Aluminium was linked with dementia in the 70s. The studies referred to long term exposure such as aluminium cookware leaching into food and daily use of anti-perspirants. This is not likely to be in any way similar to small and short term doses contained in gardisil.

I do not know if they ever proved a causal link but I don't use aluminium saucepans or aluminium containing deodorants. I WOULD however submit to gardisil shots if I was a young person