Jim Olsen is giving the CMS talk on 13 TeV results. CMS recorded 90% of the 4 inverse femtobarns delivered by the LHC, but only 2.8/fb were taken with the magnet at 3.8 Tesla (for the rest of the time the magnet was off due to a problem with the helium purity).
A plot of the dimuon invariant mass of 60,000,000 events collected by dimuon triggers was shown, which is a pleasure to watch. I will attach it here later.

CMS has 18 new searches for beyond-the-standard model effects. For objects with masses above 1 TeV the sensitivity of 2.2/fb of analyzed data may be larger than the sensitivity of 2012 data.

The diboson bump at 2 TeV is almost completely ruled out; so is the edge signal of SUSY that was seen in run 1 (a 2.6 sigma excess back then).

No deviation is seen in gluino searches. The limit extends to 1.7 TeV, thus ruling out the region favoured by Gordon Kane in a recent paper.
The narrow diphoton bump at 760 GeV seen by CMS is a 2.6 sigma effect, but once one takes into account the look-elsewhere effect, the significance goes down to 1.2 sigma. However, by combining with 8 TeV CMS data, the excess becomes a 3-sigma thing and 1.7 after accounting for the LEE correction.