# Master projects, internal

If you would like to do a project within the group, please read the description of our research below. If you see an area that you like, please contact the person directly to discuss whether he or she has time, and if yes, possible projects to do.

### Our research areas

Karen Aardal, k.i.aardal@tudelft.nl

Most of my research is on algorithms for integer optimization, but I also do research on the analysis of algorithms, in particular for various facility location problems. In integer optimization I focus on using information from the structure of the underlying lattice and investigate how this information can be used to enhance search algorithms like branch-and-bound, and cutting plane generation. More recently I am working on using machine learning to enhance optimization algorithms. I have also been working on applications of integer optimization, and one of my favorite applications is the planning of where to locate emergency vehicles, such as ambulances.

Theresia van Essen, J.T.vanEssen@tudelft.nl

My research focuses on developing new models and novel optimization based methods for problems from practice in the field of transportation, logistics and scheduling. The optimization methods I develop use elements from integer linear programming, stochastic programming, metaheuristics, problem based heuristics, cutting planes and simulation. I study both the practical and theoretical nature of the real-life problems I consider. Sometimes real-life problems give rise to a new type of optimization problem which has not been discussed in the literature. This gives the possibility to study the structure and characteristics of this problem, but also the opportunity to develop novel solution methods. My research topics include operating room planning, ambulance planning, and efficient use of automated vehicles.

Dion Gijswijt D.C.Gijswijt@tudelft.nl

My research interests lie in discrete mathematics and combinatorial optimisation. The type of problems I study usually involve graphs or related combinatorial structures (hypergraphs, matroids). The main methods I use are linear programming, semidefinite programming and algebraic methods. One area that I am particularly interested in, is the `cap set problem' and related problems from extremal combinatorics and computer science. Much progress in this area uses algebraic ideas in the form of the so-called `polynomial method'.

Leo van Iersel, L.J.J.vanIersel@tudelft.nl

Most of my research is on algorithms for hard problems and applications in biology and industry. For example, I am interested in FPT algorithms, which are algorithms for NP-hard problems that are efficient when a certain parameter is small. Phylogenetic networks also play a central role in my research. These are networks describing evolutionary relationship and reconstructing them from data is very challenging. Next to algorithmic questions, I also study these networks from a more fundamental mathematical point of view. For example, whether certain types of data uniquely determine certain networks. Recently, I have also started working on the combination of machine learning and optimization in order to develop algorithms that combine positive aspects of both fields.

David de Laat, d.delaat@tudelft.nl

My research focuses on mathematical optimization problems that can be approached using semidefinite programming and related techniques. In particular, I am interested in the use of moments and correlation functions to study composite systems, which finds applications in discrete geometry, quantum information theory, analytic number theory, and the conformal bootstrap program. This research involves techniques from convex optimization, harmonic analysis, functional analysis, and real algebraic geometry.

Fernando M. de Oliveira Filho, F.M.deOliveiraFilho@tudelft.nl

My interests lie in the theory and practice of optimization, namely conic programming (linear programming, semidefinite programming, etc.) and its applications. I am very much interested in applying optimization techniques to geometrical problems, like the kissing number problem or the sphere packing problem. In such applications, optimization methods have to be extended to an infinite-dimensional setting through the use of tools from functional and harmonic analysis.

Jos Weber, j.h.weber@tudelft.nl

My research is on error control techniques for digital transmission and storage systems. While being transmitted or stored, data may be corrupted due to noise, fading, etc. Coding techniques are applied to retrieve the original data with high probability. My focus is on the design and analysis of such error-correcting codes. Current topics under investigation are "detection and (de)coding methods for channels with unknown gain and/or offset" and "coding for DNA-based storage". The latter is considered to be a promising alternative for the present-day optical and magnetic storage media. In order to design error-correcting codes meeting the desired performance requirements with respect to efficiency, reliability, and complexity, we use tools from various fields, such as discrete mathematics, algebra, combinatorics, optimization, etc.

Krzysztof Postek, K.S.Postek@tudelft.nl

My interest are optimization problems under uncertainty such as transport/water control/power systems/inventory etc. There, you want to construct optimal decisions, but there are things not known in advance (travel times/water flows/electricity demand/etc). You have a forecast plus a degree of uncertainty around it. The idea is to take this uncertainty into account already at the optimization stage, so that your solution does not need to be fixed later. I am interested in mathematical and applied aspects of this phenomenon, which can be tackled with techniques such as continuous/discrete optimization or machine learning. I have supervised theses at TNO, ORTEC, Quo Mare, Districon, Ab Ovo, Shell, Ciphix. On my website http://sites.google.com/site/krzysztofpostek/ you can find the lecture notes of the "Optimization under uncertainty" course I taught, and a short guideline for practitioners. Please contact me if you would like to discuss a thesis idea or uncertainty in the problem you tackle.

Anurag Bishnoi, A.Bishnoi@tudelft.nl

My main research interests are in discrete mathematics. Specifically, I have worked on research problems from incidence geometry, extremal combinatorics and Ramsey theory. I have used algebraic, geometric and computational methods in tackling these problems, and I am particularly fond of the polynomial method. I have also worked on Chevalley-Warning type theorems from number theory. For more details on my work and interests, see my website: https://anuragbishnoi.wordpress.com/.