March 28, 2007

The Content of Shape

 

Edward A. Spiegel

Columbia University

First we shall look at some pictures of the kinds of patterns that we see around us in Nature and that experimentalists are busy producing in a controlled way. Such patterns are often built up from recurrent basic structures that arise in biology, fluid dynamics, chemistry and other interesting fields. These structures are thought to be subject to general physical laws though details may vary from case to case. Pattern theory attempts to rationalize the apparent universality of the patterns in terms of elementary notions such as instability and nonlinearity. The aim of the lecture is to discuss how relatively simple theoretical descriptions of pattern formation can emerge from the study of basically complex situations.