Google Scholar provides some interesting links to papers and articles surrounding my research.
Contact details
You can usually reach me at olof.sisask[AT-tecken]math.su.se.
Web polling with math
Dogl has made a free tool for creating LaTeX-friendly web polls and quizzes called Dogl MathMeter. It's super easy and quick to use, and is perfect for running in-class polls that involve math.
Dogl Calculus
I've helped make a mobile app, Dogl Calculus, that aims to make it easier for Calculus students to keep their problem solving skills fresh. The problems should be pedagogically sound, and let you practise wherever you are!
Public engagement
Have fun and understand stuff with interactive tools!
The text is in Swedish, but the ideas universal. Unfortunately these are not yet fully self-contained, and might not work terribly well on mobile phones, but they will hopefully make sense to you if you attended one of my public lectures or the teacher development day Kleinerdagen at the Royal Swedish Academy of Sciences (KVA). If you want any of the other materials we used, please email me!
Want to study the emergence of a giant puddle in the random raindrop model? Here's a visualisation. (Puddles merge according to their barycentres.)
What is the largest density of a subset of Z/pZ that does not contain a solution to either of the equations x1 + x2 = x3, x1 + 2x2 = 4x3 + 5x4? This paper shows that if p is large then the answer to such questions is essentially given by an analogous quantity in R/Z, answering a Z/pZ-version of a question of Ruzsa about subsets of [N].
A family of large density, large diameter sum-free sets in Z/pZ.
Work of Deshouillers, Freiman and Lev has shown that large sum-free subsets of Z/pZ are necessarily somewhat structured, in the sense that they have a dilate contained in a short interval. In particular, this is known to hold for sets of density at least 0.318. In this note we construct a family of sum-free sets of density 0.25 that do not have a dilate contained in a short interval.
Freiman isomorphisms between characters and linear limits of groups.
We prove that the minimum number of 3APs in a subset of Z/pZ of density delta, divided by p2, is the same as the minimum amount of 3APs in a subset of the R/Z of density delta, up to o(1) errors as p tends to infinity. In fact, our results are rather more general than this, dealing with the general question of moving between linear equation counts over any compact abelian groups. E-mail me if interested!
Bourgain's proof of the existence of long arithmetic progressions in A+B.
These are some notes I wrote while trying to understand Bourgain's proof of the existence of long arithmetic progressions in sumsets A+B. I found it easiest to think of Bourgain's work as establishing an Lp-almost-periodicity result for convolutions of functions.
This is a short note demonstrating how one may interpret the values of Zeta(2), Zeta(4) and related sums in an additive combinatorial fashion. The basic idea is that one can view these values as representing the number of solutions to some linear equation in a simple subset of Z/pZ. What about Zeta(3)? Read the note and try it yourself!