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Topic: Courant Geometry Seminar
Replies: 8   Last Post: Jan 25, 2005 9:53 PM

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Ricky Pollack

Posts: 18
Registered: 12/3/04
Courant Institute Geometry Center: Alex Nabutovsky
Posted: Jan 25, 2005 9:53 PM
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\newcommand{\R}{{\bf R}}
\title{Geometry Seminar\\
Tuesday November 30 in room 613 WWH at 6:00 P.M\\
{\bf Extremal triangulations of manifolds}}

\author{Alex Nabutovsky\\Courant Institute and University of Toronto}
We introduce a new non-constructive method
for proving the existence of triangulations
of compact manifolds of dimension $\geq 4$
with prescribed combinatorial properties.
The method involves an analysis of algorithms producing new triangulations
of a given manifold from a given triangulation. The results of
Markov and S. Novikov on the algorithmic unrecognizability of manifolds
are applied. Using Barzdin's lower bounds for the
bounded time Kolmogorov complexity of the halting problem
one can sometimes find lower bounds for the number of
considered triangulations with $\leq N$ simplices as a function of $N$.

I also plan to briefly explain the relevance of
the analysis of algorithms used here
a known approach to quantum gravity (in joint work with
Radel Ben-Av) and to comment on
a possible application of a similar technique
to variational problems in global differential geometry.


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