Dr Dzmitry Badziahin

F07 - Carslaw Building
The University of Sydney


Website Personal webpage

Biographical details

1999 - 2004: BSc at the Faculty of Applied Mathematics and Computer Science, Belarusian State University, Belarus

2005 - 2007: PhD at the University of York, UK

2008 - 2011: Research assistant at the University of York

2011 - 2014: Lecturer at Durham University, UK

2014 - 2017: Reader at Durham University, UK

Research interests

My research interests mainly lie in Diophantine Approximation, a rapidly developing area of Analytic Number Theory. They are linked with a wide range of other topics including combinatorics on words, homogeneous dynamics, measure theory and ergodic theory. One of my most recent research activities is investigating the structure of the sets of badly approximable points in Rn and more generally in complete metric spaces. I am also investigating the approximational properties of Mahler numbers and Mahler functions.

Teaching and supervision

Timetable

D_Badziahin

Awards and honours

Aug - Sep 2015: LMS Undergraduate Research Bursary for the summer project with Matthew Northey. Title of the project: ``Checking p-adic Littlewood conjecture for certain types of numbers''. Award value: £1080.

Oct 2013 - Oct 2015: EPSRC First Grant. Title: ``Theory of Badly Approximable Sets''. Award value: £99997.

Mar - Apr 2014: (joint with N. Peyerimhoff and T. Ward) LMS funding for Northern Regional Meeting 2014. Title of meeting: ``Dynamics and Analytic Number Theory''. Award value: £7500.

Aug - Sep 2013: LMS Nuffield Undergraduate Research Bursary for the summer project with Isabelle Hirst. Title of the project: ``p-adic Littlewood conjecture for some collections of numbers''. Award value: £1080.

1998 - 2003: I took part in a number of Belarusian and international mathematical and programming olympiads. There I got various awards including first prices.

Selected grants

2013

  • Theory of badly approximable sets; Badziahin D; Engineering and Physical Sciences Research Council (EPSRC)/Research Grant.

Selected publications

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Edited Books

  • Badziahin, D., Gorodnik, A., Peyerimhoff, N. (2016). Dynamics and Analytic Number Theory. UK: Cambridge University Press.

Journals

  • Badziahin, D., Harrap, S., Hussain, M. (2017). An inhomogeneous Jarnik type theorem for planar curves. Mathematical Proceedings of the Cambridge Philosophical Society, 163(1), 47-70. [More Information]
  • Badziahin, D., Levesley, J. (2017). Convergence results for simultaneous & multiplicative Diophantine approximation on planar curves. Glasgow Mathematical Journal, 49, 367-375. [More Information]
  • Badziahin, D. (2017). Finding special factors of values of polynomials at integer points. International Journal of Number Theory, 13(1), 209-228. [More Information]
  • Badziahin, D. (2017). Inhomogeneous Diophantine approximation on curves and Hausdorff dimension. Advances in Mathematics, 223, 329-351. [More Information]
  • Badziahin, D., Shalit, J. (2016). An unusual continued fraction. Proceedings of the American Mathematical Society, 144(5), 1887-1896. [More Information]
  • Badziahin, D. (2016). Computation of the Infimum in the Littlewood Conjecture. Experimental Mathematics, 25(1), 100-105. [More Information]
  • Badziahin, D. (2016). Continuant Diophantine Equations. Moscow Journal of Combinatorics and Number Theory, 6(2-3), 38-55.
  • Badziahin, D., Bugeaud, Y., Einsiedler, M., Kleinbock, D. (2015). On the complexity of a putative counterexample to the p-adic Littlewood conjecture. Compositio Mathematica, 151(9), 1647-1662. [More Information]
  • Badziahin, D., Zorin, E. (2015). Thue-Morse Constant is Not Badly Approximable. International Mathematics Research Notices, 2015 (19), 9618-9637. [More Information]
  • Badziahin, D., Velani, S. (2014). Badly approximable points on planar curves and a problem of Davenport. Mathematische Annalen, 359(3-4), 969-1023. [More Information]
  • Badziahin, D., Beresnevich, V., Velani, S. (2013). Inhomogeneous theory of dual Diophantine approximation on manifolds. Advances in Mathematics, 232(1), 1-35. [More Information]
  • Badziahin, D. (2013). On multiplicatively badly approximable numbers. Mathematika, 59(1), 31-55. [More Information]
  • Badziahin, D., Haynes, A. (2011). A note on Farey fractions with denominators in arithmetic progressions. Acta Arithmetica, 147(3), 205-215. [More Information]
  • Badziahin, D., Velani, S. (2011). Multiplicatively badly approximable numbers and generalised Cantor sets. Advances in Mathematics, 228(5), 2766-2796. [More Information]
  • Badziahin, D., Pollington, A., Velani, S. (2011). On a problem in simultaneous Diophantine approximation: Schmidt's conjecture. Annals of Mathematics, 174(3), 1837-1883. [More Information]
  • Badziahin, D., Levesley, J., Velani, S. (2011). The mixed schmidt conjecture in the theory of diophantine approximation. Mathematika, 57(2), 239-245. [More Information]

2017

  • Badziahin, D., Harrap, S., Hussain, M. (2017). An inhomogeneous Jarnik type theorem for planar curves. Mathematical Proceedings of the Cambridge Philosophical Society, 163(1), 47-70. [More Information]
  • Badziahin, D., Levesley, J. (2017). Convergence results for simultaneous & multiplicative Diophantine approximation on planar curves. Glasgow Mathematical Journal, 49, 367-375. [More Information]
  • Badziahin, D. (2017). Finding special factors of values of polynomials at integer points. International Journal of Number Theory, 13(1), 209-228. [More Information]
  • Badziahin, D. (2017). Inhomogeneous Diophantine approximation on curves and Hausdorff dimension. Advances in Mathematics, 223, 329-351. [More Information]

2016

  • Badziahin, D., Shalit, J. (2016). An unusual continued fraction. Proceedings of the American Mathematical Society, 144(5), 1887-1896. [More Information]
  • Badziahin, D. (2016). Computation of the Infimum in the Littlewood Conjecture. Experimental Mathematics, 25(1), 100-105. [More Information]
  • Badziahin, D. (2016). Continuant Diophantine Equations. Moscow Journal of Combinatorics and Number Theory, 6(2-3), 38-55.
  • Badziahin, D., Gorodnik, A., Peyerimhoff, N. (2016). Dynamics and Analytic Number Theory. UK: Cambridge University Press.

2015

  • Badziahin, D., Bugeaud, Y., Einsiedler, M., Kleinbock, D. (2015). On the complexity of a putative counterexample to the p-adic Littlewood conjecture. Compositio Mathematica, 151(9), 1647-1662. [More Information]
  • Badziahin, D., Zorin, E. (2015). Thue-Morse Constant is Not Badly Approximable. International Mathematics Research Notices, 2015 (19), 9618-9637. [More Information]

2014

  • Badziahin, D., Velani, S. (2014). Badly approximable points on planar curves and a problem of Davenport. Mathematische Annalen, 359(3-4), 969-1023. [More Information]

2013

  • Badziahin, D., Beresnevich, V., Velani, S. (2013). Inhomogeneous theory of dual Diophantine approximation on manifolds. Advances in Mathematics, 232(1), 1-35. [More Information]
  • Badziahin, D. (2013). On multiplicatively badly approximable numbers. Mathematika, 59(1), 31-55. [More Information]

2011

  • Badziahin, D., Haynes, A. (2011). A note on Farey fractions with denominators in arithmetic progressions. Acta Arithmetica, 147(3), 205-215. [More Information]
  • Badziahin, D., Velani, S. (2011). Multiplicatively badly approximable numbers and generalised Cantor sets. Advances in Mathematics, 228(5), 2766-2796. [More Information]
  • Badziahin, D., Pollington, A., Velani, S. (2011). On a problem in simultaneous Diophantine approximation: Schmidt's conjecture. Annals of Mathematics, 174(3), 1837-1883. [More Information]
  • Badziahin, D., Levesley, J., Velani, S. (2011). The mixed schmidt conjecture in the theory of diophantine approximation. Mathematika, 57(2), 239-245. [More Information]

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