Two talks about number theory [May 2016]
DATE:2016-05-12
Speaker::
Professor Timothy Scott Trudgian. Mathematical Sciences Institute. The Australian National University
Venue:
B1044
Time:
14:30-15:30, 16:00-17:00 May. 17
Title:
Linnik’s approximation to Goldbach’s conjecture
Abstract:
Goldbach’s conjecture is that 2N = p + q, for primes p and q, and for N sufficiently large. This is ‘almost’ true in that one needs to add at most finitely many powers of 2 to p+q to obtain 2N. This is Linnik’s theorem. I shall describe some of the ingredients of modern versions of Linnik’s theorem, and outline some potential improvements.
Title:
On Diophantine quintuples
Abstract:
Consider the set {1,3,8}: the product of any two of its elements is one less than a perfect square. It is conjectured that there are no sets of five natural numbers with this property. I shall describe the history of this problem, the current state of knowledge, and some possible paths to a solution.
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