Shabnam Akhtari
Assistant Professor Address: Fenton Hall Eugene, OR 974031222 USA
EMail: akhtari AT uoregon DOT edu 
Research Interests
Number Theory, Diophantine Analysis, Geometry of Numbers.
My research is funded by the National Science Foundation grant DMS1601837.
Some of my papers are available on the arXiv .
Preprints and Publications in Refereed Journals (with Kevser Aktas, Kirsti Biggs, Alia Hamieh, Kathleen Petersen and Lola Thompson) Lower Bounds for Heights in Relative Galois Extensions, submitted for publication in 2017. arXiv preprint
 (with Manjul Bhargava) A positive proportion of locally soluble Thue equations are globally insoluble (preprint, 23 pages), submitted for publication in 2016. arXiv preprint
 (with N. Saradha and D. Sharma) Thue's inequalities and the hypergeometric method, to appear in the Ramanujan Journal (2017) 45 pages. arXiv preprint
 (with Jeffrey Vaaler) Minkowski's theorem on independent conjugate units the European Journal of Mathematics, 3(1), 111149 (2017). arXiv preprint
 (with Jeffrey Vaaler) Heights, Regulators and Schinzel's determinant inequality. Acta Arithmetica 172 (2016), 285298. arXiv preprint
 Representation of small integers by binary forms. The Quarterly Journal of Mathematics: Oxford Journals. (2015) 66 (4): 10091054. arXiv preprint
 Integral points on a certain family of elliptic curves. Journal de Theorie des Nombres de Bordeaux. 27 no. 2 (2015), p. 353373. arXiv preprint
 Cubic Thue inequalities with positive discriminant. Publicationes Mathematicae Debrecen. 83/4 (2013), 727739. arXiv preprint

(with Chantal David, Heekyoung Hahn and Lola Thompson) Distribution of squarefree values of sequences associated with elliptic curves. Contemporary Mathematics, Amer. Math. Soc. Volume 606 (2013), 171188. arXiv preprint
 Representation of unity by binary forms. Transactions of the American Mathematical Society. 364 (2012), 21292155. arXiv preprint
 Upper bounds for the number of solutions to quartic Thue equations.
International Journal of Number Theory. Volume 8, Issue 2 (2012), 335360. arXiv preprint

(With N. Saradha) Irreducibility of some orthogonal polynomials. Indagationes Mathematicae. 21 (2011), 127137. pdf
 The method of ThueSiegel for quartic forms. Acta Arithmetica. 141 (2010), no. 1, 131. arXiv preprint
 (With Ryotaro Okazaki) Quartic Thue equations. Journal of Number Theory. 130 (2010) no. 1, 4060.
 The Diophantine equation aX^4  bY^2 = 1. Journal fuer die reine und angewandte Mathematik (Crelle's Journal). 630 (2009), 3357. arXiv preprint
 Cubic Thue Equations. Publicationes Mathematicae Debrecen. 75 (2009), no. 34, 459483. arXiv preprint
 (with Alain Togbe and Gary Walsh) On the equation aX^4  bY^2 = 2. Acta Arithmetica 131 (2008), 145169.
Addendum: Acta Arithmetica 137 (2009), 199202.
 (with Stephen Choi) On the cyclotomic Littlewood polynomials. Journal of Number Theory 128 (2008), no. 4, 884894. pdf
Dissertations
 Ph.D Thesis: Thue Equations and Related Topics, University of British Columbia, 2008.
 M.Sc Thesis: Characterizing Cyclotomic Littlewood Polynomials, Simon Fraser University, 2004.
Links
 Oregon Number Theory Days, supported by the NSF grant DMS1719576
 My research is featured in the music video Undercover Girl (1:28 & 2:15 & 3:23 min) by the band Loftän
 Kurt Mahler bibliography
 Number Theory Web
 UO Number Theory Seminar
 UO Colloquium
Recent and Upcoming Trips

Women in Numbers
Europe 2 (WINE2) workshop, the Nesin Mathematics Village, Turkey, 2530 September, 2016.
Relocated to Lorentz Center Leiden, the Netherlands.
 2016 Fields Medal Symposium, the Fields Institute, Toronto, 14 November, 2016.

Analytic Number Theory Session, The Canadian Mathematical Society, Winter meeting, Niagara Falls, Ontario, 25 December 2016.

Analytic Number Theory, the Mathematical Science Research Institute, Berkeley, 112 Feb, 2017.

Number Theory Seminar, Oregon State University, 14 Feb, 2017.

Thematic Program on Unlikely Intersections, Heights, and Efficient Congruencing, The Fields Institute for
Research in Mathematical Sciences, Toronto, Canada, Winter 2017.

Recent developments in Analytic Number Theory, the Mathematical Science Research Institute, Berkeley, 15 May, 2017.
 re:boot Number Theory 2017, Duke University, 13 June, 2017.

Workshop on Diophantine approximation and related fields: York2017, University of York, UK, 26 to 30 June 2017.
 Diophantine Approximation and Algebraic Curves, Banff International Research Station, Canada, 27 July 2017.

Nonstandard methods in combinatorial number theory, American Institute of Mathematics, San Jose, California, 1418 August, 2017.
 CIMPA research school on Explicit Number Theory, The Witwatersrand University, Johannesburg, South Africa, 819 January, 2018.