New MMR brackets in Starcraft II?

I believe the MMR cutoffs change too frequently to give a meaningful answer here. However the current leagues for Legacy of the Void according to Liquipedia are:

• Grandmaster: Top 200 players by region (1000 players total)
• Master: Top 4% of players by region
• Diamond: Next 23%
• Platinum: Next 23%
• Gold: Next 23%
• Silver: Next 23%
• Bronze: Bottom 4%

Each league is split into 3 tiers, with tier 1 requiring the highest MMR.

These numbers are approximate. Liquipedia cites www.rankedftw.com which you can check for more accurate numbers. (Interestingly, at the time of posting, Korea still uses the original distribution: Plat, Gold, Silver and Bronze each holding 20% and the upper 3 leagues holding the top 20% between them.)

Divisions, on the other hand, are mostly arbitrary:

There are numerous divisions within each League, with each division being composed of up to 100 players. The name of each division is made up of a word from Starcraft terminology, and a letter from the ICAO phonetic alphabet, such as Gold League/ Division Zeratul Juliet. The process of matchmaking is based solely on MMR and not on a player's division or league. This means players will often face opponents from other divisions, and may face opponents from different leagues.