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Courant Institute Geometry Center: Alex Nabutovsky
Posted:
Jan 25, 2005 9:53 PM


\documentstyle[11pt]{article}
\pagestyle{empty} \newcommand{\R}{{\bf R}} \begin{document} \title{Geometry Seminar\\ Tuesday November 30 in room 613 WWH at 6:00 P.M\\ \bigskip \bigskip {\bf Extremal triangulations of manifolds}}
\date{} \author{Alex Nabutovsky\\Courant Institute and University of Toronto} \maketitle \pagestyle{empty} \thispagestyle{empty} \begin{abstract} \begin{sloppypar} We introduce a new nonconstructive 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 BenAv) and to comment on a possible application of a similar technique to variational problems in global differential geometry.
\end{sloppypar} \end{abstract} \end{document}



