For formal professional events, everything comes together to present you in a certain way, including hair, makeup, nails, etc. So here are some generally accepted hair and beauty rules to keep in mind:
Men –> Neat, not too much gel/product. Conservative hairstyles are preferable over more trendy looks. Facial hair should be styled and trimmed.
Women –> Hair should be styled, but without too much product. Having it untied is appropriate, so long as it is short or not falling in your face and distracting you. Long hair should be in a simple ponytail, bun, undo, etc. and if it is down, should be styled such that it is not getting in your face. Generally, your hair should not be distracting to you or to individuals whom you are interacting with. Avoid colorful and distracting hairbands, clips, and other accessories.
Makeup should be simple and natural. For example, eyeliner should not be thick or obtrusive, eye shadow should not be very colorful, lipstick should not be too apparent. Makeup should be used in a manner that is natural and does not stand out too much, since that can very easily be distracting in a professional setting.
Nails should be neatly done. If painted, they should not be chipped, sparkly, patterned, etc. Having nails natural and unpainted is also appropriate, but they should be cut and clean.