Can I use the mm.dd.yy date format in academic writing?
The International Standard ISO 8601 is YYYY-MM-DD.
See Wikipedia and A summary of the international standard date and time notation.

Sadly this is not used by everyone as can be seen in this article about date formats per country:


The most popular order is day-month-year (Little-Endian, cyan in the image), used by about 57% of the world population.
Next is year-month-day (Big-Endian, yellow), used by about 29%.
Then month-day-year (Middle-Endian, magenta), used by about 6%.
The remaining 8% use a mix of the above.




But, in the end the most important is the standards used in your university or the conference or journal you are sending your papers to.