Well, you definitely caught my attention with that opening.
I can't think of much to say that hasn't been said already. You give the reader just enough about a character to begin to be intrigued, but like LTU said, the scene shifts before we can become hooked or start to truly have an interest in the character.
The reactions of the various people seem a little... weak. Unnamed townspeople cry for Alvis' blood, but Garis just exiles him, and this other guy gives the boy some boots. That seems a bit too lenient for matricide. Admittedly, I don't know much about your world yet, and it could be a slap on the wrist is customary for killing one of your parents - of course, if this is the case, you need to show it more clearly.
Both chapters also seem very, very short. This isn't necessarily a bad thing, but in the case of these two, I want to see more. There needs o be some expanding, some further development with what is going on. Everyone seems to agree to exile much too easily - why? Is there a reason they want to be rid of Matherly? I assume there is, based off Garis' thoughts.
What I would like to see, and this is just me personally, is someone insisting throughout the scene that the boy must be killed. Matherly, naturally, would disagree, some tension can build, and then Garis comes in with his 'compromise' that kills two birds with one stone - delivers a punishment for the boy, and gets the professor out of town for whatever reason. Something like that.
Going back to tension, I felt it was missing in this chapter when there were several great opportunities for it to build. You hooked me perfectly with that opening, making me want to read more. You have my attention, but you need to do better to keep it.
The same can be said about chapter two. Much to short, and lacking in force. The dialogue, I don't know. I apparently have some issues with it myself, and I can't find anything too wrong with yours. It could be better, but it could also be a lot worse. I'd focus more on setting and character before I worried to much on dialogue. You've given enough of both to be almost interesting, but it needs to be fleshed out a bit to make me really care.
Reading back over all of this, it seems rather negative, so let me clarify that I like what's there. It has potential to be very strong, but it's not there yet. For now, I say keep writing, and you can fix and expand as you go along. If you are discovery writing, then that's what you need to do - chances are you'll have sudden flash of inspiration in a later chapter, come back to chapter one and expand on whatever, making changes to everything written thus far to make the idea work.
I look forward to seeing more.