Algorithmic geometry of numbers, integer linear/nonlinear programming, computational discrete geometry and its applications, probabilistic and additive number theory.
This semester I am lecturing MA0345 Introduction to Wavelets and Data Compression.
(with M. Henk) LLL reduction for integer knapsacks,
J. Comb. Opt., accepted for publication (arXiv).
(with L. Fukshansky and M. Henk) Generalized Frobenius Numbers: Bounds and Average Behavior,
Acta Arith., accepted for publication (arXiv).
(with C. Smyth) Solving Algebraic Equations in Roots of Unity,
Forum Math., accepted for publication (arXiv).
(with M. Henk and A. Hinrichs) Expected Frobenius Numbers,
J Comb. Theory A, 118 (2011), 525-531 (arXiv).
(with M. Henk) Feasibility of Integer Knapsacks,
SIAM J. Optimization, 20 (2010), 2978--2993 (arXiv).
(with M. Henk) Integer Knapsacks: Average Behavior of Frobenius Numbers,
Mathematics of Operations Research, 34 (2009), 698-705 (arXiv).
Siegel's Lemma and Sum-Distinct Sets,
Discrete Comput. Geom., 39 (2008), 59-66 (arXiv).
(with P. M. Gruber) An Optimal Lower Bound for the Frobenius Problem,
Journal of Number Theory, 123 (2007), 71-79 (arXiv).
(with P. M. Gruber) Lattice Points in Large Borel Sets and Successive Minima,
Discrete Comput. Geom., 35 (2006), 429-435 (arXiv).
(with M. Henk) Successive Minima and Best Simultaneous Diophantine Approximations,
Monatsh. Math., 147 (2) (2006), 95-101 (arXiv).
(with A. Schinzel and W. M. Schmidt) On Vectors Whose Span Contains a Given Linear Subspace,
Monatsh. Math., 144 (2005), 177-191.
On a Decomposition of Integer Vectors, II,
Acta Arith., 102 (2002), 373-391.
On a Decomposition of Integer Vectors, I,
Bull. Pol. Ac.: Math., 49 (2001), 151-157.
(with A. Zhigljavsky)
Weyl Sequences: Asymptotic Distributions of the Partition Lengths,
Acta Arith. 88 (1999), 351-361.
(with S. Kanemitsu and A. Schinzel)
On the Metric Theory of Continued Fractions,
Colloq. Math., 77 (1998), 141-146.
(with C. Smyth) Power Maps and Subvarieties of the Complex Algebraic n-torus,
On Decomposition of Integer Vectors,
Institute of Mathematics, Polish Academy of Sciences, Warsaw, June 2001.
Supevisor: Prof. Andrzej Schinzel.