A new course will make its debut this fall at ICTP and SISSA. The focus will be on modelling and simulations. The goal will be to use these tools to cast light on real-world problems.

Math Matters

An enclosed walkway links the main building of one institution to the main building of the other. But ICTP and SISSA (the International School for Advanced Studies) are more than neighbours. They are, in fact, kindred souls. For more than 30 years, the two institutions have co-sponsored activities, shared facilities and agreed to joint research appointments--all as part of a mutual effort to advance the study of theoretical physics and mathematics.

In the early years of the relationship and indeed through the 1990s, the division of basic science into distinct disciplines often was straightforward. While mathematics served as a common language, high energy physics, condensed matter physics, cosmology, seismology and most other basic research areas travelled along clearly defined avenues of inquiry that rarely intersected. More recently, however, scientists have discovered that once-thought-to-be-separate research areas may share common ground.

ICTP and SISSA have participated in this journey of discovery through research and training activities devoted, for example, to string theory and algebraic geometry, field theory and statistical mechanics, disordered materials and chaotic systems. These activities, some of which appeared on the scientific calendars of ICTP and SISSA as early as the 1980s, often have blurred the formerly distinct boundaries between mathematics, physics and statistics.

The two institutions take another step in this direction this fall with the launching of a one-year graduate course, "Modeling and Simulation of Complex Realities. " The course will be expanded into a two-year master's degree programme in 2002. The goal is to provide students who have enjoyed solid backgrounds in mathematics and theoretical physics with the advanced training that they need to apply tools in basic science to real-world problems. An essential aspect of the second year of the master's programme will be the fostering of collaboration with industries and other institutions.

Methodologies from probability theory, stochastic processes, control and game theory, optimisation and fluid dynamics will serve as the backdrop for modelling issues ranging from population dynamics to climate change to the behaviour of consumers in emerging market economies to airline scheduling problems (see "Fiscal Physics").

What are the underlying principles in science and mathematics that provide common ground for these explorations? They are the non-linear, complex and unstable world in which we live, a world whose (dis)order can become clearer and more predictable through sophisticated use of mathematical models.

In tackling many of the world's most critical economic, environmental and even social issues, a key difficulty lies in reformulating the analyses into terms that are amenable to rigorous and quantitative scientific assessment. It's the difference between feeling that summer temperatures have been getting hotter and devising a database that proves your point and then building mathematical models that project what will happen to temperatures, cloud patterns and precipitation in the future under a variety of environmental assaults and atmospheric conditions. Use of mathematics and models, in effect, helps researchers verify what has happened in the past and propose reasonable predictions of what may happen in the months and years ahead. In short, models help scientists approximate the real world.

Where all of this leads remains difficult to predict, which may be a fitting description for an approach to science and problem-solving that seeks to better understand the complexity of the world in which we live. Yet this much is true: the frontiers of science have always resided where the greatest insights in understanding nature take place. That's just another reason why both ICTP and SISSA are seeking to expand their involvement in the emerging field of applicable mathematics.

Riccardo Zecchina
ICTP Condensed Matter Physics Group

Matteo Marsili
Italian National Institute for the Physics of Matter (INFM)
and International School for Advanced Studies (SISSA)

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