Welcome! I am Lukas Finschi. This page is about my studies at ETH Zurich and my mathematical research at the Institute for Operations Research (IFOR), including research and a catalog of oriented matroids.

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Research and Studies

1992 - 1997	Studies of Mathematics at ETH Zurich: Topics of special interest were, among others, Operations Research (Discrete and Continuous Optimization, Game Theory, Simulation, Scheduling and Planning), Algorithmics (Computer Algebra, Algorithmic Geometry, Artificial Intelligence), Algebra, Number Theory, Combinatorics. In particular I wrote a term paper and my diploma thesis at IFOR.
1995 - 1996	Auxiliary Assistance at the Institute for Operations Research (IFOR): Several smaller research projects, specifically Empirical Studies on Value at Risk and Maximum Loss (Risk Measurement in Finance), Levenberg-Marquardt Algorithm, Low-Discrepancy Sequences.
1997 - 2001	Ph.D. Thesis A Graph Theoretical Approach for Reconstruction and Generation of Oriented Matroids, supervised by Prof. Dr. H.-J. Lüthi and Prof. Dr. K. Fukuda.

Publications and Reports

1996-04-16	An Implementation of the Levenberg-Marquardt Algorithm
1996-07-05	Semesterarbeit (Term Paper): Ablaufplanung einer Fertigungszelle
1996-09-23	Quasi-Monte Carlo: An Empirical Study on Low-Discrepancy Sequences
1997-02-28	Diploma Thesis: Randomized Pivot Algorithms in Linear Programming
1997-08-22	Randomized Pivot Algorithms in Linear Programming
1998-09-10	Towards a Unified Framework for Randomized Pivoting Algorithms in Linear Programming with Komei Fukuda and Hans-Jakob Lüthi, appeared in: Operations Research Proceedings 1998 (Zurich), Springer, Berlin, pp. 113-122 (1999) https://doi.org/10.1007/978-3-642-58409-1_10
2000-01-31	Cocircuit Graphs and Efficient Orientation Reconstruction in Oriented Matroids with Eric Babson and Komei Fukuda, appeared in: European Journal of Combinatorics 22 (5), pp. 587-600 (2001) https://doi.org/10.1006/eujc.2001.0481
2000-10-31	Generation of Oriented Matroids - A Graph Theoretical Approach with Komei Fukuda, appeared in: Discrete & Computational Geometry 27, pp. 117-136 (2002) https://doi.org/10.1007/s00454-001-0056-5
2001-04-06	The Da Silva-Fukuda Conjecture on an Extension of the Sylvester-Gallai Theorem with Komei Fukuda
2001-04-30	Complete Combinatorial Generation of Small Point Configurations and Hyperplane Arrangements with Komei Fukuda, appeared in: Proceedings of the 13th Canadian Conference on Computational Geometry, University of Waterloo, Ontario, Canada, August 13-15, pp. 97-100 (2001) https://dblp.org/rec/conf/cccg/FinschiF01
2001-08-31	Dissertation (PhD Thesis): A Graph Theoretical Approach for Reconstruction and Generation of Oriented Matroids