Running the following code is known to have caused kernels to crash:
dataframe.to_parquet()

Using pyarrow instead of fastparquet seems to have resolved this issue.

On a side note, when kernels crash, its most likely a package hasn't been installed correctly, hence re-installing the package would resolve the issue. Its also possible other dependent packages could cause the package to fall over, in such cases, its best to start out with a new environment.
Finally, when using Conda environments, please avoid using pip to install packages.

Originally filed here #9347 (comment)