Durham University

Science Laboratories

South Rd

Durham, UK. DH1 3LE

Phone: +44 (0) 191 33 43110

Room: CM106

e-mail: dzmitry.badziahin(at)durham.ac.uk

- Different types of badly approximable numbers and points (multiplicatively badly approximable points)
- Approximational properties of Mahler numbers
- Combinatorics of words
- Generalised Cantor-type sets
- Littlewood conjecture and its analogues.

With S. Harrap and M. Hussain, *An Inhomogeneous JarnÃk type theorem for planar curves *, preprint.

With S. Harrap, *Cantor-winning sets and their applications*, preprint.

*On continued fraction expansion of potential counterexamples to p-adic Littlewood conjecture*, preprint.

With J. Shallit, *An Unusual Continued Fraction*, accepted by Proc. of AMS, 2015.

With Y. Bugeaud, M. Einsiedler and D. Kleinbock, *On the complexity of a putative counterexample to the p-adic Littlewood conjecture*, accepted by Comp. Math., 2015.

With E. Zorin, *Thue-Morse constant is not badly approximable*, accepted by Int. Math. Res. Not., 2014.

With S. Velani, *Badly approximable points on planar curves and a problem of Davenport*, Math. Annalen, V. 359(3-4), pp. 969-1023, 2014.

*On multiplicatively badly approximable numbers*, Mathematika, V. 59(1), pp. 31 -- 55, 2013.

With V. Beresnevich and S. Velani, *Inhomogeneous
theory of dual Diophantine approximation on manifolds*, Advances in Math., V. 232, pp. 1 -- 35, 2013.

With S. Velani. *Multiplicatively badly
approximable numbers and generalised Cantor sets*, Advances in Math., V. 228(5), pp. 2766 -- 2796, 2011.

With A. Pollington and S. Velani, *On a problem in
simultaneous Diophantine approximation: Schmidt's conjecture*,
Annals of Math., V. 174, pp. 1837 -- 1883, 2011.

With J. Levesley and S. Velani, *The mixed Schmidt
conjecture in the theory of Diophantine approximation*, Mathematika, V. 57(2), pp. 239 -- 245, 2011.

With A. Haynes, *A note on Farey fractions with
denominators in arithmetic progressions*, Acta
Arithmetica, V. 147(3), pp. 205 -- 215, 2011.

*Inhomogeneous Diophantine approximation on
curves and Hausdorff dimension*, Advances in Math., V. 223(1), pp.
329 -- 351, 2009.

With I. Morozova, *On the exact exponent of
convergence of series with small denominators.* Vestsi Nats. Akad.
Navuk Belarusi Ser. Fiz.-Mat. Navuk 2007, N. 2, pp
37 -- 40. (*in Russian*)

With J. Levesley, *Convergence results for
simultaneous and multiplicative Diophantine approximation on planar
curves*, Glasgow Math. J., V. 49, pp. 367 -- 375, 2007.

With J. Levesley, *Computation of fractional
measures in the case of convergence for Diophantine approximations
on planar curves.* Dokl. Nats. Akad. Nauk Belarusi V. 50, N. 6, pp.
24--27, 2006. (in Russian)

*Inhomogeneous Diophantine approximation and
lower bounds of Hausdorff dimension*, Vesti Nats. Acad. Navuk
Belarusi. Ser. Fiz.-Mat. Navuk 2005, N. 3, pp 32 -- 36. (*in Russian*)

With I. Morozova, * On small denominators
of product of linear forms*, proceeding of the international
mathematical conference in honor of Skorobogatko, Lvov 2004. (*in Russian*)

- Finding Mersenne primes: GIMPS
- Factoring Fermat numbers: www.fermatsearch.org
- Finding Aliquot cycles (found eight new cycles of length 4 and several hundreds of new cycles of length two): here is the link to all known cycles of length greater than two.

**Hiking and travelling**. Here are some photos: one, two, three.**Programming**. Here are webpages with programs written by me: chess program Kvetka, older programs (in Russian).