## 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.)