THE REES DISTINGUISHED LECTURER SERIES

Dr. Andrew Thomason

University of Cambridge, England

 Patterns of Random Behavior

Thursday December 2, 2004

3:30 - 4:30 104 Gore Hall

Why would you deliberately construct something that looks random – something that appears to have no pattern but that you know (because you constructed it) is built according to a pattern? There are many instances in mathematics where this is desirable; an obvious example is to produce a string of “random” numbers (as calculators often do), but there are lots of other examples throughout discrete mathematics, computer science and cryptography. What it means to “look random” depends on the intended application – what works well in one case might be a disaster elsewhere.

How can you construct something that looks random? Some simple examples will be given, based on elementary properties of numbers. As is often the case in mathematics, plenty of ideas that look good at first turn out to be noble failures. But the pursuit of these ideas can still lead to unexpected discoveries, such as the beautiful secret of the sequence 3,6,9,12,15,18,…..

 

 

Friday December 3, 2004

3:45 - 4:45 104 Gore Hall

The impetus for the study of minors (or contractions) of graphs can be traced back to Kuratowski’s classical theorem about planar graphs, as well as to the work of Wagner on the four colour conjecture, which gave rise to Hadwiger’s conjecture. What forces certain minors to appear in graphs have become much better understood lately; we describe this progress and the connection with (pseudo-) randomness in graphs.

 

Refreshments served immediately after talk in Ewing 436.