Seminar series
Date
Mon, 16 Jun 2025
16:00
16:00
Location
C3
Speaker
Aleksandra Kowalska
Organisation
University of Oxford
In 2014, Lilu Zhao counted the solutions to non-degenerate, homogeneous quadratic forms in at least nine prime variables, using the circle method. However, while the suggested formula for the number of solutions is believed to hold for forms in at least five variables, his method seems to break for general forms in less than nine variables.
In 2021, Ben Green solved the problem for forms in eight prime variables (using a very different approach), satisfying a 'genericity' condition. The aim of my project was to solve some forms in eight variables not satisfying this condition.
In the talk, I will describe my findings, which allowed me to count the number of solutions to forms in eight prime variables with off-diagonal rank 3 (i.e., which have an invertible 3x3 submatrix without diagonal entries), which is a subset of non-generic forms.