About me

My name is Evangelos Bartzos and I am a Phd student at the Department of Telecomuncations and Informatics in University of Athens under the supervision of Prof. Ioannis Z. Emiris, since 2016.

I am currently a member of the ΕρΓΑ Lab.
Our lab is part of AROMATH , a joint team affiliated with INRIA Sophia-Antipolis.
We are also affiliated with ATHENA Research Center .

My Phd is part of Arcades, a Marie Skłodowska-Curie Innovative Training Network.

Here you can find my Orchid ID .

Phd Synopsis

Algebraic elimination for modeling motion

The applications of algebraic elimination theory in modeling motion are the basis of this Ph.D. project. 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.

Scientific interests and Current Research

Algebraic Modeling, Graph Rigidity, Distance Geometry, Real Algebraic Geometry

Publications

New upper bounds for the number of embeddings of minimally rigid graphs.

with Ioannis.Z. Emiris, Raimundas Vidunas

Published in Discrete & Computational Geometry .

2020

On the multihomogeneous Bézout bound on the number of embeddings of minimally rigid graphs.

with Ioannis.Z. Emiris, Josef Schicho

Published in Applicable Algebra in Engineering, Communication and Computing (AAECC).

Source code available in zenodo .

2020

On the maximal number of real embeddings of minimally rigid graphs in $ℝ^2$, $ℝ^3$ and $S^2$.

with Ioannis.Z. Emiris, Jan Legerský, Elias Tsigaridas

Published in Journal of Symbolic Computation (J.S.C.).

Summary of the project and source code is available in Jan's webpage and in zenodo .

2019

An Explicit Isometric Reduction of the Unit Sphere into an Arbitrarily Small Ball

with Vincent Borrelli, Roland Dennis, Francis Lazarus, Damien Rohmer, Boris Thibert

Published in Foundations of Computational Mathematics .

More information about this project can be found in HEVEA webpage.

2017

Conferences/ Workshops

The m-Bézout Bound and Distance Geometry

with Ioannis.Z. Emiris, Charalambos Tzamos

Appears in the proceedings of CASC 2021 .

This presentation included results that generalize the use of graph orientations to compute the multihomogeneous bound of polynomial systems modeled by simple graphs.

Sochi, Russia, 2021

Bounds on the number of embeddings of minimally rigid graphs

part of a joint project with I.Z.Emiris and J.Schicho

French Computational Geometry Days /Journées de Géométrie Algorithmique .

This presentation included results on the multi-homogeneous Bézout bounds for the embeddings of minimally rigid graphs and a conjecture on the degree of their determinantal varieties.

Marseille, 2020

Algebraic and combinatorial methods for bounding the number of the complex embeddings of minimally rigid graphs

part of a joint project with I.Z.Emiris and J.Schicho

Geometric constraint systems: rigidity, flexibility and applications ( slides ).

This presentation included results on the computation of the multi-homogeneous Bézout bound for the embeddings of minimally rigid graphs and its exactness.

Lancaster, 2019

On the maximal number of real embeddings of spatial minimally rigid graphs

with Ioannis.Z. Emiris, Jan Legerský, Elias Tsigaridas

Appears in the proceedings of ISSAC 2018 (see also the slides the presentation).

The results of this work constitute a subset of our publication in J.S.C. .

New York, 2018

Lower bounds on the maximal number of realizations

with G.Grasegger and J.Legerský

Bond-Node Structures .

This presentation is based on our article in J.S.C. and Lower Bounds on the Number of Realizations of Rigid Graphs by G.Grasegger, C.Koutschan & E.Tsigaridas.

Lancaster, 2018

ARCADES events

ARCADES training included a variety of events (doctoral shools, industrial and software workshops and other activities).

An overview of these events can be found here here .

2016 - 2019