Undergraduate Mathematical Sciences Seminar
Wednesday, 8 November 2006, 12:30--1:50pm
z^alpha
Don Marshall
Hendrik Lenstra will be visiting the UW next week to give a series of talks. Our seminar this week is intended to provide you with some background that will be relevant to his talks.
Lenstra's talk is based on this function of a complex variable z with a complex power alpha. We'll start with the definition of complex numbers and work our way up to a visualization of z^alpha.
Lenstra's talks:
Math Colloquium
Tuesday, 4:00pm November 14
Smith 304
TITLE:
Searching for abc triples
ABSTRACT:
Now that Fermat's Last Theorem has been proved, many number theorists view the abc conjecture as their new Holy Grail. Its elementary formulation, to be given in the lecture, contrasts sharply with our complete lack of insight into the subject matter of the conjecture. Recently a project was started that aims to improve our understanding by means of numerical experimentation. The lecture is devoted to the mathematically interesting aspects of the project.
Wednesday, 4:00pm November 15
PAA A102
TITLE:
Escher and the Droste effect
ABSTRACT
In 1956, the Dutch graphic artist M.C. Escher made an unusual lithograph with the title `Print Gallery'. It shows a young man viewing a print in an exhibition gallery. Amongst the buildings depicted on the print, he sees paradoxically the very same gallery that he is standing in. A lot is known about the way in which Escher made his lithograph. It is not nearly as well known that it contains a hidden `Droste effect', or infinite repetition; but this is brought to light by a mathematical analysis of the studies used by Escher. On the basis of this discovery, a team of mathematicians at Leiden produced a series of hallucinating computer animations. These show, among others, what happens inside the mysterious spot in the middle of the lithograph that Escher left blank.