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Curriculum Vitae

Alan K. Haynes

 

Employment History

2011 - pres           EPSRC Fellow, University of Bristol.

Summer 2011    Heilbronn Research Fellow, University of Bristol.

Spring 2011         Research Visitor, University of Texas at Austin.

2008 - 2011         Research Associate, University of York.

2007 - 2008         Instructor, Brandeis University.

2006 - 2007         Lecturer, University of Texas at Austin.

2003 - 2006         Assistant Instructor, University of Texas at Austin.

2001 - 2003         Teaching Assistant, University of Texas at Austin.

 

Degrees Earned

Aug 2006              Ph.D. in Mathematics, University of Texas at Austin.

May 2001             B.S. in Mathematics, University of Texas at Austin.

Specializations     Analytic number theory, probability theory, dynamical systems.       

 

Academic History

2000 - 2006         University of Texas at Austin.

1998 - 2000         California Institute of Technology (Caltech).

1996 - 1998         University of North Texas, Texas Academy of Mathematics and Science.

 

Publications

[1]                   A note on Farey fractions with odd denominators, J. Number Theory, 98 (2003), no.1, 89-104. arxiv:0907.2168.

 

[2]                   The distribution of special subsets of the Farey sequence, J. Number Theory, 107 (2004), no.1, 95-104. arxiv:0907.2171.

 

[3]                   Tools and techniques in Diophantine approximation, thesis, University of Texas at Austin, 2006, 154pp. UT Austin Libraries.

 

[4]                   Martingale differences and the metric theory of continued fractions, Illinois J. Math., 52 (2008), no.1, 213-242. arxiv:0906.5428. (with J. Vaaler)

 

[5]                   The group ring of Q/Z and an application of a divisor problem, Proc. Amer. Math. Soc., 137 (2009), 1285-1293. arxiv:0907.0158. (with K. Homma)

 

[6]                   Intermediate convergents and a metric theorem of Khinchin, Bull. Lond. Math. Soc., 41 (2009), 396-410. arxiv:0907.0161.

 

[7]                   The metric theory of p-adic approximation, International Math Research Notices, (2010), no.1, 18-52. arxiv:0907.0141.

 

[8]                   Numerators of differences of nonconsecutive Farey fractions, Int. J. Number Theory, 6 (2010), no.3, 1-12. arxiv:0907.0162.

 

[9]              A note on Farey fractions with denominators in arithmetic progressions, Acta. Arith., 147 (2011), no.3, 205-215. arxiv:0907.0163. (with D. Badziahin)

 

[10]              Metric considerations concerning the mixed Littlewood Conjecture, Int. J. Number Theory, 7 (2011), no. 3, 593-609. arxiv:0909.3923. (with Y. Bugeaud and S. Velani)

 

[11]              Inhomogeneous approximation by coprime integers, New York Journal of Mathematics, 18 (2012) 249-259. arxiv:1202.5986.

 

[12]                   The Duffin-Schaeffer Conjecture with extra divergence, Math. Ann., to appear. arxiv:0811.1234. (with A. Pollington and S. Velani)

 

[13]              Metrical musings on Littlewood and friends, Proc. Amer. Math. Soc., to appear. arxiv:1204.0938. (with J. L. Jensen and S. Kristensen)

 

[14]              Multiplicative zero-one laws and metric number theory, Acta. Arith., to appear. arxiv:1012.0675. (with V. Beresnevich and S. Velani)

 

[15]              Incomplete Kloosterman sums and multiplicative inverses in short intervals, Int. J. Number Theory, to appear. arxiv:1204.6374. (with T. D. Browning)

 

[16]              Quantitative ergodic theorems for weakly integrable functions, Ergodic Theory Dynam. Systems, to appear. arxiv:1112.1585.

 

[17]              Deformation quantization and irrational numbers, Journal of Symplectic Geometry, to appear. arxiv:1105.5541. (with E. Hawkins)

 

[18]              The Duffin-Schaeffer Conjecture with extra divergence II, Math Z., to appear. arxiv:1201.1210. (with V. Beresnevich, G. Harman, and S. Velani)

 

[19]              The mixed Littlewood conjecture for pseudo-absolute values, Math. Ann., to appear. arxiv:1012.0191. (with S. Harrap)

 

[20]              Projective metric number theory, submitted. arxiv:1112.0128. (with A. Ghosh)

 

[21]              Equivalence relations on separated nets arising from linear toral flows, submitted. arxiv:1112.0128. (with M. Kelly and B. Weiss)

 

[22]              On the sum of the reciprocals of the sequence n\alpha mod 1, in preparation. (with V. Beresnevich, J. Vaaler, and S. Velani)

 

Grants and Fellowships

2011-2016             EPSRC Career Acceleration Fellowship.

2011             Heilbronn Fellowship, Heilbronn Institute for Mathematical Research.

2008-2010             RA on EPSRC grant EP/F027028/1.

2005                      Edward Louis and Alice Laidman Dodd Fellowship, UT Austin.

2004                      Bruton Fellowship, UT Austin.

2002-2003         NSF VIGRE support, UT Austin.

2001                      NSF REU grant, UIUC.

 

Recent Conferences and Seminars

Nov 2012               Oxford University.

Nov 2012               One Day Ergodic Theory Meeting, Queen Mary University.

May 2012               One Day Ergodic Theory Meeting, University of Surrey.

Nov 2011               Aarhus University, Denmark.

Oct 2011               Analysis and Applied Math Conference, Cardiff University, UK.

Oct 2010               University of Manchester, UK.

Oct 2010               Ben Gurion University, Israel.

Sep 2010               University of East Anglia, UK.

Sep 2010               Diophantine approximation and transcendence, CIRM, Luminy, France.

July 2010              ETH, Switzerland.

July 2010              Homogeneous dynamics and number theory, Oberwolfach, Germany.

May 2010             EU Young and Mobile Workshop: Dynamical Systems and Number Theory, Edinburgh, UK.

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