Evangelos Bartzos (ESR2)

2014-15: Master 2 Recherche- Mathématiques en Action (Université Lyon 1)
2013-14: Master 2 Recherche- Mathématiques Avancées (École Normale Supérieure de Lyon)
2009-13: Bachelor in Mathematics (University of Patras)
2003-08: Bachelor in Molecular Biology and Genetics (University of Thrace)

Research activities:
E. Bartzos, V. Borelli, R. Denis, F. Lazarus, B. Thibert. ”An Explicit Isometric Reduction of the Unit Sphere into an Arbitrarily Small Ball”, Foundations of Computational Mathematics, 2017

Project: Algebraic elimination for modelling motion

Supervisor: Ioannis Emiris
Institution: ATHENA Research and Innovation Center, Greece

Algebraic systems have been widely used in modeling motion. For example, in robot kinematics we can model the workspace of mechanisms and find solutions to the forward and inverse kinematic problems. Sparse elimination theory provides very strong mathematical tools that can be used in algebraic problem solving and in studying such systems. Methods derived from discrete geometry, including Newton polytope, Minkowski sum, and mixed volume, are essential in this field.

Our current project is focused on rigid graphs and their number of embeddings in $\mathbb{R}^ 3$. The combinatorial properties of these graphs can lead to certain algebraic and semi-algebraic systems, applying distance geometry tools. Sparse elimination techniques are used to obtain optimal upper bounds. In order to find a maximal number of real postures, we have developed tools of stochastic optimization and semidefinate programming implementing code in Matlab, Maple and Sage.

The project will take place at ATHENA RC at the ErGA Lab. The PhD will be awarded by the Dept. of Informatics and Telecoms of the University of Athens.

Secondments are planned at JKU (Linz, Austria) and at industrial partner Missler (France).