There’s a really good reason you didn’t find any existing projects. There aren’t any.
Do you know how a single phase ac induction motor manages to rotate when there is no rotational vector in a single phase supply? Better research that first. Hopefully you’ve studied that famous guy... what’s his name? Tes something or the other. Oh, right, Tesla.
If you have any doubts, rather than believe some unknown person on the Internet, call Marathon, give them the motor part number and ask them if you can run it on PWM. It should be a short, one word answer.
Hopefully you’ll quickly realize that a single phase motor wasn't such a good idea. If that’s the case, now is a good time to rethink your decision. There is a common motor design suited to PWM speed control. In fact, more of those motors are sold every day than single phase. If the professor selected the motor, you should ask for a refund - that is unless the course is to demonstrate how to destroy an otherwise perfectly good motor.
Maybe, just maybe, you might get lucky and you be able to control the motor speed, for a short time, assuming it’s unloaded. Put a load on it or run it below a certain speed and it’s game over. Quickly. Unfortunately, it will fail in a rather unspectacular fashion since it is a totally enclosed motor. No openings for the smoke to come out. What will be spectacular will be the IGBT’s blowing up. They’ll glow red for a second before that happens though. Watch closely, oh wait, no, don’t. They become shrapnel.
Finally, some (more) free advise. If you ever decide to test that power supply, better stand way back when you turn that on and make sure it’s fused! Do you have any idea of what the peak current in that diode bridge is going be? Hopefully there will be enough impedance in the feeder circuit that the bridge doesn’t go boom.