![Iskander Aliev](https://profiles-cardiff.imgix.net/attachments/6283?w=200&h=200&auto=format&crop=faces&fit=crop&q=90")
Professor Iskander Aliev
Personal Chair
- ALIEVI@cardiff.ac.uk
- +44 29208 75547
- Abacws, Room 4.23, Senghennydd Road, Cathays, Cardiff, CF24 4AG
Overview
Research Interests:
- Integer Optimisation (Algebraic and Geometric Methods)
- Discrete Mathematics (Geometry of Numbers, Discrete Geometry)
- Number Theory (Diophantine Approximations, Additive Number Theory)
Editorial positions:
- Editor of Beiträge zur Algebra und Geometrie
- Editor of Combinatorics and Number Theory
Publication
2024
- Aliev, I., Celaya, M. and Henk, M. 2024. Sparsity and integrality gap transference bounds for integer programs. Presented at: IPCO 2024: The 25th Conference on Integer Programming and Combinatorial Optimization, Wroclaw, Poland, 3-5 July 2024 Presented at Vygen, J. and Byrka, J. eds.Integer Programming and Combinatorial Optimization: 25th International Conference, IPCO 2024, Wroclaw, Poland, July 3–5, 2024, Proceedings. Association for Computing Machinery pp. 1-13., (10.1007/978-3-031-59835-7_1)
- Aliev, I., Henk, M., Hogan, M., Kuhlmann, S. and Oertel, T. 2024. New bounds for the integer Caratheodory rank. SIAM Journal on Optimization 34(1), pp. 190-200. (10.1137/23M1561312)
2023
- Aliev, I. and Henk, M. 2023. Minkowski’s successive minima in convex and discrete geometry. Communications in Mathematics 31(2), article number: 3. (10.46298/cm.11155)
2022
- Alasmari, A. and Aliev, I. 2022. On unique recovery of finite‑valued integer signals and admissible lattices of sparse hypercubes. Optimization Letters (10.1007/s11590-022-01927-0)
- Aliev, I., Averkov, G., Loera, J. A. D. and Oertel, T. 2022. Sparse representation of vectors in lattices and semigroups. Mathematical Programming 192, pp. 519-546. (10.1007/s10107-021-01657-8)
2021
- Aliev, I. 2021. On the volume of hyperplane sections of a d-CUBE. Acta Mathematica Hungarica 163, pp. 547-551. (10.1007/s10474-020-01057-y)
- Aliev, I., Celaya, M., Henk, M. and Williams, A. 2021. Distance-sparsity transference for vertices of corner polyhedra. SIAM Journal on Optimization 31(1) (10.1137/20M1353228)
2020
- Aliev, I., Henk, M. and Oertel, T. 2020. Distances to lattice points in knapsack polyhedra. Mathematical Programming 182(1-2), pp. 175-198. (10.1007/s10107-019-01392-1)
- Aliev, I., Averkov, G., De Lora, J. A. and Oertel, T. 2020. Optimizing sparsity over lattices and semigroups. Lecture Notes in Computer Science
2019
- Aliev, I. 2019. On polynomial-time solvable linear Diophantine problems. Moscow Journal of Combinatorics and Number Theory 8(4), pp. 357-365.
2018
- Aliev, I., De Loera, J. A., Eisenbrand, F., Oertel, T. and Weismantel, R. 2018. The support of integer optimal solutions. SIAM Journal on Optimization 28(3), pp. 2152-2157. (10.1137/17M1162792)
2017
- Aliev, I., Bassett, R., De Loera, J. A. and Louveaux, Q. 2017. A quantitative Doignon-Bell-Scarf theorem. Combinatorica 37, pp. 313-332. (10.1007/s00493-015-3266-9)
- Aliev, I., Loera, J. D., Oertel, T. and O'Neill, C. 2017. Sparse solutions of linear diophantine equations. SIAM Journal on Applied Algebra and Geometry 1(1), pp. 239-253., article number: 2470-6566. (10.1137/16M1083876)
- Aliev, I., Henk, M. and Oertel, T. 2017. Integrality gaps of integer knapsack problems. Lecture Notes in Computer Science 10328, pp. 25-38. (10.1007/978-3-319-59250-3_3)
2016
- Aliev, I. 2016. A sharp upper bound for the Lattice Programming Gap. Moscow Journal of Combinatorics and Number Theory 6(2-3), pp. 121-129.
- Aliev, I., De Loera, J. and Louveaux, Q. 2016. Parametric polyhedra with at least k lattice points: their semigroup structure and the k-Frobenius problem. In: Beveridge, A. et al. eds. Recent Trends in Combinatorics. The IMA Volumes in Mathematics and its Applications Springer, pp. 753-778., (10.1007/978-3-319-24298-9_29)
2015
- Aliev, I. 2015. On the lattice programming gap of the group problems. Operations Research Letters 43(2), pp. 199-202. (10.1016/j.orl.2015.01.008)
- Aliev, I. and Mohammed, D. 2015. On the distance between Frobenius numbers. Moscow Journal of Combinatorics and Number Theory 5(4), pp. 205-214.
2014
- Aliev, I. and Letchford, A. 2014. Iterated Chvátal--Gomory cuts and the geometry of numbers. SIAM Journal on Optimization 24(3), pp. 1294-1312. (10.1137/130926389)
2013
- Aliev, I., Henk, M. and Linke, E. 2013. Integer points in knapsack polytopes and s-covering radius. Electronic Journal of Combinatorics 20(2), article number: P42.
2012
- Aliev, I. and Henk, M. 2012. LLL-reduction for integer knapsacks. Journal of Combinatorial Optimization 24(4), pp. 613-626. (10.1007/s10878-011-9411-5)
- Aliev, I. and Smyth, C. 2012. Solving algebraic equations in roots of unity. Forum Mathematicum 24(3), pp. 641-665. (10.1515/form.2011.087)
- Aliev, I., Fukshansky, L. and Henk, M. 2012. Generalized Frobenius numbers: bounds and average behavior. Acta Arithmetica 155, pp. 53-62.
2011
- Aliev, I., Henk, M. and Hinrichs, A. 2011. Expected Frobenius numbers. Journal of Combinatorial Theory, Series A 118(2), pp. 525-531. (10.1016/j.jcta.2009.12.012)
2010
- Aliev, I. and Henk, M. 2010. Feasibility of integer knapsacks. Siam Journal of Optimization 20(6), pp. 2978-2993. (10.1137/090778043)
2009
- Aliev, I. and Henk, M. 2009. Integer knapsacks: average behavior of the Frobenius numbers. Mathematics of Operations Research 34(3), pp. 698-705. (10.1287/moor.1090.0393)
2008
- Aliev, I. 2008. Siegel's lemma and sum-distinct sets. Discrete & Computational Geometry 39(1-3), pp. 59-66. (10.1007/s00454-008-9059-9)
2007
- Aliev, I. and Gruber, P. M. 2007. An optimal lower bound for the Frobenius problem. Journal of Number Theory 123(1), pp. 71-79. (10.1016/j.jnt.2006.05.020)
2006
- Aliev, I. and Gruber, P. M. 2006. Lattice points in large Borel sets and successive minima. Discrete & Computational Geometry 35(3), pp. 429-435. (10.1007/s00454-005-1228-5)
- Aliev, I. and Henk, M. 2006. Successive minima and best simultaneous Diophantine approximations. Monatshefte für Mathematik 147(2), pp. 95-101. (10.1007/s00605-005-0344-x)
- Aliev, I. and Gruber, P. M. 2006. Best simultaneous diophantine approximations under a constraint on the denominator. Contributions to Discrete Mathematics 1(1), pp. 29-46.
2005
- Aliev, I., Schinzel, A. and Schmidt, W. M. 2005. On vectors whose span contains a given linear subspace. Monatshefte für Mathematik 144(3), pp. 177-191. (10.1007/s00605-004-0267-y)
2002
- Aliev, I. 2002. On a decomposition of integer vectors, II.. Acta Arithmetica 57(2), pp. 159-164.
2001
- Aliev, I. 2001. On a decomposition of integer vectors, I.. Bulletin of the Polish Academy of Sciences Mathematics 49, pp. 141-146.
1999
- Aliev, I. and Zhigljavsky, A. 1999. Weyl sequences: asymptotic distributions of the partition lengths. Acta Arithmetica 88(4), pp. 351-361.
1998
- Aliev, I., Kanemitsu, S. and Schinzel, A. 1998. On the metric theory of continued fractions. Colloquium Mathematicum 77, pp. 141-145.
Articles
- Aliev, I., Henk, M., Hogan, M., Kuhlmann, S. and Oertel, T. 2024. New bounds for the integer Caratheodory rank. SIAM Journal on Optimization 34(1), pp. 190-200. (10.1137/23M1561312)
- Aliev, I. and Henk, M. 2023. Minkowski’s successive minima in convex and discrete geometry. Communications in Mathematics 31(2), article number: 3. (10.46298/cm.11155)
- Alasmari, A. and Aliev, I. 2022. On unique recovery of finite‑valued integer signals and admissible lattices of sparse hypercubes. Optimization Letters (10.1007/s11590-022-01927-0)
- Aliev, I., Averkov, G., Loera, J. A. D. and Oertel, T. 2022. Sparse representation of vectors in lattices and semigroups. Mathematical Programming 192, pp. 519-546. (10.1007/s10107-021-01657-8)
- Aliev, I. 2021. On the volume of hyperplane sections of a d-CUBE. Acta Mathematica Hungarica 163, pp. 547-551. (10.1007/s10474-020-01057-y)
- Aliev, I., Celaya, M., Henk, M. and Williams, A. 2021. Distance-sparsity transference for vertices of corner polyhedra. SIAM Journal on Optimization 31(1) (10.1137/20M1353228)
- Aliev, I., Henk, M. and Oertel, T. 2020. Distances to lattice points in knapsack polyhedra. Mathematical Programming 182(1-2), pp. 175-198. (10.1007/s10107-019-01392-1)
- Aliev, I., Averkov, G., De Lora, J. A. and Oertel, T. 2020. Optimizing sparsity over lattices and semigroups. Lecture Notes in Computer Science
- Aliev, I. 2019. On polynomial-time solvable linear Diophantine problems. Moscow Journal of Combinatorics and Number Theory 8(4), pp. 357-365.
- Aliev, I., De Loera, J. A., Eisenbrand, F., Oertel, T. and Weismantel, R. 2018. The support of integer optimal solutions. SIAM Journal on Optimization 28(3), pp. 2152-2157. (10.1137/17M1162792)
- Aliev, I., Bassett, R., De Loera, J. A. and Louveaux, Q. 2017. A quantitative Doignon-Bell-Scarf theorem. Combinatorica 37, pp. 313-332. (10.1007/s00493-015-3266-9)
- Aliev, I., Loera, J. D., Oertel, T. and O'Neill, C. 2017. Sparse solutions of linear diophantine equations. SIAM Journal on Applied Algebra and Geometry 1(1), pp. 239-253., article number: 2470-6566. (10.1137/16M1083876)
- Aliev, I., Henk, M. and Oertel, T. 2017. Integrality gaps of integer knapsack problems. Lecture Notes in Computer Science 10328, pp. 25-38. (10.1007/978-3-319-59250-3_3)
- Aliev, I. 2016. A sharp upper bound for the Lattice Programming Gap. Moscow Journal of Combinatorics and Number Theory 6(2-3), pp. 121-129.
- Aliev, I. 2015. On the lattice programming gap of the group problems. Operations Research Letters 43(2), pp. 199-202. (10.1016/j.orl.2015.01.008)
- Aliev, I. and Mohammed, D. 2015. On the distance between Frobenius numbers. Moscow Journal of Combinatorics and Number Theory 5(4), pp. 205-214.
- Aliev, I. and Letchford, A. 2014. Iterated Chvátal--Gomory cuts and the geometry of numbers. SIAM Journal on Optimization 24(3), pp. 1294-1312. (10.1137/130926389)
- Aliev, I., Henk, M. and Linke, E. 2013. Integer points in knapsack polytopes and s-covering radius. Electronic Journal of Combinatorics 20(2), article number: P42.
- Aliev, I. and Henk, M. 2012. LLL-reduction for integer knapsacks. Journal of Combinatorial Optimization 24(4), pp. 613-626. (10.1007/s10878-011-9411-5)
- Aliev, I. and Smyth, C. 2012. Solving algebraic equations in roots of unity. Forum Mathematicum 24(3), pp. 641-665. (10.1515/form.2011.087)
- Aliev, I., Fukshansky, L. and Henk, M. 2012. Generalized Frobenius numbers: bounds and average behavior. Acta Arithmetica 155, pp. 53-62.
- Aliev, I., Henk, M. and Hinrichs, A. 2011. Expected Frobenius numbers. Journal of Combinatorial Theory, Series A 118(2), pp. 525-531. (10.1016/j.jcta.2009.12.012)
- Aliev, I. and Henk, M. 2010. Feasibility of integer knapsacks. Siam Journal of Optimization 20(6), pp. 2978-2993. (10.1137/090778043)
- Aliev, I. and Henk, M. 2009. Integer knapsacks: average behavior of the Frobenius numbers. Mathematics of Operations Research 34(3), pp. 698-705. (10.1287/moor.1090.0393)
- Aliev, I. 2008. Siegel's lemma and sum-distinct sets. Discrete & Computational Geometry 39(1-3), pp. 59-66. (10.1007/s00454-008-9059-9)
- Aliev, I. and Gruber, P. M. 2007. An optimal lower bound for the Frobenius problem. Journal of Number Theory 123(1), pp. 71-79. (10.1016/j.jnt.2006.05.020)
- Aliev, I. and Gruber, P. M. 2006. Lattice points in large Borel sets and successive minima. Discrete & Computational Geometry 35(3), pp. 429-435. (10.1007/s00454-005-1228-5)
- Aliev, I. and Henk, M. 2006. Successive minima and best simultaneous Diophantine approximations. Monatshefte für Mathematik 147(2), pp. 95-101. (10.1007/s00605-005-0344-x)
- Aliev, I. and Gruber, P. M. 2006. Best simultaneous diophantine approximations under a constraint on the denominator. Contributions to Discrete Mathematics 1(1), pp. 29-46.
- Aliev, I., Schinzel, A. and Schmidt, W. M. 2005. On vectors whose span contains a given linear subspace. Monatshefte für Mathematik 144(3), pp. 177-191. (10.1007/s00605-004-0267-y)
- Aliev, I. 2002. On a decomposition of integer vectors, II.. Acta Arithmetica 57(2), pp. 159-164.
- Aliev, I. 2001. On a decomposition of integer vectors, I.. Bulletin of the Polish Academy of Sciences Mathematics 49, pp. 141-146.
- Aliev, I. and Zhigljavsky, A. 1999. Weyl sequences: asymptotic distributions of the partition lengths. Acta Arithmetica 88(4), pp. 351-361.
- Aliev, I., Kanemitsu, S. and Schinzel, A. 1998. On the metric theory of continued fractions. Colloquium Mathematicum 77, pp. 141-145.
Book sections
- Aliev, I., De Loera, J. and Louveaux, Q. 2016. Parametric polyhedra with at least k lattice points: their semigroup structure and the k-Frobenius problem. In: Beveridge, A. et al. eds. Recent Trends in Combinatorics. The IMA Volumes in Mathematics and its Applications Springer, pp. 753-778., (10.1007/978-3-319-24298-9_29)
Conferences
- Aliev, I., Celaya, M. and Henk, M. 2024. Sparsity and integrality gap transference bounds for integer programs. Presented at: IPCO 2024: The 25th Conference on Integer Programming and Combinatorial Optimization, Wroclaw, Poland, 3-5 July 2024 Presented at Vygen, J. and Byrka, J. eds.Integer Programming and Combinatorial Optimization: 25th International Conference, IPCO 2024, Wroclaw, Poland, July 3–5, 2024, Proceedings. Association for Computing Machinery pp. 1-13., (10.1007/978-3-031-59835-7_1)
- Aliev, I., Bassett, R., De Loera, J. A. and Louveaux, Q. 2017. A quantitative Doignon-Bell-Scarf theorem. Combinatorica 37, pp. 313-332. (10.1007/s00493-015-3266-9)
- Aliev, I., Loera, J. D., Oertel, T. and O'Neill, C. 2017. Sparse solutions of linear diophantine equations. SIAM Journal on Applied Algebra and Geometry 1(1), pp. 239-253., article number: 2470-6566. (10.1137/16M1083876)
- Aliev, I., De Loera, J. and Louveaux, Q. 2016. Parametric polyhedra with at least k lattice points: their semigroup structure and the k-Frobenius problem. In: Beveridge, A. et al. eds. Recent Trends in Combinatorics. The IMA Volumes in Mathematics and its Applications Springer, pp. 753-778., (10.1007/978-3-319-24298-9_29)
- Aliev, I. and Letchford, A. 2014. Iterated Chvátal--Gomory cuts and the geometry of numbers. SIAM Journal on Optimization 24(3), pp. 1294-1312. (10.1137/130926389)
Research
My research interests are in mathematical optimisation and discrete mathematics, including algebraic and geometric methods of integer optimisation, discrete geometry and algorithmic geometry of numbers. I am also interested in Diophantine approximations and additive number theory.
Research Groups:
Teaching
I teach the following modules:
- MA3007 Coding Theory
- MA3603 Optimisation
Biography
PhD: IM PAN, supervisor: Prof. Andrzej Schinzel.
MSc: St.-Petersburg State University, supervisor: Prof. Yuri Matiyasevich.