Shabnam Akhtari
Assistant Professor Address: Fenton Hall Eugene, OR 97403-1222 USA
E-Mail: akhtari AT uoregon DOT edu |

**Research Interests**

Number Theory, Diophantine Analysis, Geometry of Numbers.

My research is funded by the ** National Science Foundation** grant DMS-1601837.

Some of my papers are available on the arXiv .

**Preprints and Publications in Refereed Journals**

- (with Vaaler. J.) Minkowski's theorem on independent conjugate units (preprint, 36 pages), submitted for publication in 2016.
- (with Bhargava. M.) A positive proportion of locally soluble Thue equations are globally insoluble (preprint, 20 pages), submitted for publication in 2016.
- (with Saradha. N. and Sharma. D.) Thue's inequalities and the hypergeometric method (preprint, 41 pages), submitted for publication in 2016.
- (with Vaaler. J.) Heights, Regulators and Schinzel's determinant inequality.
**Acta Arithmetica**172 (2016), 285-298. - Representation of small integers by binary forms.
**The Quarterly Journal of Mathematics: Oxford Journals**. (2015) 66 (4): 1009-1054. - Integral points on a certain family of elliptic curves.
**Journal de Theorie des Nombres de Bordeaux**. 27 no. 2 (2015), p. 353-373. - Cubic Thue inequalities with positive discriminant.
**Publicationes Mathematicae Debrecen**. 83/4 (2013), 727-739. -
(with David. C., Hahn. H. and Thompson. L.) Distribution of squarefree values of sequences associated with elliptic curves.
**Contemporary Mathematics, Amer. Math. Soc.**Volume 606 (2013), 171-188. - Representation of unity by binary forms.
**Transactions of the American Mathematical Society**. 364 (2012), 2129-2155. - Upper bounds for the number of solutions to quartic Thue equations.
**International Journal of Number Theory**. Volume 8, Issue 2 (2012), 335-360. -
(With Saradha. N.) Irreducibility of some orthogonal polynomials.
**Indagationes Mathematicae**. 21 (2011), 127-137. - The method of Thue-Siegel for quartic forms.
**Acta Arithmetica**. 141 (2010), no. 1, 1-31. - (With Okazaki. R.) Quartic Thue equations.
**Journal of Number Theory**. 130 (2010) no. 1, 40-60. - The Diophantine equation aX^4 - bY^2 = 1.
**Journal fuer die reine und angewandte Mathematik**(Crelle's Journal). 630 (2009), 33-57. - Cubic Thue Equations.
**Publicationes Mathematicae Debrecen**. 75 (2009), no. 3-4, 459-483. - (with Togbe. A. and Walsh. P. G.) On the equation aX^4 - bY^2 = 2.
**Acta Arithmetica**131 (2008), 145-169. Addendum: Acta Arithmetica 137 (2009), 199-202. - (with Choi. K. K.) On the cyclotomic Littlewood polynomials.
**Journal of Number Theory**128 (2008), no. 4, 884-894.

** WORKS IN PROGRESS**

- (with Vaaler. J.) Minkowski's units and relative units with small height.
- (with Vaaler. J.) On norm form equations.
- On the Diophantine equation ax^r - by^r =c

**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
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** Recent and Upcoming Trips
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- Women in Numbers Europe 2 (WINE2) workshop, the Nesin Mathematics Village, Turkey, 25-30 September, 2016.
- 2016 Fields Medal Symposium, the Fields Institute, Toronto, 1-4 November, 2016.
- Diophantine Approximation and Algebraic Curves, Banff International Research Station, Canada, 2-7 July 2017.

**I am the organizer of**