Our goal is to raise awareness among children, youth, and the public at large, about the importance and essential nature of mathematics in everyday life and in all the sciences.

]]>*Registration and application for participant support now open*

Summer School: August 6-27, 2013

-Mini-Course on Valuing and Trading Correlation Structures in Commodities

-Mini-Course on Financialization of the Commodity Markets and Mean Field Games

-Mini-Course on Stochastic Models of Electricity Markets

Workshop on Electricity, Energy and Commodities Risk Management: August 14-16, 2013

Workshop on Stochastic Games, Equilibrium, and Applications to Energy & Commodities Markets: August 27-29, 2013

]]>The main topics to be addressed in this program are: cell biology, population dynamics, quantitative modeling for drug development, systems biology, and evolutionary biology.

A **summer school** will be dedicated to recent progresses in multiscale modeling, with applications in the life sciences.

http://mathbio2013.sciencesconf.org/

Schedule (Please click on the links for further information):

- Conference: “Biological invasions and evolutionary biology, stochastic and deterministic models”, March 11-15, 2013,
- Conference: “Cell biology”, March 25-29, 2013,
- Conference: “Systems Biology Approach to Infectious Processes”, May 13-15, 2013,
- Summer school: “Multiscale modeling in the life sciences”, May 27-31, 2013,
- Conference in honour of Michael Mackey’s 70th birthday, June 3-6, 2013,

Organizing committee: M. Adimy (INRIA), J. Bérard (UCBL), S. Bernard (CNRS, UCBL), H. Berry (INRIA), V. Calvez (CNRS, ENS de Lyon), F. Crauste (CNRS, UCBL), O. Gandrillon (CNRS, UCBL), E. Grenier (ENS de Lyon), Th. Lepoutre (INRIA), L. Pujo-Menjouet (UCBL), G. Raoul (CNRS, CEFE), B. Ribba (INRIA), V. Volpert (CNRS, UCBL), B. You (CHU Lyon).

This program is funded by the “laboratoire d’excellence” MILYON, an initiative from the French ministry of research.

]]>The purpose of this programme is to bring together scientists from very different perspectives in models of the dynamics of the fluid components of the Earth system. This interest may be directly into the modelling, also numerical, or at a more abstract modelling level in terms of understanding the climate system as a complex dynamical system. This programme aims to prove that there is a close connection between “core” questions and problems of pure and applied mathematics and “core” questions of geophysical fluid dynamics relevant for the investigation of the climate system and of its component, and that these are closely linked to defining rigorously what is a good model for a complex system. The aim of the programme is to provide a common ground for fostering mutually stimulating and inspiring exchanges and for creating opportunities for future research. This programme is part of the international initiative “Mathematics for Planet Earth 2013” supported by mathematical societies and institutes around the world (http://mpe.dimacs.rutgers.edu).

The programme features three main macro-themes of interest where the progress has been impressive on the mathematical side and in terms of the investigation – theoretical, model-assisted, and observational – of the planet Earth: *a) Dynamical Systems and Statistical Mechanics; b) Extreme Events; c) Partial Differential Equations*. Work at these interfaces has, realistically, the potential to provide huge breakthroughs in the next years. These themes have mutual connections at mathematical level, which definitely need to be strengthened, with the possibility of obtaining new general results of great significance. Moreover, each theme has a huge potential for future breakthroughs at the boundary between mathematics and natural science. Finally, a crucial thread linking all of these themes is that related to the approaches and methodologies of modelling and analysing model outputs. In complex, multiscale system an ubiquitous issue is the choice of the specific details to model, of how to model them and parametrize the unresolved scales, how to implement efficiently a model, how to validate the model with sparse and uncertain data, how to control the model error, how to define robust observable, how to convincingly perform upscaling and downscaling procedures, and how to deal with coarse-graining.

The programmes at the Isaac Newton Institute benefit from a careful combination of structured, non-structured, and improvised events fostering scientific exchange. As for the first category, the following initiatives are being actively prepared:

- One introductory satellite workshop taking place in Exeter during the week before the start of the programme;
- Two workshops taking place at the Institute during the programme, the first one dedicated to themes more directly relevant for the first two streams of activity, and the second one dedicated to the third stream;
- Tutorial lectures, given by scientists active at the interface between the macro-themes;
- Other events will include seminars, round tables, discussions with non-academic stakeholders, plus, of course, a range of social events;
- Editorial activities, e.g. collection of selected contributions into an edited book or special issue of a journal.

The programme shall foster the development of advanced mathematical descriptions of the coupling of the bulk dynamics of complex fluids and active media with the dynamics of free surfaces, interfaces and contact lines. Thereby the programme will initiate new collaborations between applied mathematicians and the different communities of physicists or engineers involved in biological physics, soft condensed matter science, chemical/mechanical engineering, nano- and microfluidics, and related fields. The programme combines research seminars, embedded workshops and a summer school with a number of short instructional courses. The latter will particularly allow younger researchers to better integrate concepts of mathematical modelling and non-equilibrium, nonlinear, and soft matter science into the presently active research fields.

]]>A fascinating feature of polynomial optimisation is that it can be approached from several different directions. In addition to traditional techniques drawn from operational research, computer science and numerical analysis, new techniques have recently emerged based on concepts taken from algebraic geometry, commutative algebra and moment theory. In this regard, polynomial optimisation provides a valuable opportunity for researchers from previously unrelated disciplines to work together.

The plan for this four-week programme is as follows. During the first week (15th-19th July 2013), there will be a “summer school” and a “workshop”. The “summer school” will consist of a series of tutorials from internationally respected invited speakers, and the workshop will consist of a series of contributed talks and possibly a poster session. These events will be open not only to official programme participants, but also to other interested academics, PhD students and post-doctoral researchers (space permitting).

The following three weeks will be open only to invited persons. Each of the three weeks will focus on a specific sub-topic:

1. Algebraic Approaches (22nd-26th July 2013). This will concern the development of new theory and algorithms based on techniques from relevant areas of pure mathematics, such as real algebraic geometry, commutative and noncommutative algebra, moment theory and the theory of sums-of-squares representations.

2. Convex Relaxations and Approximations (29th July-2nd August). This will be devoted to the study of convex relaxations (and hierarchies of relaxations) of certain important specially-structured problem classes, along with associated approximation algorithms (and inapproximability results).

3. Algorithms and Software (5th-9th August). This will be devoted to the development of new algorithms and their implementation as software. This may include, for example, algorithms for computing lower and upper bounds, algorithms for generating strong valid inequalities, and algorithms for solving instances to proven optimality.

**Please Note:** The list of Invited Participants only includes people who plan to attend during the last three weeks of the programme. The list of participants in the summer school and workshop held during the first week will be posted at a separately.

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The four-week programme will:

- take stock of progress in the last twenty years, following on from the original Newton meeting; to assess where we are today and provide a synthesis;
- take a systematic look at the use of models to inform public health decisions, and to analyse where and why models fail in their predictions;
- set the agenda for future research and in particular determine the main challenges, both in understanding & public health needs and in methodology;
- foster collaboration and a new generation of young talented researchers with the aim of starting to address some of the challenges identified above, through a programme of concrete research activities.

A notable aspect of many of the most important recent developments is the importance of increasingly sophisticated techniques from mathematics and theoretical computer science: examples include the use of random states and operations, techniques from operator theory and functional analysis, and convex geometry. The range of mathematical techniques already employed is diverse, but the expertise is rather scattered within the community. We also see other areas of mathematics that offer the potential to make a major future impact in the field, random matrix theory being an example of particular current interest.

Among the mathematical challenges addressed during the semester will be some of the big open questions in the field, as well as recently opened up directions:

- Additivity violations of capacities and minimal output entropies; “weak additivity” for certain quantities?
- Existence of bound entanglement with non-positive partial transpose? The question, originally of information theoretic origin, can be cast as a problem about positivity and 2-positivity of matrix maps.
- Abstract positivity and complete positivity: In quantum zero-error communication a link to operator systems was exhibited, promising a functional analytic generalisation of graph theory.
- Techniques from convexity and convex optimisation have had high impact in non-local games. One question of particular importance is whether non-local games with shared entanglement obey a parallel repetition theorem (Raz) – this is known with only classical correlation and with arbitrary no-signalling help, but for shared entanglement it is only proved in special cases. Another one is the complexity of maximum quantum violations of Bell inequalities.
- Is there a quantum version of the PCP theorem? Likewise, it is open whether in QMA, witnesses can be made unique (echoing a well-known classical probabilistic reduction of Valiant-Vazirani).
- Measurement-based quantum computation poses questions on characterising the complexity of quantum computations via the properties of the “resource states” used.
- Random matrix theory: starting with its use in proofs of non-additivity, new problems motivated by quantum information have emerged. These include largest eigenvalue fluctuations and spectra of higher tensor equivalents of Wishart ensembles; perturbations of Wigner ensembles by diagonal matrices with fixed or deterministic statistics – information on the distribution of eigenvectors of such matrices would have deep implications on quantum statistical mechanics.

We plan to hold a week-long workshop at the beginning, drawing together all topics of the above proposal. In addition we propose to hold a smaller and more focussed workshop, in the middle of the meeting. Finally we will hold a workshop at the end of the programme that will survey the state of the field as it stands following the work during the programme; there will be an emphasis on open problems and directions for the future.

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