Interdisciplinary Research
Mathematics has, since ancient times, been associated with many
disparate areas of human inquiry,
ranging from art and philosophy to science and engineering. This
fruitful interchange has led to important mathematical discoveries,
and has also stimulated the development of whole new fields
of study. This tradition continues today in the Mathematics
Department, where a wide variety of interdisciplinary research is
conducted, both singly and in collaboration with researchers in other
departments and universities.
Mathematical physics is a major field of interdisciplinary research.
In this area,
Mikhail Shubin
has been working on
several problems related to miscellaneous questions in quantum physics,
in particular relations between completeness properties of classical
and quantum problems,
spectral behavior of Schrodinger operators, applications of
non-commutative geometry to
the quantum Hall effect. He also studied singular perturbations of
oscillating systems by
non-standard analysis methods. Chris King has
worked on a variety of problems in mathematical physics, including
resonances in quantum mechanics, lattice gauge field theory, and
lattice models in statistical mechanics. Maxim Braverman
has conducted research in hydrodynamics.
Quantum information theory and quantum computing are new and exciting
fields of interdisciplinary research, bringing together researchers
from mathematics, physics and computer science.
Sam Gutmann
works on quantum computing,
mostly on algorithms, a new paradigm for computing based on quantum
adiabatic evolution, and the quantum walk. Chris King
works on foundational questions in quantum information theory, mostly
concerning the role of entanglement in noisy quantum systems.
In the area of philosophy of science, Mark Bridger has
turned his constructive viewpoint to some problems related to the
ancient paradoxes of Zeno and the Eleatic philosophers. Recent work
has included a modern mathematical analysis of
so-called "supertasks" and "infinity machines." John Frampton
and Sam
Gutmann work in the area of linguistics, and have written several
articles about
Chomsky's recent syntactic theory.
In the area of interdisciplinary research related to computer
science, Jayant
Shah has been working on problems related to Computer Vision. His
current work involves application of Differential Geometry to shape
representation and a study of variations in brain structures either
due to disease or due to population differencees. Chris King has
worked on data compression for IP routing tables, and is currently
working on traffic control problems for wireless networks.
Last modified June 16, 2004
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