For the purposes of this market, I won't count:
Negotiations where one of the parties is not present (such as the UN summit proposed by Ukrainian FM Kuleba)
Negotiations about matters not including a permanent peace settlement (such as the grain deal or an armistice)
Negotiations conducted through intermediaries/backchannels (e.g. oligarchs or other third parties)
An announcement of peace talks without them actually taking place
UPD: See also
Here's my own assessment of the situation at the moment.
After the discovery of Russian war crimes, Ukraine has put a law in place forbidding any negotiations so long as Putin is in power. Recently, the Ukrainian FM Kuleba stated that "Russia must face a war-crimes tribunal before his country directly talks with Moscow", something Russia will certainly not agree to.
On the other side, Russia has had a remarkably consistent position since the breakdown of the first stage of peace talks in late March: It says it's prepared to hold peace talks at any moment, Ukraine just has to accept some preliminaries, which, if you read them, more or less boil down to surrender. That's certainly not something Ukraine will agree to.
So, at the moment, I don't see any interest in negotiations on either side. However, a year is a long time, and significant military successes for Ukraine, internal troubles or issues with Putin's health could bring changes about in Russia. In Ukraine, I think the most likely (though not necessarily likely in absolute terms) factor might be a significant deterioration of the humanitarian situation. Some of those can cause the sides to drop their maximum demands (which are presumably meant as bargaining chips) and seriously consider negotiations.
I’m surprised this is being predicted so highly. Ukraine has shown no willingness to enter ceasefire/peace talk agreements and I highly doubt that changes. Ukraine has the backing of major powers and unless NATO decide to cut back aid drastically I don’t see any movement from Ukraine.