Algorithmic geometry of numbers, integer optimization, computational discrete geometry and its applications, probabilistic and additive number theory.
Autumn semester: MA3006 Introduction to Coding Theory and Data Compression.
Spring semester: MA3500 Discrete Optimization.
(with A. N. Letchford) Iterated Chvatal-Gomory Cuts and the Geometry of Numbers,
SIAM J. Optim., 24 (2014), no. 3, 1294-1312 (arXiv).
(with J. De Loera and Q. Louveaux)
Integer Programs with Prescribed Number of Solutions and a Weighted Version of Doignon-Bell-Scarf Theorem,
to appear in proceedings of IPCO 2014 (volume 8494 of Springer Lecture Notes in Computer Science).
(with M. Henk and E. Linke) Integer Points in Knapsack Polytopes and s-covering Radius,
Electron. J. Combin., 20 (2013), no. 2, Paper 42, 17 pp (arXiv).
(with M. Henk) LLL Reduction for Integer Knapsacks,
J. Comb. Opt., 24 (2012), no. 4, 613-626 (arXiv).
(with L. Fukshansky and M. Henk) Generalized Frobenius Numbers: Bounds and Average Behavior,
Acta Arith., 155 (2012), 53-62 (arXiv).
(with C. Smyth) Solving Algebraic Equations in Roots of Unity,
Forum Math., 24 (2012), 641-665. (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. Opt., 20 (2010), 2978--2993 (arXiv).
(with M. Henk) Integer Knapsacks: Average Behavior of Frobenius Numbers,
Math. Oper. Res., 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,
J. 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 J. A. De Loera and Q. Louveaux)
Semigroups of Polyhedra with Prescribed Number of Lattice Points and the k-Frobenius Problem,
(with R. Bassett, J. A. De Loera and Q. Louveaux)
A Quantitative Doignon-Bell-Scarf Theorem,
On the Maximum Gap of the Group Relaxations,
(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.