As a sign of good faith, North Korea has promised not to test any more missiles or nuclear bombs before the unprecedented meeting. Although the United States and its allies will continue their military training in this period, it is hoped that their war games will not be unnecessarily provocative.
There are two ways to read what happens next. The first is that we are about to watch a "peace in our time" moment, as with the ill-fated meeting between Neville Chamberlain and Adolf Hitler in 1938. In this scenario, the meeting is used as a stepping stone to war, as one side seeks to mislead the other and continue its aggressive actions, using the pause in tensions to get another jump ahead in military advantage.
In our time, the basis for this pessimistic line of reasoning is that North Korea has been playing cat and mouse with the United States and the international community since 1993, and there is no reason to expect this time will be any different.
Through a succession of negotiations to disarm their nuclear programme, every time the two sides get close to, or conclude an actual arrangement, North Korea either cheats or breaks and runs away at the last minute. Today, if North Korea was playing for time, it would be to perfect its inter-continental missile delivery systems.
The second way we can read what happens next is the Ronald Reagan and Mikhail Gorbachev type of moment in 1987, when the President that no one thought would do anything except cause a war, did the exact opposite and secured an excellent peace deal that started the process which ended the Cold War.
In today's setting, the basis for this type of reasoning is that North Korea is being economically crippled by sanctions imposed upon it and is seeking a pathway out of the pain to a normal type of existence. This type of thinking has recent precedent with Iran, which decided to end its nuclear activities after the weight of sanctions finally became too heavy.
The problem with this optimistic type of approach is that sanctions only work when those in power care what their population feels. It is questionable how far this type of logic applies in a communist dynasty that has a long history of its citizens tolerating extreme pain.
The second problem is why would North Korea opt for giving up its nuclear arsenal now, when it finally has achieved what it always wanted? That is, why now give up the dozens of nuclear weapons which are much more powerful than what destroyed Hiroshima, that are finally possibly capable of hitting the United States?
The answer probably has something to do with the word "denuclearisation" that both the United States and North Korea are using. It is likely each side has a different understanding of the same word.
For the United States, the word probably means North Korea possesses zero nukes. For North Korea, it probably means a stabilisation or slight reduction of numbers they possess, in exchange for the United States giving up something in South Korea, such as an end to military exercises, a missile defence shield, or American troops being stationed there.
The one thing America needs to be clear about is that North Korea will never give up its nuclear weapons if its sovereignty is secured only by words written in a treaty telling them they are safe. The last country that gave up its nuclear weapons on such grounds was the Ukraine in 1994. Twenty years later, Russia took back the Crimea and fuelled an insurgency in the east of the country.
The North Korean leader will also be very aware of what happened to the dictators in Libya, Iraq and Syria, when their iron grip was loosened.
Accordingly, the solution to this problem is not just about the management of nuclear weapons, but also the security of North Korea and the longevity of its ruling dynasty. With the help of China and Russia, if the last two items can be secured, progress may be possible.
• Alexander Gillespie is a professor of law at Waikato University.