**Special afternoon around the abc-conjecture**
On Friday November 26 DIAMANT organises a special afternoon around the

abc-conjecture. Invited speakers are

David Masser (Basel),

Joseph Oesterlé (Paris) and

Willem-Jan Palenstijn (Antwerp). The venue is

Het Bosgoed, Lunteren.

The abc conjecture has originally been formulated in the 1980s by David
Masser and Joseph Oesterlé, two of the three afternoon speakers. It has
a central role in modern number theory. Roughly the conjecture says
that when

*a, b* are coprime positive integers, and

*c=a+b*, then the product

*abc* cannot have, in some precise sense, only a few number of prime factors. The first talk is about the search for triples

*(a,b,c)* that challenge the abc-conjecture. The second talk discusses an analogue of the abc-conjecture in the polynomial ring over

**C**. The third talk discusses an analogue of the abc-conjecture in a function field in characteristic

*p*.

The programme is as follows:

13.30 - 14.20 Willem-Jan Palenstijn

* - Enumerating abc-triples*

14.30 - 15.30

* *Joseph Oesterlé

* - abc over ***C***[t]*

15.30 - 16.00 tea

16.00 - 17.00

* *David Masser

* - abcd... over ***F**_{p}*(t,u,...)*
*
*

Participation in this special afternoon is free, but

*registration is required*. If you are interested in participating, but do not want to register for the whole

DIAMANT symposium (November 25 and 26), please send an email to Robin de Jong (find address

here) before November 19.

### Mathematics cluster DIAMANT

### Upcoming events

**3 DIAMANT PhD positions awarded***19-12-2017*
NWO, following a shortlist provided by the DIAMANT board, has decided to award 3 PhD positions to young DIAMANT members: Dion Gijswijt (TU Delft), Jan Steffen Müller (RUG) and Arno Kret (UvA).

Read more.

**DIAMANT funding continued ***19-12-2017*
The funding of all four mathematics clusters has been continued by NWO. For the coming two years 85 kE will be available in each cluster.

Read more.

**NWO Call for Tenure Track positions***22-7-2016*
NWO has opened a call for tenure track positions. Proposals for these positions, which include one PhD position for each tenure track position, can be submitted directly to NWO by professors from the 4 mathematics clusters, including Diamant. Diamant professors are warmly encouraged to submit proposals. Read more.

**Dion Gijswijt and Jordan Ellenberg independently substantially improve capset bound ***25-5-2016*
A capset in a finite dimensional vector space over the field with 3 elements is a subset that contains no 3-term arithmetic progressions. Dion Gijswijt (TU Delft) and Jordan Ellenberg have independently obtained a bound on the size of a capset that for the first time improves substantially on the trivial bound 3^n. Read more in Terence Tao's blog about these developments.