Algebraic topology and sums of squares formulas
Akhil Mathew - UChicago
It is a classical fact that the product of a sum of two squares with a sum of two squares is naturally a sum of two squares. (One can also replace "two" by "four" or "eight.") But in general, it is not known exactly when a product of the sum of m squares with a sum of n squares can be represented as a sum of p squares. I will discuss how methods of algebraic topology have been used to study this question. In particular, the tools of algebraic topology produce tools to obstruct the existence of such formulas in general. Moreover, these tools can be adapted to study the analogous question in positive characteristic.
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