Confront the King
Traven knows what the Black Soul Gem you recovered from Falcar was intended for: him. The Necromancers were planning an assault on the Arcane University itself with the intent of taking Traven's soul to increase the King Of Worms' powers. Your actions at Silorn have deprived them of that and now it's time for you to take the fight to them. Traven will use the soul gem, although not as Mannimarco intended because it will protect you from Mannimarco. He tells you that he's leaving the guild in your care and hopes that you will lead it well. Then he Soul Traps himself and dies, leaving you with a Collossal Black Soul Gem and a dead Arch-Mage. You're now the guy in charge.
Your destination is Echo Cave, more or less west of Bruma and Cloud Ruler Temple. There is a guard out front, Bolor Savel, who says that he'll die defending the door. I'm sure you can accomodate his request. Being the sneak that I am, I like to approach from above and snipe rather than do the head-on confrontation, so I don't get to do the conversation very often. Of course I also get visited by the Dark Brotherhood a lot, too. If you're capable of it, it's possible to pickpocket the key and sneak by rather than fight him.
Echo Cave is a three-level Necromancer Lair and, of course, Mannimarco is at the bottom of the 3rd level. The areas in between are populated by (what else?) Necromancers and Undead. When you get down to the third level, you have a couple of choices - the head-on approach or the stealth approach. The head-on approach is simple enough - go in with guns blazing and hope that you don't end up dead (or un-) in the process. The stealth approach is a bit subtler, but will get you closer when it's time for the fighting.
Rather than go through the gate and across the bridge, take the underwater route to come out on the side of the lake surrounding his little island. Then sneak over. With luck, you can get off a really good bow backstab before he even knows you're there (you can't get close enough for a melee backstab). This should short-circuit his villain rant and launch right into the combat.
If not, you'll have to endure the rant (your controls are locked, so there isn't anything you can do until he finishes). He'll offer you the choice of opposing him and he'll turn you into a Worm Thrall or serve him, but by serving him he means as a Worm Thrall. Since you have to die either way, it's not really a choice. Once your controls are unlocked, lay into him. Surprisingly enough, he's a leveled creature, seven levels higher than you. He has a nifty ability that fortifies his intelligence (20 points), fortifies his health (100 points), increases his magic resistance (50%), resists paralysis (50%) and resists normal weapons (50%). However, he's a High Elf, so you've got built-in weaknesses to fire, frost and shock on your side and that Wizard's Fury that Polus taught you might be really handy about right now.
Once he's joined his followers, you can get to the looting. Lots of goodies in the chests and barrels around here and there's always his Staff of Worms if you decide to go into the Necromancer business.
When you get back to the Arcane University, Polus confirms your position as Arch-Mage and you pick up another quest. You need to talk to Julienne Fanis about the Alchemical Chest in the Arch-Mage's quarters. Once that is done, the chest will function.
So now you have some things in the Arch-Mage's Quarters to help you along: your own Spellmaker, your own Item-Maker and your ingredient chest. The ingredient chest is pretty simple. Place one sample of almost any ingredient into it, wait 24 hours and get 11 out of it. There are two excptions to this that I know of: Vampire Dust and Nirnroot.
If you put Vampire Dust into it, you'll get 11 additional portions instead of 10. Does anyone else hear that "ka-ching" sound? If you have completed the "Order of the Virtuous Blood" quest, you get 250 gold for each Vampire Dust that you collect, so that's 2500 gold per week by turning in the Vampire Dust. The second item is Nirnroot - the chest doesn't recognise it as being an ingredient, so if you put one in, you'll only get one out. Sorry, no shortcut to completing that quest. There may be a couple of other oddball ingredients that the chest doesn't recognise, but I didn't bounce a complete list off of the script. If there is a mod out there that adds additional ingredients to the game, you'll have to check to see whether the author also modified the script for this chest.
Anyway, you can only use the chest once per week. And if you do not take the ingredients out before the week is up, you'll lose all of them.