Hendrik Lenstra

Universiteit Leiden

Escher and the Droste effect

Wednesday, April 16, 2014

7:00-8:00PM

LSC 100 Aro J. Oopik 1978 Auditorium, Class of 1978 Life Sciences Center

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.

NB: PDF version of this announcement (suitable for posting).

Sums of digits and divisibility

Undergraduate Colloquium

Thursday, April 17, 2014

4:00-5:00PM

008 Kemeny Hall

Abstract: Many number theorists consider the operation of adding the digits of a positive integer, when written in a certain number base, as belonging to recreational mathematics. In the lecture we shall see that some properties of the operation can nevertheless be taken seriously.

This talk will be accessible to graduate students.

NB: PDF version of this announcement (suitable for posting).

Missing values of polynomial maps over finite fields

Colloquium

Friday, April 18, 2014

4:00-5:00PM

008 Kemeny Hall

If a polynomial map over a finite field misses not too many values, then it misses no values at all. In the lecture we shall see that existing results of this nature can be improved by perfectly elementary means. (Joint work with Michiel Kosters.)