Ryan Manion
University of Pennsylvania
About Me
Origins
I was born and raised in Pittsburgh, PA. I went to undergrad at the wonderful University of Pittsburgh. Contrary to popular belief that Pittsburgh is a wasteland clouded with soot, it is actually a nice place. And of course, I am a huge Steelers and Penguins fan! Who doesn't love Hines Ward and Sidney Crosby?
While at Pitt, I was an undergraduate teaching assistant and/or math tutor for 3 years. Teaching has always been a passion of mine.
Mathematical Interests
In one sentence, I'm interested in complex algebraic geometry and its applications to mathematial physics. In a few more sentences, I'm working in the theory of stacks and how they can be utilized as geometric backgrounds for string theory. This requires computations of sheaf cohomology on the stacks, to which one can develop and apply an intersection theory/Riemann-Roch theorem on stacks. In the process I've grown a love for equivariant geometry and its various localization theorems. The localization theorem of the Grothendieck group of coherent sheaves on a stack is pivotal in the formulation of the Riemann-Roch theorem, which can be nicely interpreted in terms of sheaf cohomology on the inertia stack.
Typical examples of equivariant spaces are symplectic manifolds and toric varieties, which are both interests of mine which I wish I knew more about. Other interests sparked from the above are in intersection theory, representation theory, and gauge theory. I'm also interested in Hodge theory, many other things involving the word "theory", and linear algebra over the complex numbers, in particular the Jordan Canonical form. :)
Complement of Mathematical Interests
Like most people, I'm into music. Like most guys who wanted to pick up girls at some point in their life, I play guitar. I enjoy fingerstyle guitar in the vein of Chet Atkins the most. Also, I'm in love with Radiohead, even though their latest album was a Let Down.
I'm a big fan of video games (mostly the old ones on NES/SNES). I've played Warcraft 2 online off and on since around 1998. Yes, some people still play it! Not to toot my own horn or anything, but I'm pretty good at it by now.
My two old roommates from Pitt and I are working on a video game of our own called Smiley's Maze Hunt. Check it out in the links section!
Other random interests include playing board games, biking, cooking, piano, watching really awful movies, playing ultimate frisbee, playing with my cats, and eating at Kim's.
Contact
Office: 3E6A
Office hours
Mon 2-3, Wed 6-7
