# Glen M. Wilson

Email: glen.m.wilson (at) ntnu.no
Office: ...
Office hours: By appointment
Curriculum Vita (Last Updated 8/2018)
Mathematical interests: Algebraic topology, homotopy theory, differential topology, algebraic geometry, K-theory, category theory.

### Neat math stuff

Visual Insight, a blog edited by John Baez.
• Interesting formulas about the Steenrod operations: $$(\mathrm{Sq}^{12})^6 = \mathrm{Sq}^{49}\mathrm{Sq}^{17}\mathrm{Sq}^5\mathrm{Sq}^{1}$$ and $$(\mathrm{Sq}^{12})^7 = 0.$$ In the paper The Steenrod Algebra and its Dual (corollary 7 p. 169), John Milnor showed that for any $$i \geq 1$$ there exists a smallest integer $$n$$ for which $$(\mathrm{Sq}^i)^{n} = 0$$. The integer $$n$$ is called the height of $$\mathrm{Sq}^i$$. Can you figure out a formula for how $$n$$ depends on $$i$$? Here is a list of the powers $$(\mathrm{Sq}^{i})^n$$ expressed in terms of the admissible basis for $$i \leq 32$$.
• Exciting update about the question above pertaining to the Steenrod algebra. Kenneth Monks determined upper bounds and explicit formulas for the "nilpotence" (or height) of elements of the Steenrod algebra in the paper Nilpotence in the Steenrod algebra.