writing in the Disciplines was supported by a generous grant through Elon University's Center for the Advancement of Teaching and Learning. In 2016, Dr. Awtrey received the Award for Distinguished Teaching by a Beginning Faculty Member from the Southeastern Section of the Mathematical Association of America.
Dr. Awtrey currently serves as Associate Director of Undergraduate Research at Elon. Since 2014, he has served as a councilor for CUR (in the Division of Mathematics and Computer Science) and on the national council of Pi Mu Epsilon (PME), the national mathematics honor society; first as a councilor and currently as Secretary-Treasurer. In addition, he currently serves as Co-Organizer for the UNC Greensboro Regional Mathematics and Statistics Conference and as an editor of the North Carolina Journal of Mathematics and Statistics.
Tables of Wildly Ramified p-adic Fields
Tables of wildly ramified extensions of the p-adic numbers can be accessed HERE. These are based on papers , , , , , , and  listed below.
* denotes an undergraduate student
** denotes a graduate student
- Computing Galois groups of Eisenstein polynomials over p-adic fields, with J. Milstead**, and S. Pauli, submitted.
- Subfields of solvable sextic field extensions, with P. Jakes*, North Carolina J. Math. Stat., 4, 1-11, 2018.
- Efficient computation of Galois groups of even sextic polynomials, with P. Jakes*, submitted. Magma implementation can be accessed HERE.
- Constructing Galois 2-extensions of the 2-adic numbers, with J. Beuerle, and J. Schrader*, North Carolina J. Math. Stat., 3, 21-33, 2017.
- Determining Galois groups of reducible polynomials via discriminants and linear resolvents, with T. Cesarski*, and P. Jakes*, JP J. Algebra, Num. Theory Appl., 39, no. 5, 685-702, 2017.
- Algorithms for computing quartic Galois groups over fields of characteristic 0, with J. Beuerle, and M. Keenan*, Int. J. Pure Appl. Math., 112, no. 4, 709-740, 2017.
- Galois groups of degree 12 2-adic fields with trivial automorphism group, with B. Barkley*, N. Miles*, C. Shill*, and E. Strosnider*, JP J. Algebra, Num. Theory Appl., 38, no. 5, 457-471, 2016.
- Degree 12 2-adic fields with automorphism group of order 4, with B. Barkley*, N. Miles*, C. Shill*, and E. Strosnider*, Rocky Mountain J. Math., 45, no. 6, 1755-1764, 2016.
- Irreducible sextic polynomials and their absolute resolvents, with R. French*, P. Jakes*, and A. Russell, Minn. J. Undergraduate Math., 1, no. 1, 14-32, 2015.
- Centralizers of transitive permutation groups and applications to Galois theory, with N. Mistry* and N. Soltz*, Missouri J. Math. Sci., 27, no. 1, 16-32, 2015
- On Galois group of degree 15 polynomials, with K. Mazur, S. Rodgers*, N. Soltz*, and J. Weed*, Int. J. Pure Appl. Math., 104, no. 3, 407-420, 2015.
- Degree 14 2-adic fields, with N. Miles*, J. Milstead**, C. Shill*, and E. Strosnider*, Involve, 8, no. 2, 329-336, 2015.
- Groups of order 16 as Galois groups over the 2-adic numbers, with J. Johnson*, J. Milstead**, and B. Sinclair**, Int. J. Pure Appl. Math., 103, no. 4, 781-795, 2015.
- Absolute resolvents and masses of irreducible quintic polynomials, with C. Shill*, Collaborative Mathematics and Statistics Research: Topics from the 9th Annual UNCG Regional Mathematics in Statistics Conference, Springer Proceedings of Mathematics & Statistics, Springer, New York, 109, 31-41, 2015.
- A linear resolvent for degree 14 polynomials, with E. Strosnider*, Collaborative Mathematics and Statistics Research: Topics from the 9th Annual UNCG Regional Mathematics in Statistics Conference, Springer Proceedings of Mathematics & Statistics, Springer, New York, 109, 43-50, 2015.
- Resolvents, masses, and Galois groups of irreducible quartic polynomials, with B. Barkley*, M. McCraw*, and J. Guinn*, Pi Mu Epsilon Journal, 13, no. 10, 609-618, 2014.
- Galois groups of degree 12 2-adic fields with automorphism group of order 6 or 12, with C. Shill*, Topics from the 8th Annual UNCG Regional Mathematics and Statistics Conference, Springer Proceedings in Mathematics & Statistics, Springer, New York, 64, 55-65, 2013.
- Impossible geometric constructions: a calculus writing project, PRIMUS, 23, 141-149, 2013.
- Dihedral p-adic fields of prime degree, with T. Edwards*, Int. J. Pure Appl. Math., 75, 185-194, 2012.
- Masses, discriminants, and Galois groups of tame quartic and quintic extensions of local fields, Houston J. Math., 38, 397-404, 2012.
- Dodecic 3-adic fields, Int. J. Number Theory, 8, 933-944, 2012.
- On Galois groups of totally and tamely ramified sextic extensions of local fields, Int. J. Pure Appl. Math., 70, 855-863, 2011.