Shabnam Akhtari Assistant Professor Address: Fenton Hall Department of Mathematics University of Oregon Eugene, OR 97403-1222 USA E-Mail: akhtari AT uoregon DOT edu

Research Interests

Number Theory, Diophantine Analysis, Geometry of Numbers.

Research Statement

Curriculum Vitae

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 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), 111-149 (2017). arXiv preprint

• (with Jeffrey Vaaler) Heights, Regulators and Schinzel's determinant inequality. Acta Arithmetica 172 (2016), 285-298. arXiv preprint

• Representation of small integers by binary forms. The Quarterly Journal of Mathematics: Oxford Journals. (2015) 66 (4): 1009-1054. arXiv preprint

• Integral points on a certain family of elliptic curves. Journal de Theorie des Nombres de Bordeaux. 27 no. 2 (2015), p. 353-373. arXiv preprint

• Cubic Thue inequalities with positive discriminant. Publicationes Mathematicae Debrecen. 83/4 (2013), 727-739. 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), 171-188. arXiv preprint

• Representation of unity by binary forms. Transactions of the American Mathematical Society. 364 (2012), 2129-2155. arXiv preprint

• Upper bounds for the number of solutions to quartic Thue equations. International Journal of Number Theory. Volume 8, Issue 2 (2012), 335-360. arXiv preprint

• (With N. Saradha) Irreducibility of some orthogonal polynomials. Indagationes Mathematicae. 21 (2011), 127-137. pdf

• The method of Thue-Siegel for quartic forms. Acta Arithmetica. 141 (2010), no. 1, 1-31. arXiv preprint

• (With Ryotaro Okazaki) 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. arXiv preprint

• Cubic Thue Equations. Publicationes Mathematicae Debrecen. 75 (2009), no. 3-4, 459-483. arXiv preprint

• (with Alain Togbe and Gary Walsh) On the equation aX^4 - bY^2 = 2. Acta Arithmetica 131 (2008), 145-169. Addendum: Acta Arithmetica 137 (2009), 199-202.

• (with Stephen Choi) On the cyclotomic Littlewood polynomials. Journal of Number Theory 128 (2008), no. 4, 884-894. 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 DMS-1719576
• 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, 25-30 September, 2016.

  Relocated to Lorentz Center Leiden, the Netherlands.

• 2016 Fields Medal Symposium, the Fields Institute, Toronto, 1-4 November, 2016.
• Analytic Number Theory Session, The Canadian Mathematical Society, Winter meeting, Niagara Falls, Ontario, 2-5 December 2016.

• Analytic Number Theory, the Mathematical Science Research Institute, Berkeley, 1-12 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, 1-5 May, 2017.

• re:boot Number Theory 2017, Duke University, 1-3 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, 2-7 July 2017.
• Nonstandard methods in combinatorial number theory, American Institute of Mathematics, San Jose, California, 14-18 August, 2017.

• CIMPA research school on Explicit Number Theory, The Witwatersrand University, Johannesburg, South Africa, 8-19 January, 2018.