Office: C-518 Wells Hall.
Office Hour: Wednesday 2:30-3:30pm (SS18)
Email: ustun (a t) mailbox (d o t) org (PGP Public Key)
I am interested in G2 and Spin(7) manifolds. More specifically, I am working on problems related to their
calibrated submanifolds (they are of dimension 3 or 4). In my current project, I use algebro geometric techniques to understand the minimal
compactification of the (complexified) Cayley Grassmannian. I am also interested in Seiberg-Witten theory, low
dimensional topology and applications of algebraic geometry to these topics.
You can find the class page at D2L.
I have written some code in Haskell to help me with my calculations.
They are intended to be used in an Haskell interpreter but you may always fork the repository to suit your own needs or email me if you want to contribute.
Specifically, it is helpful with
complex octonions (of course, you can restrict to any subalgebra or if you only use real coefficients, you get the octonions with the positive definite metric)
matrices (including induced matrices on exterior algebra)
multiple cross products
associative, coassociative and Cayley calibrations
a little bit of exterior algebra calculus