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\textsc{Seminar}
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\textit{Gromov's polynomial growth theorem}
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Aaron Abrams\par
Emory University
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\textbf{Abstract:} We will spend several weeks in the seminar studying and discussing Gromov's remarkable theorem, which revolutionized the field of geometric group theory. This week will be partly organizational, and in addition I'll explain enough background to understand the words in the statement of the theorem. All are welcome to attend.

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In short, the theorem says that a finitely generated group G has polynomial growth if and only if G is "almost" nilpotent. Having polynomial growth is a geometric condition on the Cayley graph, whereas being almost nilpotent is an entirely algebraic
property. It is not too hard to show that almost nilpotent groups have polynomial growth; the hard part of the theorem is the converse, and Gromov introduced several new geometric notions in order to convert the geometric information into an algebraic conclusion. These ideas have become the basis for many current strategies for approaching problems in this field.\vspace{\fill}
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Wednesday, February 20, 2008, 3:00 pm\par
Mathematics and Science Center: E408
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\textsc{Mathematics and Computer Science}\par
\textsc{Emory University}
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