# Ustun Yildirim

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)

### Teaching (SS2018)

You can find the class page at D2L.

### Research Interests

I am interested in $$G_2$$ and Spin(7) manifolds. More specifically, I am working on problems related to their calibrated submanifolds (which are volume minimizing submanifolds of dimension 3 in $$G_2$$ case or 4 in Spin(7) case). I am also interested in Seiberg-Witten theory, low dimensional topology and applications of algebraic geometry to these topics.

### Preprints

2) (with S. Akbulut) Complex $$G_2$$ manifolds

1) On the minimal compactification of the Cayley Grassmannian

### Slides

Associative and Cayley Grassmannians (GSTGC 2018)

### Coding

Octonions and Cayley Grassmannian repository

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)
• Laurent polynomials
• Jacobian calculations
• matrices (including induced matrices on exterior algebra)
• multiple cross products
• associative, coassociative and Cayley calibrations
• a little bit of exterior algebra calculus
• and more

### Other

My blog (not very active)

I use MathJax to render math on web. E.g. $$e^{it}=\cos(t)+i\sin(t)$$.