Our daily life environment is increasingly interacting with digital information. An important amount of this information is of geometric nature. It concerns the representation of our environment, the analysis and understanding of “real” phenomena, the control of physical mechanisms or processes. The interaction between physical and digital worlds is two-way. Sensors are producing digital data related to measurements or observations of our environment. Digital models are also used to “act” on the physical world. Objects that we use at home, at work, to travel, such as furniture, cars, planes, ... are nowadays produced by industrial processes which are based on digital representation of shapes. CAD-CAM (Computer Aided Design – Computer Aided Manufacturing) software is used to represent the geometry of these objects and to control the manufacturing processes which create them. The construction capabilities themselves are also expanding, with the development of 3D printers and the possibility to create daily-life objects “at home” from digital models.

The impact of geometry is also important in the analysis and understanding of phenomena. The 3D conformation of a molecule explains its biological interaction with other molecules. The profile of a wing determines its aeronautic behavior, while the shape of a bulbous bow can decrease significantly the wave resistance of a ship. Understanding such a behavior or analyzing a physical phenomenon can nowadays be achieved for many problems by numerical simulation. The precise representation of the geometry and the link between the geometric models and the numerical computation tools are closely related to the quality of these simulations. This also plays an important role in optimisation loops where the numerical simulation results are used to improve the “performance” of a model.

Geometry deals with structured and efficient representations of information and with methods to treat it. Its impact in animation, games and VAMR (Virtual, Augmented and Mixed Reality) is important. It also has a growing influence in e-trade where a consumer can evaluate, test and buy a product from its digital description. Geometric data produced for instance by 3D scanners and reconstructed models are nowadays used to memorize old works in cultural or industrial domains.

Geometry is involved in many domains (manufacturing, simulation, communication, virtual world...), raising many challenging questions related to the representations of shapes, to the analysis of their properties and to the computation with these models. The stakes are multiple: the accuracy in numerical engineering, in simulation, in optimization, the quality in design and manufacturing processes, the capacity of modeling and analysis of physical problems.

The accurate description of shapes is a long standing problem in mathematics, with an important impact in many domains, inducing strong interactions between geometry and computation. Developing precise geometric modeling techniques is a critical issue in CAD-CAM. Constructing accurate models, that can be exploited in geometric applications, from digital data produced by cameras, laser scanners, observations or simulations is also a major issue in geometry processing. A main challenge is to construct models that can capture the geometry of complex shapes, using few parameters while being precise.

Our first objective is to develop methods, which are able to describe accurately and in an efficient way, objects or phenomena of geometric nature, using algebraic representations.

The approach followed in CAGD, to describe complex geometry is based on parametric representations called NURBS (Non Uniform Rational B-Spline). The models are constructed by trimming and gluing together high order patches of algebraic surfaces. These models are built from the so-called B-Spline functions that encode a piecewise algebraic function with a prescribed regularity at the seams. Although these models have many advantages and have become the standard for designing nowadays CAD models, they also have important drawbacks. Among them, the difficulty to locally refine a NURBS surface and also the topological rigidity of NURBS patches that imposes to use many such patches with trims for designing complex models, with the consequence of the appearing of cracks at the seams. To overcome these difficulties, an active area of research is to look for new blending functions for the representation of CAD models. Some examples are the so-called T-Splines, LR-Spline blending functions, or hierarchical splines, that have been recently devised in order to perform efficiently local refinement. An important problem is to analyze spline spaces associated to general subdivisions, which is of particular interest in higher order Finite Element Methods. Another challenge in geometric modeling is the efficient representation and/or reconstruction of complex objects, and the description of computational domains in numerical simulation. To construct models that can represent efficiently the geometry of complex shapes, we are interested in developing modeling methods, based on alternative constructions such as skeleton-based representations. The change of representation, in particular between parametric and implicit representations, is of particular interest in geometric computations and in its applications in CAGD.

We also plan to investigate adaptive hierarchical techniques, which can locally improve the approximation of a shape or a function. They shall be exploited to transform digital data produced by cameras, laser scanners, observations or simulations into accurate and structured algebraic models.

The precise and efficient representation of shapes also leads to the problem of extracting and exploiting characteristic properties of shapes such as symmetry, which is very frequent in geometry. Reflecting the symmetry of the intended shape in the representation appears as a natural requirement for visual quality, but also as a possible source of sparsity of the representation. Recognizing, encoding and exploiting symmetry requires new paradigms of representation and further algebraic developments. Algebraic foundations for the exploitation of symmetry in the context of non linear differential and polynomial equations are addressed. The intent is to bring this expertise with symmetry to the geometric models and computations developed by aromath.

In many problems, digital data are approximated and cannot just be
used as if they were exact. In the context of geometric modeling,
polynomial equations appear naturally, as a way to describe
constraints between the unknown variables of a problem. *An
important challenge is to take into account the input error in order
to develop robust methods for solving these algebraic constraints.*
Robustness means that a small perturbation of the input should produce
a controlled variation of the output, that is forward stability, when
the input-output map is regular. In non-regular cases,
robustness also means that the output is an exact solution, or the
most coherent solution, of a problem with input
data in a given neighborhood, that is backward stability.

Our second long term objective is to develop methods to robustly and efficiently solve algebraic problems that occur in geometric modeling.

Robustness is a major issue in geometric modeling and algebraic computation. Classical methods in computer algebra, based on the paradigm of exact computation, cannot be applied directly in this context. They are not designed for stability against input perturbations. New investigations are needed to develop methods, which integrate this additional dimension of the problem. Several approaches are investigated to tackle these difficulties.

One is based on linearization of algebraic problems based on “elimination of variables” or projection into a space of smaller dimension. Resultant theory provides strong foundation for these methods, connecting the geometric properties of the solutions with explicit linear algebra on polynomial vector spaces, for families of polynomial systems (e.g., homogeneous, multi-homogeneous, sparse). Important progresses have been made in the last two decades to extend this theory to new families of problems with specific geometric properties. Additional advances have been achieved more recently to exploit the syzygies between the input equations. This approach provides matrix based representations, which are particularly powerful for approximate geometric computation on parametrized curves and surfaces. They are tuned to certain classes of problems and an important issue is to detect and analyze degeneracies and to adapt them to these cases.

A more adaptive approach involves linear algebra computation in a hierarchy of polynomial vector spaces. It produces a description of quotient algebra structures, from which the solutions of polynomial systems can be recovered. This family of methods includes Gröbner Basis, which provides general tools for solving polynomial equations. Border Basis is an alternative approach, offering numerically stable methods for solving polynomial equations with approximate coefficients. An important issue is to understand and control the numerical behavior of these methods as well as their complexity and to exploit the structure of the input system.

In order to compute “only” the (real) solutions of a polynomial system in a given domain, duality techniques can also be employed. They consist in analyzing and adding constraints on the space of linear forms which vanish on the polynomial equations. Combined with semi-definite programming techniques, they provide efficient methods to compute the real solutions of algebraic equations or to solve polynomial optimization problems. The main issues are the completness of the approach, their scalability with the degree and dimension and the certification of bounds.

Singular solutions of polynomial systems can be analyzed by computing differentials, which vanish at these points. This leads to efficient deflation techniques, which transform a singular solution of a given problem into a regular solution of the transformed problem. These local methods need to be combined with more global root localisation methods.

Subdivision methods are another type of methods which are interesting for robust geometric computation. They are based on exclusion tests which certify that no solution exists in a domain and inclusion tests, which certify the uniqueness of a solution in a domain. They have shown their strength in addressing many algebraic problems, such as isolating real roots of polynomial equations or computing the topology of algebraic curves and surfaces. The main issues in these approaches is to deal with singularities and degenerate solutions.

The main domain of applications that we consider for the methods we develop is Computer Aided Design and Manufacturing.

Computer-Aided Design (CAD) involves creating digital models defined by mathematical constructions, from geometric, functional or aesthetic considerations. Computer-aided manufacturing (CAM) uses the geometrical design data to control the tools and processes, which lead to the production of real objects from their numerical descriptions.

CAD-CAM systems provide tools for visualizing, understanding, manipulating, and editing virtual shapes. They are extensively used in many applications, including automotive, shipbuilding, aerospace industries, industrial and architectural design, prosthetics, and many more. They are also widely used to produce computer animation for special effects in movies, advertising and technical manuals, or for digital content creation. Their economic importance is enormous. Their importance in education is also growing, as they are more and more used in schools and educational purposes.

CAD-CAM has been a major driving force for research developments in geometric modeling, which leads to very large software, produced and sold by big companies, capable of assisting engineers in all the steps from design to manufacturing.

Nevertheless, many challenges still need to be addressed. Many problems remain open, related to the use of efficient shape representations, of geometric models specific to some application domains, such as in architecture, naval engineering, mechanical constructions, manufacturing ...Important questions on the robustness and the certification of geometric computation are not yet answered. The complexity of the models which are used nowadays also appeals for the development of new approaches. The manufacturing environment is also increasingly complex, with new type of machine tools including: turning, 5-axes machining and wire EDM (Electrical Discharge Machining), 3D printer. It cannot be properly used without computer assistance, which raises methodological and algorithmic questions. There is an increasing need to combine design and simulation, for analyzing the physical behavior of a model and for optimal design.

The field has deeply changed over the last decades, with the emergence of new geometric modeling tools built on dedicated packages, which are mixing different scientific areas to address specific applications. It is providing new opportunities to apply new geometric modeling methods, output from research activities.

A major bottleneck in the CAD-CAM developments is the lack of interoperability of modeling systems and simulation systems. This is strongly influenced by their development history, as they have been following different paths.

The geometric tools have evolved from supporting a limited number of tasks at separate stages in product development and manufacturing, to being essential in all phases from initial design through manufacturing.

Current Finite Element Analysis (FEA) technology was already well
established 40 years ago, when CAD-systems just started to
appear, and its success stems from using approximations of both the
geometry and the analysis model with low order finite elements (most
often of degree

There has been no requirement between CAD and numerical simulation, based on Finite Element Analysis, leading to incompatible mathematical representations in CAD and FEA. This incompatibility makes interoperability of CAD/CAM and FEA very challenging. In the general case today this challenge is addressed by expensive and time-consuming human intervention and software developments.

Improving this interaction by using adequate geometric and functional descriptions should boost the interaction between numerical analysis and geometric modeling, with important implications in shape optimization. In particular, it could provide a better feedback of numerical simulations on the geometric model in a design optimization loop, which incorporates iterative analysis steps.

The situation is evolving. In the past decade, a new paradigm has emerged to replace the traditional Finite Elements by B-Spline basis element of any polynomial degree, thus in principle enabling exact representation of all shapes that can be modeled in CAD. It has been demonstrated that the so-called isogeometric analysis approach can be far more accurate than traditional FEA.

It opens new perspectives for the interoperability between geometric modeling and numerical simulation. The development of numerical methods of high order using a precise description of the shapes raises questions on piecewise polynomial elements, on the description of computational domains and of their interfaces, on the construction of good function spaces to approximate physical solutions. All these problems involve geometric considerations and are closely related to the theory of splines and to the geometric methods we are investigating. We plan to apply our work to the development of new interactions between geometric modeling and numerical solvers.

Keywords: Algorithm , CAD , Numerical algorithm , Geometric algorithms

Scientific Description

Axl is an algebraic geometric modeler that aims at providing “algebraic modeling” tools for the manipulation and computation with curves, surfaces or volumes described by semi-algebraic representations. These include parametric and implicit representations of geometric objects. Axl also provides algorithms to compute intersection points or curves, singularities of algebraic curves or surfaces, certified topology of curves and surfaces, etc. A plugin mechanism allows to extend easily the data types and functions available in the plateform.

Functional Description

Axl is a cross platform software to visualize, manipulate and compute 3D objects. It is composed of a main application and several plugins. The main application provides atomic geometric data and processes, a viewer based on VTK, a GUI to handle objects, to select data, to apply process on them and to visualize the results. The plugins provides more data with their reader, writer, converter and interactors, more processes on the new or atomic data. It is written in C++ and thanks to a wrapping system using SWIG, its data structures and algorithms can be integrated into C# programs, as well as Python. The software is distributed as a source package, as well as binary packages for Linux, MacOSX and Windows.

Participants: Emmanouil Christoforou, Nicolas Douillet, Anaïs Ducoffe, Valentin Michelet, Bernard Mourrain, Meriadeg Perrinel, Stéphane Chau and Julien Wintz

Contact: Bernard Mourrain

URL: http://

Collaboration with Elisa Berrini (MyCFD, Sophia), Tor Dokken (Gotools library, Oslo, Norway), Angelos Mantzaflaris (GISMO library, Linz, Austria), Laura Saini (Post-Doc GALAAD/Missler, TopSolid), Gang Xu (Hangzhou Dianzi University, China), Meng Wu (Hefei University of Technology, China).

Keywords: Algorithm, Numerical algorithm, Geometric algorithm, Scaffolding, Implicit surface, Mesh generation

Scientific Description

Skelton is a C++ library for skeleton-based modeling with convolution surfaces. It supports skeletons made of line segments and arcs of circle, including circular splines, and features an anisotropic extension to circular splines. The library can generate a quad dominant mesh that surrounds, and follows, the structure of the skeleton. The mesh is generated with an advanced scaffolding algorithm that works for skeletons of any topology.

Functional Description

Skelton is a multi-platform C++ library distributed as source code. It provides a class hierarchy for creating and manipulating geometric objects generated with anisotropic convolution. It can take the skeleton as an input file or defined directly by the user. The library supports an improved version of convolution surfaces and permits the design of anisotropic surfaces. The scaffolding algorithm can be used independently of the implicit surface definition. The library has a command line interface that controls most of the functionality. The user can subclass elements of the library for extended behavior.

Participants: Alvaro Fuentes, Evelyne Hubert.

Contacts: Alvaro Fuentes, Evelyne Hubert.

This is a joint work with Simon Telen and Marc Van Barel (Univ. Leuven, Belgium)

Joint work with Gabriel Sticlaru (Faculty of Mathematics and Informatics, Ovidius University, Romania).

Joint work with Gabriel Sticlaru (Faculty of Mathematics and Informatics, Ovidius University, Romania).

Assuming the variety of a polynomial set is invariant under a group action, we construct, in , a set of invariants that cut the same variety. The construction can be seen as a generalization of the previously known construction for finite groups. The result though has to be understood outside an invariant variety which is independent of the polynomial set considered. We introduce the symmetrizations of a polynomial that are polynomials in a generating set of rational invariants. The generating set of rational invariants and the symmetrizations are constructed w.r.t. a section of the orbits of the group action.

This is a joint work with P. Görlach (Max Planck institute, Leipzig) and T. Papadopoulo (EPI Athena, Inria SAM)

Quadrature is an approximation of the definite integral of a function by a weighted sum of function values at specified points, or nodes, within the domain of integration. Gaussian quadratures are constructed to yield exact results for any polynomials of degree

Joint work with M. Collowald, (previously Université Nice Sophia Antipolis).

This is a joint work with Vissarion Fisikopoulos (Oracle Corp., Athens, Greece).

This is a joint work with Ludovic Calées (EU JRC, Ispra, Italy), and Vissarion Fisikopoulos (Oracle Corp., Athens, Greece).

This is a joint work with J. Legersky (JK University, Linz, Austria) and E. Tsigaridas (PolSys, Inria).

Meshes with curvilinear elements hold the appealing promise of enhanced geometric flexibility and higher-order numerical accuracy compared to their commonly-used straight-edge counterparts. However, the generation of curved meshes remains a computationally expensive endeavor with current meshing approaches: high-order parametric elements are notoriously difficult to conform to a given boundary geometry, and enforcing a smooth and non-degenerate Jacobian everywhere brings additional numerical difficulties to the meshing of complex domains. In the paper , we propose an extension of Optimal Delaunay Triangulations (ODT) to curved and graded isotropic meshes. By exploiting a continuum mechanics interpretation of ODT instead of the usual approximation theoretical foundations, we formulate a very robust geometry and topology optimization of Bézier meshes based on a new simple functional promoting isotropic and uniform Jacobians throughout the domain. We demonstrate that our resulting curved meshes can adapt to complex domains with high precision even for a small count of elements thanks to the added flexibility afforded by more control points and higher order basis functions.

Joint work Leman Feng (ENPC), Pierre Alliez (EPI Titane), Hervé Delingette (EPI Asclepios) and Mathieu Desbrun (CalTech, USA),

This is joint work with A. Panotopoulou (Dartmouth College), E. Ross (MESH consultants), K. Welker (University of Trier), G. Morin (Intitut de Recherche en Informatique de Toulouse).

Modeling and computing of trivariate parametric volumes is an important research topic in the field of three-dimensional isogeometric analysis. In , we propose two kinds of exact conversion approaches from Bézier tetrahedra to Bézier hexahedra with the same degree by reparametrization technique. In the first method, a Bézier tetrahedron is converted into a degenerate Bézier hexahedron, and in the second approach, a non-degenerate Bézier tetrahedron is converted into four non-degenerate Bézier hexahedra. For the proposed methods, explicit formulae are given to compute the control points of the resulting tensor-product Bézier hexahedra. Furthermore, in the second method, we prove that tetrahedral spline solids with

This is a joint work with Gang Xu (Hanghzou, China), Yaoli Jin (Hanghzou, China), Zhoufang Xiao (Hanghzou, China), Qing Wu (Hanghzou, China), Timon Rabczuk (Weimar, Germany).

This is a joint work with Gang Xu (Hanghzou, China), Ming Li (Zhejiang, China), Timon Rabczuk (Weimar, Germany), Jinlan Xu (Hangzhou, China), Stéphane P.A. Bordas (Luxembourg).

Gaussian-Process based optimization methods have become very popular in recent years for the global optimization of complex systems with high computational costs. These methods rely on the sequential construction of a statistical surrogate model, using a training set of computed objective function values, which is refined according to a prescribed infilling strategy. However, this sequential optimization procedure can stop prematurely if the objective function cannot be computed at a proposed point. Such a situation can occur when the search space encompasses design points corresponding to an unphysical configuration, an ill-posed problem, or a non-computable problem due to the limitation of numerical solvers. To avoid such a premature stop in the optimization procedure, we propose in to use a classification model to learn non-computable areas and to adapt the infilling strategy accordingly. Specifically, the proposed method splits the training set into two subsets composed of computable and non-computable points. A surrogate model for the objective function is built using the training set of computable points, only, whereas a probabilistic classification model is built using the union of the computable and non-computable training sets. The classifier is then incorporated in the surrogate-based optimization procedure to avoid proposing new points in the non-computable domain while improving the classification uncertainty if needed. The method has the advantage to automatically adapt both the surrogate of the objective function and the classifier during the iterative optimization process. Therefore, non-computable areas do not need to be a priori known. The proposed method is applied to several analytical problems presenting different types of difficulty, and to the optimization of a fully nonlinear fluid-structure interaction system. The latter problem concerns the drag minimization of a flexible hydrofoil with cavitation constraints. The efficiency of the proposed method compared favorably to a reference evolutionary algorithm, except for situations where the feasible domain is a small portion of the design space.

This is joint work with Matthieu Sacher (IRENAV), Régis Duvigneau (ACUMES), Olivier Le Maitre (LIMSI), Mathieu Durand (K-Epsilon), Frédéric Hauville (IRENAV), Jacques-André Astolfi (IRENAV).

This is a joint work with Jean Rajchenbach (LPMC, UCA) and Bernard Rousselet (JAD, UCA).

The Capillary Equation correctly predicts the curvature evolution and the length of a quasi-static vapour formation. It describes a two-phase interface as a smooth curve resulting from a balance of curvatures that are influenced by surface tension and hydrostatic pressures. The present work provides insight into the application of the Capillary Equation to the prediction of single nu-cleate site phase change phenomena. In an effort to progress towards an application of the Capillary Equation to boiling events, a procedure to generating a numerical solution, in which the computational expense is reduced, is reported in .

This is a joint work with Frédéric Lesage (LCPI, UCA), Sebastian Minjeaud (JAD, UCA).

This is a joint work with Angelos Mantzaflaris (JKU, Austria), Julien Wintz (SED, Inria).

Our team AROMATH participates to the VADER project for VIRTUAL MODELING of RESPIRATION, UCA Jedi, axis “Modélisation, Physique et Mathématique du vivant". http://

Program: Marie Skłodowska-Curie ITN

Project acronym: ARCADES

Project title: Algebraic Representations in Computer-Aided Design for complEx Shapes

Duration: January 2016 - December 2019

Coordinator: I.Z. Emiris (NKUA, Athens, Greece, and ATHENA Research Innovation Center)

Scientist-in-charge at Inria: L. Busé

Other partners: U. Barcelona (Spain), Inria Sophia Antipolis (France), J. Kepler University, Linz (Austria), SINTEF Institute, Oslo (Norway), U. Strathclyde, Glascow (UK), Technische U. Wien (Austria), Evolute GmBH, Vienna (Austria).

Webpage: http://

Abstract: ARCADES aims at disrupting the traditional paradigm in Computer-Aided Design (CAD) by exploiting cutting-edge research in mathematics and algorithm design. Geometry is now a critical tool in a large number of key applications; somewhat surprisingly, however, several approaches of the CAD industry are outdated, and 3D geometry processing is becoming increasingly the weak link. This is alarming in sectors where CAD faces new challenges arising from fast point acquisition, big data, and mobile computing, but also in robotics, simulation, animation, fabrication and manufacturing, where CAD strives to address crucial societal and market needs. The challenge taken up by ARCADES is to invert the trend of CAD industry lagging behind mathematical breakthroughs and to build the next generation of CAD software based on strong foundations from algebraic geometry, differential geometry, scientific computing, and algorithm design. Our game-changing methods lead to real-time modelers for architectural geometry and visualisation, to isogeometric and design-through-analysis software for shape optimisation, and marine design & hydrodynamics, and to tools for motion design, robot kinematics, path planning, and control of machining tools.

NSFC collaboration project with Gang Xu, Hangzhou Dianzi University, China, “Research on theory and method of time-varying parameterization for dynamic isogeometric analysis”, 2018-2021.

Aron Simis, University of Recife, Brazil, visited L. Busé for a week (October 8-12) to work on birationality of rational map by means of syzygy-based techniques.

Ibrahim Adamou, Univ. Dan Dicko Dankoulodo de Maradi, Niger, visited B. Mourrain (26 Nov.- 21 Dec.) to work on 3-dimensional VoronoïDiagrams of half-lines and medial axes of curve arcs.

Yairon Cid Ruiz, a PhD srudent at Barcelona in the Arcades network, visited L. Busé for 6 months (October 2017- March 2018) to work on birationality criteria for multi-graded rational maps with a view towards free form deformation problems.

Clément Laroche, a PhD student in Greece in the Arcades network, visited L. Busé and F. Yildirim for one month (October) for a collaboration on implicization matrices of rational curve in arbitrary dimension by means of quadratic relations.

Kim Perriguey, did a six months internship with L. Busé (December 2017-May 2018). She developed paramteric models for the human walk for the extraction of locomotive parameters. This work was done in collaboration with Pierre Alliez (EPI Titane) and the start-up Ekinnox (Sophia Antipolis).

F. Yildirim was on secondment at MISSLER Topsolid (France), for 3 months (Mai-July).

From October 25th to November 25th, E. Hubert visited the Institute for Computational and Experimental Research in Mathematics (Providence USA) during the program *Nonlinear Algebra*.

Evelyne Hubert was the general and scientific chair for the conference
*Symmetry and Computation* held at the
Centre International de Recherche en Mathematiques (Marseille, France) April 3-7.

Laurent Busé organized the second “Learning Week” of the ARCADES Network : “Opportunity Recognition” at Inria Sophia Antipolis, March 19-23, 2018.

Bernard Mourrain was reviewer for the conference ISSAC.

Bernard Mourrain is associate editor of the Journal of Symbolic Computation (since 2007) and of the SIAM Journal on Applied Algebra and Geometry (since 2016).

Ioannis Emiris is associate editor of the Journal of Symbolic Computation (since 2003) and of Mathematics for Computer Science (since 2017).

Evelyne Hubert is associate editor of the Journal of Symbolic Computation (since 2007) and of Foundations of Computational Mathematics (since 2017).

Laurent Busé reviewed for
the journal *Linear Algebra and its Applications*,
the journal *Computer Aided Geometric Design*,
the journal of *Advances in Applied Mathematics*,
the *Journal of Computational and Applied Mathematics*,
the journal *Applicable Algebra in Engineering, Communication and Computing*, the journal *Computer Aided Design*,
the *SIAM Journal on Applied Algebra and Geometry*.

Ioannis Emiris reviewed for
the *SIAM Journal on Applied Algebra and Geometry*,
the *Symposium of Computational Geometry*.

Bernard Mourrain reviewed for
the *Journal of Algebra and its Application*,
the journal *Computer Methods in Applied Mechanics and Engineering*,
the journal *Computer Aided Geometric Design*,
the *Journal of Computational and Applied Mathematics*,
the *Journal of Symbolic Computation*,
the journal *Mathematics of Computation*.
He is also guest editor of the Special Issue of the
*Journal Of Symbolic Computation* after MEGA 2017 .

Evelyne Hubert reviewed for
the *Journal of Symbolic Computation*,
the journal *Foundations of Comptutational Mathematics*,
and the *Journal of Algebra*.

Laurent Busé was an invited speaker at the conference “Applied and Computational Geometry” that took place at Loughborough University, Centre for Geometry and Applications, September 12-14, 2018.

Ioannis Emiris was an invited speaker at JRC Ispra, Italy, February 2018, at JK University (and gave a course), Linz, Austria, April-May 2018, at the “2nd Intern. Workshop on Geometry and Machine Learning” , within Computational Geometry Week, Budapest, Hungary, June 2018, at the “Symposium on Discrete Mathematics”, of the German Mathematical Society, Graz, Austria, June 2018, at Chipset Training School on Large-Scale Data Mining and Machine Learning for Big Data Analytics (and gave a course), Thessaloniki, 19 September 2018.

Bernard Mourrain was an invited speaker at the Workshop “Structured Matrix Days”, Lyon, 14-15 May, at the International conference on Approximation and Matrix Functions, Lille, May 31 - June 1, at the Workshop “Tensors” (and gave a course), Torino, 10-14 September, at the Workshop “A two-day journey in Computational Algebra and Algebraic Geometry” dedicated to Margherita Roggero, Torino, 27-28 Sep. He was invited at Univ. of Texas, Austin, for a collaboration with Pr. Chandajit Bajaj (29 January - 9 February), an invited participant of the semester on Nonlinear Algebra at ICERM, Providence, RI, USA from 1 to 19 Oct.

Evelyne Hubert gave a keynote lecture at the conference
*Symmetry & Computation*, CIRM (Marseille, France)
and was invited to give talks at
the conference *Algebraic and Geometric Aspects
of Numerical Methods for Differential Equations*
held at the Mittag-Leffler Institute (Stockholm, Sweden),
the *Séminaire différentiel*,
jointly organized by Université Versailles St Quentin and Inria SIF,
and the conference *Nonlinear Algebra in Applications* held at the Institute for Computational and Experimental Mathematics (Providence, USA).

Evelyne Hubert was part of the hiring committees for the positions of Directeur de Recherche 2ème classe at Inria and for the position of Chargé de Recherche at Inria NGE. As part of the Commission d'Evaluation, she was also part of the promotion committee of Inria researchers (CRHC, DR1, DR0).

Evelyne Hubert was the external reviewer for the promotion of Wei Li to the rank of associate professor at the Chinese Academy of Science (Beijing).

Laurent Busé is a board member of the (national) labex AMIES (CRI-SAM representative) and a member of the steering committee of the MSI,
*Maison de la Modélisation, de la Simulation et des Interactions*
of the University Côte d'Azur.
He is also an elected member of the CPRH (Commission Permanente de Ressources Humaines) of the math laboratory of the university of Nice, and is the Inria Sophia Antipolis centre representative at the “Academic Council” and the “Research Commission” of the University of Nice Sophia Antipolis. He participated to the hiring jury of junior researchers in Inria Sophia Antipolis.

Evelyne Hubert is a member of the Comission d'Evaluation, the national Inria evaluation committee. She is nominated to represent Inria at the Academic Council of the Université Côte d'Azur.

Bernard Mourrain is member of the BCEP (Bureau du Comité des Equipes Projet) of the center Inria- Sophia Antipolis.

Master : Laurent Busé, Geometric Modeling, 27h ETD, M2, EPU of the University of Nice-Sophia Antipolis.

Master 2: Bernard Mourrain, Symbolic-Numeric Computation, 6h, Master ACSYON, Limoges.

PhD in progress: Evangelos Anagnostopoulos, Geometric algorithms for massive data, LAMBDA Marie Skłodowska-Curie RISE Network, started in September 2016, supervised by Ioannis Emiris.

PhD in progress: Ahmed Blidia, New geometric models for the design and computation of complex shapes. ARCADES Marie Skłodowska-Curie ITN, started in September 2016, supervised by Bernard Mourrain.

PhD in progress: Apostolos Chalkis, Sampling in high-dimensional convex regions, started in June 2018, supervised by Ioannis Emiris.

PhD in progress: Emmanouil Christoforou, Geometric approximation algorithms for clustering, Bioinformatics scholarship, started in January 2018, supervised by Ioannis Emiris.

PhD in progress: Alvaro-Javier Fuentes-Suàrez, Skeleton-based modeling of smooth shapes. ARCADES Marie Skłodowska-Curie ITN, started in October 2016, supervised by Evelyne Hubert.

PhD: Jouhayna Harmouch, Low rank structured matrix decomposition and applications. Cotutelle Univ. Liban, cosupervised by Houssam Khalil, Mustapha Jazar and Bernard Mourrain. Defended in December.

PhD in progress: Rima Khouja, Tensor decomposition, best approximations, algorithms and applications. Cotutelle Univ. Liban, started in November 2018, cosupervised by Houssam Khalil and Bernard Mourrain.

PhD in progress: Evangelos Bartzos, Algebraic elimination and Distance graphs. ARCADES Marie Skłodowska-Curie ITN, started in June 2016, supervised by Ioannis Emiris.

PhD in progress: Clément Laroche, Algebraic representations of geometric objects. ARCADES Marie Skłodowska-Curie ITN, started in November 2016, supervised by Ioannis Emiris.

PhD in progress: Ioannis Psarros, Dimensionality reduction and Geometric search, Greek scholarship foundation, started in Sep. 2015, supervised by Ioannis Emiris.

PhD in progress: Erick David Rodriguez Bazan, Symmetry preserving algebraic computation. CORDI Inria SAM, started in November 2017, supervised by Evelyne Hubert.

PhD in progress: Fatmanur Yildirim, Distances between points, rational Bézier curves and surfaces by means of matrix-based implicit representations. ARCADES Marie Skłodowska-Curie ITN, started in October 2016, supervised by Laurent Busé.

L. Busé was a member of the committee of the PhD of Rémi Bignalet-Cazalet entitled *Géométrie de la projectivisation des idéaux et applications aux problèmes de birationalité*, University Bourgogne Franche-Comté, Dijon, France, October 24th.

I. Emiris was a member of two 3-person supervisory committees of PhD students Anuj Sharma and Emmanouil Kamarianakis, who defended their theses in December 2018, at NK University of Athens, and University of Crete, Greece, respectively.

E. Hubert was a member of the PhD committee of Timothé Pecatte
from Ecole Normale Supérieure de Lyon, section informatique :
*Bornes Inférieures et Algorithmes de Reconstruction pour
des Sommes de Puissances Affines*.

Ioannis Emiris was an invited speaker at “Open Science Days”, Athens, 29 November 2018, and at “Mathematics Education Forum” within the Greek Mathematical Society annual meeting, Athens, December 2018.