Large and Small Gaps in the Primes

Prof Terence Tao
Department of Mathematics
University of California, Los Angeles

Location: Adelaide Town Hall
Date: 28th September 2015

 

Schedule:

6:00 - 6:45PM - Reception at Adelaide Town Hall
6:45 - 7:00PM - Intermission
7:00 - 8:00PM - Public Lecture: "Large and Small Gaps in the Primes"
8:00 - 8:30PM - Intermission
8:30 - 9:30PM - Musical Recital

 

Abstract:

There are many questions about the gaps between consecutive prime numbers which are not completely solved, even after decades of effort.  For instance, the twin prime conjecture, which asserts that the gap between primes can equal 2 infinitely often, remains open. However, there has been recent progress in understanding both very small and very large gaps between primes.  In 2013, in a breakthrough work of Yitang Zhang, it was shown that there were infinitely many gaps between primes of bounded size; Zhang's original bound here was 70 million, but it has since been cut down to 246 thanks to the efforts of James Maynard and an online collaborative "Polymath" project.  In the opposite direction, recent work of Kevin Ford, Ben Green, Sergei Konyagin, and myself have shown the existence of prime gaps significantly larger than their average spacing, improving upon earlier work of Rankin, Pintz, and others.  The two proofs are somewhat different in nature; the first argument relies on sieve theory methods, whereas the second argument uses probabilistic arguments combined with the results of Ben Green and myself in arithmetic progressions in the primes.  We present the main ideas of both of these results in this lecture.

 

Prof Terence Tao - 1992 Flinders University graduate Terence Tao was born in Adelaide, Australia, in 1975.  He has been a professor of mathematics at UCLA since 1999, having completed his PhD under Elias Stein at Princeton in 1996.  Tao's areas of research include harmonic analysis, PDE, combinatorics, and number theory.  He has received a number of awards, including the Salem Prize in 2000, the Bocher Prize in 2002, the Fields Medal  in 2006, the MacArthur Fellowship in 2007 and Crafoord prize in 2012.  Terence Tao also currently holds the James and Carol Collins chair in mathematics at UCLA, and is a Fellow of the Royal Society and the Australian Academy of Sciences. 

 

 

Public Transports from Flinders University to the Adelaide Town Hall

We strongly recommend "the earlier the better" to avoid disappointment or overcrowding. The following buses all depart from the interchange near the Library and Registry buildings at Flinders University, which are next to the conference location.

Bus G40     The fastest and most direct way (approx. 35 minutes) is via the bus G40. Get on it at Flinders. After the bus travels eastwards on Grote Street, it turns left, and the next stop is labelled U2 in Victoria Square. It a short walk (2 minutes?)  to the Town Hall (northwards)  which is on the other side of King William street.  Should you arrive at the next stop labelled W2, about 2 minutes later, the walk is a little shorter.

Bus G10     The next fastest and direct way (approx. 40 minutes) is via the bus G10. Get on it at Flinders. After the bus travels eastwards on Grote Street, it turns left, and the next stop is labelled V1 on King William street, more or less opposite the town Hall.

Bus 719      Not quite so direct (approx. 40 minutes), is bus Number 719. Get on it at Flinders. After the bus travels eastwards on Grote Street, it turns left, and the next stop is labelled U1 in Victoria Square. It a short walk (3 minutes?)  to the Town Hall (northwards)  which is on the other side of King William street.

Bus-train-tram.  (approx. 45 minutes in total if you get the appropriate  681 bus). For the more adventurous, there is a bus-train-tram option. Begin with bus 681 to Hallet Cove Beach). Get off after 5 minutes at bus stop 28 on Sturt Road. Walk (about two minutes across Sturt Road) to Tonsley Rail station. Take the train to Adelaide rail station, (23 minutes).  Exit the rail station (up escalator) onto North terrace, wait for the tram (it is free) on the side nearest the station. (It comes about every 8 minutes, to destination Glenelg or South Terrace). The second stop on King William Street is at  Pirie/Waymouth street,  just short of the Town Hall on east side.

 

If you are staying in Glenelg, you can return to your accommodation easiest by catching a tram from the Town Hall. In the evening, the tram leaves every twenty minutes up until midnight.

 

On Monday September 28th the buses listed above operate according to the following schedule:

Flinders Interchange Stop V1
Leave Arrive
4-27 pm     G10 5-08pm
4-40  pm     G10  5-21pm
4-55 pm     G10 5-35 pm
5-10 pm     G10 5-50 pm
5-24 pm     G10 6-03 pm
5-38 pm     G10 6-17 pm

 

Flinders Interchange Stop U2
Leave Arrive
4-25 pm     G40 4-58  pm
4-40 pm     G40 5-13 pm
4-55 pm     G40 5-28 pm
5-15 pm     G40 5-48 pm
5-35 pm     G40 6-03 pm

 

Flinders Interchange Stop U1 
Leave Arrive
5-04 pm    719  via FMC 5-42 pm
5-27 pm    719 via FMC 6-05 pm

 

 

Flinders Interchange Stop 28 Tonsley Rail Adelaide Rail Station Tram
Leave Arrive Leave Arrive Leave
4-15 pm   681 4-20 pm 4-39 pm 5-02 pm Tram
4-30 pm    681  4-35 pm 4-39 pm 5-02 pm Tram
4-45 pm   681 4-50 pm 5-09 pm 5-32 pm Tram
 4-45 pm 601 via FMC 4-53 pm 5-09 pm  5-32 pm Tram
5-00 pm   681 5-05 pm 5-09 pm 5-32 pm Tram
5-20 pm   681 5-25 pm 5-39 pm 6-02 pm Tram