As a hetero male that is relatively new to management, what can I do to let my direct reports, indirect reports, and other colleagues know that they can report these kinds of things to me, and I will take them seriously? I don't have any women reporting directly to me right now, but it's very likely to happen over the next year, and I want to be proactive from the get-go.
Your eagerness to help is very good, and I think expressing that you care about these issues to your employees is great, but unless you tattoo it on your forehead, most employees won't know about your personal stances. Your personal stance will come much more into play when a complaint is brought to management level, since the odds of you being the one randomly handed it are pretty low.
I think the lowest hanging fruit in your own workplace will be to make sure the escalation structures that already exist are strong, protect those who are afraid, and have clearly defined expected fair outcomes for when a complaint is heard. Too often reports of problems just disappear into management and die down before anything happens because nobody's planned out what they are suppose to do if there is a problem.
