I think this is exactly what the strata of polite behavior known as "civility" and "professionalism" were invented for. If you must interact with him in order to do your job, do so in a calm and professonal manner, with absolutely no reference to his prior behavior. You need not make any overtures of friendship, or be warm or chatty in any way. By the same token, you need not be rude in return. Whenever you do not need to interact with him, avoid him.
I don't think snarky looks deserve the "cut direct", so if you encounter him in the hallway or he speaks to you, you should respond with neutral, conventional phrases ("good morning"), or a nod. Again, no friendliness required.
If he apologizes or excuses his rudness in manner satisfactory to you, or if enough time passes that you feel he should be given another chance, you can become as cordial as you were previously. But there is no specific obligation, or time frame when you are "supposed" to do this.