My name is Evangelos Bartzos and 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 was part of Arcades, a Marie Skłodowska-Curie Innovative Training Network. Here you can find my Orchid ID .

Rigidity theory is the branch of mathematics that studies the embeddings (or equivalently realizations) of graphs in an euclidean space or a manifold. If the number of realizations satisfying edge length constraints is finite up to rigid motions, then the embedding is called rigid, otherwise it is called flexible. These embeddings can be related to the real solutions of certain algebraic systems and their complex solutions extend the notion of rigidity to complex eucledian spaces. One of the major open problems in rigidity theory is to find tight upper bounds on the numbers of rigid graph realizations in an embedding space for a given number of vertices. In this thesis, we display methods that reduce the gap between the existing upper bounds and asymptotic lower bounds on the maximal number of realizations on euclidean spaces or spheres.

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

with Ioannis.Z. Emiris, Charalambos Tzamos

Published in Discrete Applied Mathematics .

2023

with Ioannis.Z. Emiris, Raimundas Vidunas

Published in Discrete & Computational Geometry .

2020

with Ioannis.Z. Emiris, Josef Schicho

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

Source code available in zenodo .

2020

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

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

with I.Emiris and C.Tzamos

Graph rigidity and applications .

This presentation included the methods that led to improved upper bounds on graph embedings.

Lancaster, 2023

with Ioannis.Z. Emiris, Ilias Kotsireas, Charalambos Tzamos

Appears in the proceedings of ISSAC 2022 .

In this presentation we relate the computation of the m-Bézout bound with constrained hypergraph orientations.

Lille, France, 2022

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

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

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

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

with G.Grasegger and J.Legerský

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 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

Intership in the context of Master2 Mathématique Avancées in ENS Lyon.

Supervisor: Vincent Borrelli. .

Member of HEVEA team at that time.

2014

Supervisor: David Holcman .

Member of Group of Applied Mathematics and Computational biology at that time.

2015

ARCADES Network publications

ISSAC Conference

Special Semester on Rigidity and Flexibility, Linz, Austria

DIMACS Workshop on Distance Geometry

Images des Mathématiques

Quanta Magazine