Abstract:

Much of mathematics is devoted to giving solutions to equations,
calculating solutions to problems, classifying structures according
to invariants and the like. Natural questions arize as to when
this is not possible. This talk looks at questions such as this
tracing, in a idiosynchratic way, a historical line leading to
modern incarnations wherein logic allows us to show that
no invariants are possible for (e.g.) certain problems in group theory.
This is done by showing that normal mathematical structures
can be caused to emulate computation in faithful ways.

This talk is aimed at a very general audience, and will be accessible
to beginning graduate or even advanced undergraduate students.




Speaker information:

Rod Downey was an undergratuate at Queensland University, and received his
PhD at Monash University in 1982. After positions at the National University
of Singapore and the University of Illinois at Urbana, he
accepted a position at the Vistoria University of Wellington in 1986.
He has held a personal chair there since 1995. He has held visiting around
the world including the MSRI at Berkeley, Cornell University,
the University of Chicago, the University of Notre Dame, the University of
Wisconsin Madison, the University of Siena, etc. He has won numerous awards
for his work in logic and his work in theortical computer science.
These include the inaugural MacLaurin Fellowship, the Hamilton Prize
of the Royal Society of NZ, the New Zealand Association of Scientists
Research Medal, the New Zealand Mathematics Society Research Award,
and the Vice Chancellor's Award for Research. He was elected a Fellow
of both the Royal Society of New Zealand and the New Zealand Mathematics
Society. He is only the second New Zealander to be elected a Fellow
of the Accisiation for Computing Machinery.
He is an editor of numerous journals, and chaired the prizes
committee of the Association for Symbolic Logic. He is the only New Zealand
based mathematician to give an invited lecture  at
the International Congress of Mathematicians, and has given invited
addresses an numerous conferences including the International Congress of
Logic Methodology and Philosophy of Science, and the IEEE Conference on
Computational Complexity.