Using a DC voltage as the base for a transistor to amplify AC Voltage
I'm impressed with the thought that must have gone into your circuit, but unfortunately it is fundamentally wrong.

For one: it is not the base voltage that you want to control / increase, but the voltage across base to emitter or even better the current flowing from base to emitter. The transformer and the load (lamp) prevent this.

Another thing that will potentially go wrong is that your transistor at 120V(AC) will dissipate an impressive amount of heat during 30 minutes, eventually killing it. 

I can probably list several other things explaining why your circuit won't work, but the goal of this site is to help people creating electronics, rather than undermine their self confidence ;o)

The last issue I want to mention is that you force AC through the transistor where a BJT is only capable of controlling DC. As @JohnD mentioned in one of the comments, you should investigate how a TRIAC controls a lamp's brightness using phase control.

And at all times be very careful with mains power, it can seriously hurt you.