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, Transcendence theory.

Some of my papers are available on the arXiv .

**List of Publications in Refereed Journals**

- Cubic Thue inequalities with positive discriminant.
**Publicationes Mathematicae Debrecen**. 83/4 (2013), 727-739. -
(with David, C., Hahn, H. and Thompson, H.) 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 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
**

- Representation of small integers by binary forms. (submitted)
- (with Bhargava. M.) Binary cubic forms that do not represent 1.
- Integral points on a family of elliptic curves.
**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****Upcoming Trips**- Diophantine Equations, Shimla, India, June 30-July 19, 2014.
- Workshop: Analytic Number Theory, Mathematik-Zentrum, Bonn, Germany, July 11-18, 2014.
- Visiting Max Planck Institute, Bonn, Germany, August and September 2014.
- Approximation diophantienne et transcendance, CIRM, Luminy, France, September 15-September 19, 2014.

**Past Trips**- Hausdorff Institute, Bonn, Germany, Jan-March 2013.
- AMS Western Section meeting in Boulder, 13-14 April 2013.
- University of Texas, Austin, 18 April 2013.
- ARCTIC NUMBER THEORY WORKSHOP, SAARISELKÄ, LAPLAND, FINLAND, 15-20 June 2013.
- KTH, Stockholm, Sweden, June 26-June 29, 2013.
- Thue 150, Bordeaux, France, September 30-October 4, 2013. (Supported by AWM-NSF Travel Grant).
- Grenoble, Lyon and Saint-Etienne Number Theory seminar, Saint-Etienne, France, October 10, 2013.
- Programme on Heights in Diophantine geometry, group theory and additive combinatorics, ESI, Vienna, Austria, Nov 2013.

- Ph.D Thesis: Thue Equations and Related Topics, University of British Columbia, 2008.