# Boris Hasselblatt

## Research/Areas of Interest

Dynamical systems: Hyperbolicity, invariant foliations, geodesic flows, contact flows, and related topics

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Hasselblatt's research, undertaken with colleagues from several continents, is in the modern theory of dynamical systems, with an emphasis on hyperbolic phenomena and on geometrically motivated systems. He also writes expository and biographical articles, writes and edits books, and organizes conferences and schools. His publication profile can be viewed at https://mathscinet.ams.org/mathscinet/author?authorId=270790 (with a subscription). Former doctoral students of his can be found in academic positions at Northwestern University, George Mason University, the University of New Hampshire, and Queen's University as well as among the winners of the New Horizons in Mathematics Prize.

## Education

- PhD, Mathematics, California Institute of Technology, USA, 1989
- MA, Mathematics, University of Maryland, United States, 1984
- Diplom-Vorprüfung (BS), Physics, Technische Universität Berlin, Germany, 1981

## Biography

Dynamics:

Dynamical systems is the mathematical theory of systems, such as in classical dynamics, that evolve in time. The motivations for this field come from classical and celestial mechanics as well as, more recently, from population dynamics, meteorology, economics, physiology, neuroscience, medicine, genomics, i.e. all across the natural and social sciences. In the modern theory of these systems the central aim is often to answer qualitative questions about long-term behavior directly from a study of the governing laws rather than through explicit expressions of the evolution itself. The grandest of these questions is whether the solar system is stable (or whether, for instance, the earth might, without influences external to the solar system, leave the solar system for good at some point). Just over 100 years ago this question started the modern theory of dynamical systems and led to the first glimpse of "chaos", and it led to another quantum leap, the KAM-theory of "order", in the 1950s. "Chaos theory" is a popular name for the study of dynamics in which the cumulative effects of the tiniest discrepancies grow exponentially over time and give rise to behavior that looks random and unpredictable. (If two people with different calculators start with x=0.3, compute 4�x�(1�x), and repeatedly apply the same formula to the output of the previous step, they will likely quite soon find wild mismatches between their results due to accumulated deviations from differences in rounding.) Hyperbolic dynamics is the mathematical study of these systems, and much of Hasselblatt's work has been in uniformly hyperbolic dynamics, which represents this sensitivity to initial conditions in the purest and strongest way and has been called the crown jewel of dynamical systems.

For a pure mathematician this is a beautiful subject to study because in these systems the truly messy long-term behavior of any particular time evolution coexists with smooth and orderly global structures in the space of possible states whose study on one hand provides a way of understanding the possible long-term behaviors and on the other hand can provide insights into the origins of the …