## About Me

I have a B.Sc. degree from the Mathematical Engineering and an M.Sc degree from the Computational Science and Engineering Department in the Istanbul Technical University, Turkey.

I am currently doing Ph.D. under the supervision of Dr. Oliver Mason at the Hamilton Institute, NUI Maynooth, Ireland. I am going to finish my study in November 2012.

My research interests are mostly based on the combination of different disciplines such as linear algebra, max algebra, numerical analysis, parallel computation and optimisation.

## Research Topics

- Non-negative Matrix Theory (Perron-Frobenius Theory)
- Spectral Theory over the Max Algebra
- Modeling and Stability Analysis of Positive Dynamical Systems
- Ranking in Multiple Criteria Decision Making Problems (Analytic Hierarchy Process)
- Multi-objective Optimization (Pareto Optimality)
- Parallelization Approaches for the Solution of Large-scale Linear Problems and Preconditioning

## Publications

## Journal articles under preparation:

- B. Benek Gursoy, S. Kirkland, O. Mason and S. Sergeev,
On the Markov Chain Tree Theorem in Semirings.## Journal articles under review:

- B. Benek Gursoy, S. Kirkland, O. Mason and S. Sergeev,
On the Markov Chain Tree Theorem in the Max Algebra, arXiv:1210.3607 (2012).- B. Benek Gursoy, O. Mason and S. Sergeev,
The Analytic Hierarchy Process, Max Algebra and Multi-objective Optimisation, arXiv:1207.6572v1 (2012).## Peer reviewed journal articles:

- B. Benek Gursoy and O. Mason,
P1max and Smax properties and asymptotic stability in the max algebra, Linear Algebra Appl. 435 (2011) 1008–1018.- B. Benek Gursoy and O. Mason,
Spectral properties of matrix polynomials in the max algebra, Linear Algebra Appl. 435 (2011) 1626-1636.## Conference and Workshop Abstracts

- B. Benek Gursoy, O. Mason and S. Sergeev,
Application of the Max Algebra to Ranking Schemes in AHP, Workshop of the LMS Joint Research Group: Tropical Mathematics and its Applications, 2012, Birmingham, UK.- B. Benek Gursoy and O. Mason,
P1max and Smax properties and asymptotic stability in the tropical linear algebra, International Linear Algebra Society (ILAS), 2011, Braunschweig, Germany.- B. Benek Gursoy and O. Mason,
Matrix Polynomials in the Max Algebra; Eigenvalues, Eigenvectors and Inequalities, International Linear Algebra Society (ILAS), 2010, Pisa, Italy.- B. Benek and M. Demiralp,
Approximation Methods for the Solution of Quantum Evolution Equations at the Zero Fluctuation Limit, Multivariate Analysis and its Application in Science and Engineering (MAASE), 2008, Istanbul.- B. Benek and H. Dag,
A Comparison of Decomposition Techniques for Structurally Symmetric Sparse Matrices for Parallel Incomplete LU Factorization, International Conference on Computational Science and Education (ICCSE), 2006, Rochester NY.- H. Dag, G. Soykan and B. Benek,
Can Interval Arithmetic Based Preconditioner Work For Nonlinear Systems?, International Conference on Computational Science and Engineering (ICCSE), 2005, Istanbul.

## Activities

- Reviewer for AMS Mathematical Reviews.
- In the organising committee of the 4th International Symposium on Positive Systems, Hamilton Institute, Ireland (September 2-4, 2012).
- Representative of postgraduate students at the Hamilton Institute (2010-2012).
- Member of International Linear Algebra Society (2010-2013).
- Tutoring in the 2nd year science courses: Calculus III-IV, Linear Algebra and Introduction to Statistics, Department of Mathematics and Statistics, NUI Maynooth, Ireland (2010 - 2012).
- Irish HAE (Higher Education Authority) for 4 years covering full tuition and stipend for Ph.D. at the Hamilton Institute, NUI Maynooth, Ireland (2008-2012).
- TUBITAK (Scientific and Technological Research Council of Turkey) Success Scholarship, Informatics Institute, Istanbul Technical University, Turkey (2007 - 2008).
- High Honour Degree and Ranked 2nd in the Mathematical Engineering Department, Faculty of Science and Letters, Istanbul Technical University, Turkey.
- Ranked 1st in High School, Babaeski Super High Schoool, Kirklareli, Turkey.

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