Office: Hylan 1001

Phone: (585) 276-7854 (not preferred)

Office Hours: Wed 2-5pm or by appt.

Email (work): ustun.yildirim (a t) rochester (d o t) edu

Email (personal): ustun (a t) mailbox (d o t) org

Lectures: MW 9-10:15 in Lattimore 201

Lectures: MW 2-3:15 in Gavett 312

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.

2) (with S. Akbulut) Complex \(G_2\) manifolds and Seiberg-Witten Equations

1) On the minimal compactification of the Cayley Grassmannian

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

- Symbolic tensor calculus on manifolds: a SageMath implementation
- My blog (not active)
- Some photos from our meetings with Selman
- I use MathJax to render math on web. E.g. \(e^{it}=\cos(t)+i\sin(t)\).

- Bernie Sanders: How corporate media threatens our democracy
- Richard Stallman's TEDx Talk: "Introduction to Free Software and the Liberation of Cyberspace"
- Protect your privacy and everyone's freedom. Use Tor browser.
- Here is my public key for authentic and/or private communication. (What is public key cryptography?)
- Maybe things above make more sense now, a year after I have posted them. Incidentally, this is why you can make a lot of money with "big data".
- How a handful of tech companies control billions of minds every day
- Privacy tools
- If you use Wikipedia every week, consider donating them a dollar or two.
- Do you want to buy a cute puppy?
- Natural vs Synthetic