Jason Polak, PhD

I am a postdoctoral fellow at the University of Melbourne until June 2018. I am currently looking for a new job.

What kind of research do I do? Here's an idea: did you know that the polynomial function f(x) = x3 + 6x2 + x permutes the elements of Z/9 (the integers modulo nine)? Not all polynomials permute the elements of the underlying coefficient ring. The ones that do are called permutation polynomials, and for finite coefficient rings the corresponding permutations form a group! Check out this recent paper to learn more about these polynomials.

Other than that, I'm interested mostly in algebra, finite rings and combinatorics, and related topics. I like to focus on concrete problems, often with a computational angle. Speaking of computational things: are you interested in finding colourful patterns? Try the game Znocks, my Znax clone written in JavaScript.

Papers

The Ring Structure on the Grothendieck Group of Commuting Endomorphisms over a Field
Submitted 2017-08-31!

The Polypermutation Group of an Associative Ring
Submitted 2017-07-02!

Counting Separable Polynomials in Z/n[x]
Published online in the Canadian Mathematical Bulletin 2017-04-13

A Cotriple Construction of a Simplicial Algebra Used in the Definition of Higher Chow Groups
Theory and Applications of Categories, Vol. 31, No. 13 (2016), pp. 384-387
Exposing Relative Endoscopy in Unitary Symmetric Spaces
Res. Math. Sci. Vol. 2. No. 1 (2015)
A Note on VH Subdivisions (with Daniel T. Wise)
Publ. Mat. 57 (2013), pp. 421-428.

Contact

You can contact me at . Please consider using my PGP public key (keyserver link) to encrypt the mail (see how to do this). But if you're sending me sensitive information, you should verify that this key has not been compromised.

Key fingerprint: F50B 455E F406 CA05 DBED 673F 6C62 3CB6 1BA5 D66C
The Yellow-tailed Black Cockatoo (Zanda funereus). Photo taken by Jason in Yarra Bend Park, Melbourne.