What branch can convene and adjourn congress?

Technically, yes. Article 2, Section 3 of the Constitution does give the President some power to adjourn (and convene) Congress, but under specific circumstances: "He may, on extraordinary Occasions, convene both Houses, or either of them, and in Case of Disagreement between them, with Respect to the Time of Adjournment, he may adjourn them to such Time as he shall think proper."

The conditions for adjournment are so limited that no president has ever exercised this administrative power.