When mAthemAticS & computer ScienceS

meet New perspectives for research

Models and algorithms: from the discrete to the continuous

Models and algorithms: from the discrete to the continuous

An exceptionAl AcAdemic environment

Less than 30 minutes from the center of Paris

The Bézout Labex is part of the Université Paris-Est pole of research and higher education (UPE), which

brings together two universities, four prestigious engineering schools, including Ecole des Ponts Paris Tech and

ESIEE Paris, three Ecoles Nationales Supérieures d’Architecture, one national veterinary school, five research and

development institutes, four operating agencies, one competitiveness cluster and over 70 research laboratories.

UPE was built in 2007 and is a major international campus offering multi-disciplinary libraries and student

housing. Convenient public transport is available between the different sites. The campus also offers student sup-

port services. Students and researchers alike can get involved in various campus organizations and enjoy cultural

life in the area. UPE also has partnerships with sport centers, events venues and local authorities to offer a truly

dynamic place to live and work.

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The Bézout Labex specializes in research on the cutting edge between

mathematics and computer science. It includes three laboratories located

east of Paris in Marne-la-Vallée and Créteil – LIGM, which specializes in

computer science, and CERMICS and LAMA, which specialize in mathe-

matics. These laboratories bring together over 200 active researchers,

including PhD students.

Several research groups within these laboratories are leaders in France in

their area of specialization, including algorithmics, combinatorics, analy-

sis in high dimension, probabilistic modelling, multifractal analysis, dif-

ferential geometry, numerical methods, financial mathematics and image

processing. By fostering the cross-fertilization of ideas between mathe-

maticians and computer scientists, the Bézout Labex serves as a top-level

international center in the areas of research at the crossroads of the fields

of mathematics and computer science.

One of the main objectives of the Bézout Labex is to develop solutions for

major technological challenges in areas such as urban planning, enginee-

ring, telecommunications, health and medicine. The Bézout Labex also

promotes the application of its research within industry and services, in

areas such as imaging, telecommunications, networks and finance.

Every year, prestigious foreign scientists are selected to share the Bézout

Research Chair. Each comes for up to three months to work on a specific

scientific topic related to the Labex’s four main areas of research.

liGmThe Laboratoire d’Informatique

Gaspard-Monge

is a research unit associated with the Centre National de Recherche Scientifique (CNRS), the Université Paris-Est Marne-la-Vallée (UPEMLV) and the engineering schools École des Ponts Paris Tech (ENPC) and ESIEE Paris.

cermicSThe Centre d’Enseignement

et de Recherche en Mathématiques

et Calcul Scientifique

is the laboratory of applied mathematics and scientific computing of the Ecole des Ponts Paris Tech.

lAmAThe Laboratoire d’Analyse

et de Mathématiques Appliquées

is a research unit of the CNRS, the UPEMLV and the Université Paris-Est Créteil Val-de-Marne (UPEC).

The Bézout Labex currently offers a one-year research position for a promising junior researcher (PhD with post-doctoral experience). For more information and to apply online: www.bezout.org

Who was Bézout?

Étienne Bézout (1730-1783) was a famous French mathematician and academic during the Age of Enlightenment. Considered as the founder of algorithmics, he also played a key role in the development of science and the teaching of mathematics in France. Both algebra and algorithmics find some of their common fundamental principles in the seminal work of Etienne Bézout.

What does “Labex” stand for?

In 2010, the French government launched the “Investing for the Future” program and began investing heavily in research. This program led to the development of several projects including the creation of what are now called “Laboratories of Excellence.” The goal of the Labex project is to select renowned French research laboratories and offer them additional resources so they can become more competitive in the international arena. The laboratories that have been selected use an integrated approach that combines research, training and concrete applications for industry.

At the croSSroAdS of mAthemAticS & computer ScienceS

4 StrAteGic AreAS of reSeArch

CLAUDE LE briS, a professor at the Bézout Labex, held the Aisenstadt Research Chair from 2009 to 2010 at the University of Montreal.

StochaStic and deterMiniStic ModelS

Stochastic and deterministic modelling constitutes an emerging area of research, where significant advances in several fields of application can be expected. Certain new contributions have a significant impact in the areas of banking and insurance, for instance in modelling with jump processes and Malliavin calculus and in the modelling of dependence in multiple dimensions. Another important topic concerns numerical methods for fluid mechanics and materials for biological systems from microscopic to macroscopic scale. In the context of Markovian dynamics, new topics to be developed concern long-time behaviour, metastable dynamics, piecewise deterministic Markov processes and random trees – which all have important applications in physics and biology.

DjALiL ChAFAï, a professor at the Bézout Labex, became member of the IUF (Institut Universitaire de France) and received the Audin award in 2012.

high-diMenSional phenoMena

High-dimensional phenomena are ubiquitous in modern applications such as telecommunications, genomics or imaging. These models, based on mathematical and algorithmic analyses, involve tools from asymptotic geometric analysis, random matrices and combinatorics. Large Random Matrix Theory has proved to be very efficient for finding solutions to many current issues in telecommunications. This theory makes it possible to handle the averaging effect that appears in high-dimensional random systems, and it is currently one of the key devices used to analyze and improve the performance of cellular networks.

hUGUES tALbot, a professor at the Bézout Labex, received the Society of Australian Engineers Award in 2005 and the DuPont award in 2006.

iMageS and geoMetry

Important breakthroughs can be made in the areas of 3D photography and medical image analysis by solving open mathematical problems. In medicine, finding better ways to read images will make it possible to visualize complex phenomena that are currently poorly understood, such as how blood flows inside the brain, what happens during a heart attack or even how cancer develops or disappears. In the area of 3D photography, 3D models for individual buildings or entire areas can be developed and then used in construction, cinema, video games, virtual tourism, heritage preservation, etc. Semantically rich 3D models as well as image analysis can also be used to draft or supplement building information models (BIMs) which are increasingly used in the construction industry.

PhiLiPPE biAnE, a professor at the Bézout Labex, received the Rollo-Davidson Award from the London Mathematical Society in 1995 and the Lecomte Award from the French Academy of Sciences in 1998.

diScrete MatheMaticS & algorithMS

With the growing use of the Internet and new communications technologies, massive amounts of information and data are being produced and made available every day. One of the major challenges today is thus to find efficient, automatic ways to sort very large data or data sets of various kinds – such as textual, linguistic, multimedia or biological data. Researchers at the Bézout Labex are addressing this pressing issue by exploring formal models, syntactic methods and multifractal systems. They are also designing probabilistic and approximate algorithms, and developing methods to structure, classify and index big data. One of the objectives of this work is produce software devoted to applications in bio-informatics, linguistics and computer science code analysis.

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The Bézout Labex has developed a unique cross-disciplinary International

Master’s Program which combines computer science and mathematics:

the “Bézout Excellence Track.”

This one-year program is open to students from foreign academic institutions

who have completed a bachelor’s degree in mathematics or computing

sciences as well as the first year of a Master’s or PhD program. The best

students will be invited to join the PhD program of the Doctoral School

MSTIC (Mathematics, Sciences and Information and Communication

Technology) of Université Paris-Est.

With courses both in English and French, the Bézout Excellence Track

mainly focuses on:

– image processing,

– computing sciences and biology,

– discrete geometry,

– applied mathematics & mathematical finance.

Students are encouraged to develop a personalized curriculum and select the

mathematics and computer science classes that they find most interesting.

The Bézout Excellence Track offers students the opportunity to acquire

sought-after skills in both mathematics and computer science that can be

used in industry or academia.

An internAtionAl mASter’S proGrAm

“”

Camille Couprie completed her Master’s course work in 2008 in what is now known as the Bézout Master’s Program. Her thesis focused on computer vision and earned her a prize from the EADS Foundation in 2012 for the best interdisciplinary thesis. Camille was also the runner-up for the French IT Society’s Gilles Khan Prize in 2011. Currently working as a post-doctoral fellow at New York University’s Courant Institute of Mathematical Sciences, she has been recruited to join IFP Energies Nouvelles (IFPEN) as a research engineer.

My career wouldn’t be the same

without my Master’s degree. The program’s

world-renowned professors really know how to

prepare students for the world of research.

And thanks to their contacts, I was able to go

the US and work in my field of expertise.

Scholarships are available for seven Master’s students. For more information and to apply online: www.bezout.org

cermicS

> école deS pontS pAriS tech

6-8, av. blaise Pascal – Cité Descartes

Champs-sur-Marne

77455 Marne la Vallée Cedex 2 – France

t. + 33 1 64 15 30 00

lAmA

> upemlv

5, bd Descartes – Champs-sur-Marne

77454 Marne-la-Vallée Cedex 2 – France

t. + 33 1 60 95 75 20

> upec

61, av. du Général de Gaulle

94010 Créteil Cedex

t. + 33 1 45 17 16 42

liGm

> upemlv

5, bd Descartes – Champs-sur-Marne

77454 Marne-la-Vallée Cedex 2 – France

t. + 33 1 60 95 75 20

www.bezout.org

For any further information, please contact:

Stéphane Jaffard, Head of the Bézout Labex

LAMA, UMr CnrS 8050, Faculté des Sciences et technologie 61, av. du Général de Gaulle – 94010 Créteil Cedex – France

jaffard@u-pec.fr

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Models and algorithms: from the discrete to the continuous