![Iskander Aliev](https://profiles-cardiff.imgix.net/attachments/6283?w=200&h=200&auto=format&crop=faces&fit=crop&q=90")
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
2025
- Aliev, I. , Celaya, M. and Henk, M. 2025. Sparsity and proximity transference in integer programming. Mathematical Programming (10.1007/s10107-024-02191-z)
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. Published in: 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. et al. 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) 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. et al. 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. et al. 2021. Distance-sparsity transference for vertices of corner polyhedra. SIAM Journal on Optimization 31 (1)(10.1137/20M1353228)
2020
- Aliev, I. et al. 2020. Optimizing sparsity over lattices and semigroups. Lecture Notes in Computer Science
- 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)
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. et al. 2018. The support of integer optimal solutions. SIAM Journal on Optimization 28 (3), pp.2152-2157. (10.1137/17M1162792)
2017
- Aliev, I. et al. 2017. A quantitative Doignon-Bell-Scarf theorem. Combinatorica 37 , pp.313-332. (10.1007/s00493-015-3266-9)
- 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. et al. 2017. Sparse solutions of linear diophantine equations. SIAM Journal on Applied Algebra and Geometry 1 (1), pp.239-253. 2470-6566. (10.1137/16M1083876)
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., 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) P42.
2012
- Aliev, I. , Fukshansky, L. and Henk, M. 2012. Generalized Frobenius numbers: bounds and average behavior. Acta Arithmetica 155 , pp.53-62.
- 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)
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. Best simultaneous diophantine approximations under a constraint on the denominator. Contributions to Discrete Mathematics 1 (1), pp.29-46.
- 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)
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
- 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. et al. 2018. The support of integer optimal solutions. SIAM Journal on Optimization 28 (3), pp.2152-2157. (10.1137/17M1162792)
- 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. 2001. On a decomposition of integer vectors, I.. Bulletin of the Polish Academy of Sciences Mathematics 49 , pp.141-146.
- Aliev, I. 2002. On a decomposition of integer vectors, II.. Acta Arithmetica 57 (2), pp.159-164.
- Aliev, I. 2019. On polynomial-time solvable linear Diophantine problems. Moscow Journal of Combinatorics and Number Theory 8 (4), pp.357-365.
- 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. 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. 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. et al. 2020. Optimizing sparsity over lattices and semigroups. Lecture Notes in Computer Science
- Aliev, I. et al. 2022. Sparse representation of vectors in lattices and semigroups. Mathematical Programming 192 , pp.519-546. (10.1007/s10107-021-01657-8)
- Aliev, I. et al. 2017. A quantitative Doignon-Bell-Scarf theorem. Combinatorica 37 , pp.313-332. (10.1007/s00493-015-3266-9)
- Aliev, I. et al. 2021. Distance-sparsity transference for vertices of corner polyhedra. SIAM Journal on Optimization 31 (1)(10.1137/20M1353228)
- Aliev, I. , Celaya, M. and Henk, M. 2025. Sparsity and proximity transference in integer programming. Mathematical Programming (10.1007/s10107-024-02191-z)
- Aliev, I. , Fukshansky, L. and Henk, M. 2012. Generalized Frobenius numbers: bounds and average behavior. Acta Arithmetica 155 , pp.53-62.
- 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. Best simultaneous diophantine approximations under a constraint on the denominator. Contributions to Discrete Mathematics 1 (1), pp.29-46.
- 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. 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. 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 Henk, M. 2023. Minkowski’s successive minima in convex and discrete geometry. Communications in Mathematics 31 (2) 3. (10.46298/cm.11155)
- 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. , 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. et al. 2024. New bounds for the integer Caratheodory rank. SIAM Journal on Optimization 34 (1), pp.190-200. (10.1137/23M1561312)
- Aliev, I. , Henk, M. and Linke, E. 2013. Integer points in knapsack polytopes and s-covering radius. Electronic Journal of Combinatorics 20 (2) P42.
- 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. , 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. , Kanemitsu, S. and Schinzel, A. 1998. On the metric theory of continued fractions. Colloquium Mathematicum 77 , pp.141-145.
- 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. et al. 2017. Sparse solutions of linear diophantine equations. SIAM Journal on Applied Algebra and Geometry 1 (1), pp.239-253. 2470-6566. (10.1137/16M1083876)
- 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. , 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. 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. and Zhigljavsky, A. 1999. Weyl sequences: asymptotic distributions of the partition lengths. Acta Arithmetica 88 (4), pp.351-361.
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., 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. Published in: 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)
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.
Recent Research Funding:
EPSRC grant EP/Y032551/1. Project title: Average-case proximity for integer optimisation
June 1st 2024 - May 31st 2025
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.