
Integer programming and combinatorial optimisation (algebraic and geometric methods), discrete mathematics (algorithmic geometry of numbers and discrete geometry) and computational number theory.
Autumn semester: MA3006 Introduction to Coding Theory and Data Compression.
Spring semester: MA3500 Discrete Optimization.
(with R. Bassett, J. A. De Loera and Q. Louveaux)
A Quantitative DoignonBellScarf Theorem,
accepted for publication in Combinatorica
(arXiv).
On the Lattice Programming Gap of the Group Problems,
Oper. Res. Lett., 43 (2015), no. 2, 199202
(arXiv).
(with A. N. Letchford) Iterated ChvatalGomory Cuts and the Geometry of Numbers,
SIAM J. Optim., 24 (2014), no. 3, 12941312 (arXiv).
(with J. De Loera and Q. Louveaux)
Integer Programs with Prescribed Number of Solutions and a Weighted Version of DoignonBellScarf Theorem,
Integer Programming and Combinatorial Optimization, Springer Lecture Notes in Computer Science, vol. 8494, 2014, 3751.
(with M. Henk and E. Linke) Integer Points in Knapsack Polytopes and scovering 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, 613626 (arXiv).
(with L. Fukshansky and M. Henk) Generalized Frobenius Numbers: Bounds and Average Behavior,
Acta Arith., 75th birthday volume for Prof. Andrzej Schinzel, 155 (2012), 5362 (arXiv).
(with C. Smyth) Solving Algebraic Equations in Roots of Unity,
Forum Math., 24 (2012), 641665. (arXiv).
(with M. Henk and A. Hinrichs) Expected Frobenius Numbers,
J. Comb. Theory A, 118 (2011), 525531 (arXiv).
(with M. Henk) Feasibility of Integer Knapsacks,
SIAM J. Optim., 20 (2010), 29782993 (arXiv).
(with M. Henk) Integer Knapsacks: Average Behavior of Frobenius Numbers,
Math. Oper. Res., 34 (2009), 698705 (arXiv).
Siegel's Lemma and SumDistinct Sets,
Discrete Comput. Geom., 20th Anniversary Volume, 39 (2008), 5966 (arXiv).
(with P. M. Gruber) An Optimal Lower Bound for the Frobenius Problem,
J. of Number Theory, 123 (2007), 7179 (arXiv).
(with P. M. Gruber) Lattice Points in Large Borel Sets and Successive Minima,
Discrete Comput. Geom., 35 (2006), 429435
(arXiv).
(with M. Henk) Successive Minima and Best Simultaneous Diophantine Approximations,
Monatsh. Math., 147 (2) (2006), 95101 (arXiv).
(with P. M. Gruber) Best Simultaneous Diophantine Approximations under a Constraint on the Denominator,
Contrib. Discrete Math.,
1 (2006), 2946 (arXiv).
(with A. Schinzel and W. M. Schmidt) On Vectors Whose Span Contains a Given Linear Subspace,
Monatsh. Math., 144 (2005), 177191.
On a Decomposition of Integer Vectors, II,
Acta Arith., 102 (2002), 373391.
On a Decomposition of Integer Vectors, I,
Bull. Pol. Ac.: Math., 49 (2001), 151157.
(with A. Zhigljavsky)
Weyl Sequences: Asymptotic Distributions of the Partition Lengths,
Acta Arith. 88 (1999), 351361.
(with S. Kanemitsu and A. Schinzel)
On the Metric Theory of Continued Fractions,
Colloq. Math., 77 (1998), 141146.
(thanks to this paper, my Erdös number is 2)
(with J. A. De Loera and Q. Louveaux)
Semigroups of Polyhedra with Prescribed Number of Lattice Points and the kFrobenius Problem,
(arXiv).
(with C. Smyth) Power Maps and Subvarieties of the Complex Algebraic ntorus,
(arXiv).
On Decomposition of Integer Vectors,
Institute of Mathematics, Polish Academy
of Sciences, Warsaw, June 2001.
Supevisor: Prof. Andrzej Schinzel.
