Synonym for the job title of assistant professor I often go to meetings and professional events outside academia.

I am meeting new people all the time, and most of them are not acquainted with academic ranks and job titles. It happens often that when they realize that my job title is 'assistant professor' they slightly dismiss me and suddenly give an impression that they see me inferior. 

Some even ask me who my professor is. So I don't think I am misinterpreting the situations.
Outside academia 'assistant' has often a connotation of a lower and dependent ranking, which may explain it.

I am not obsessed with titles, and I am happy with my job and position, but I have a feeling that in these situations it may close doors as I am getting dismissed before I can show anything.

As I am getting convinced that this happens only because of the job title, I started to think who can I introduce myself with another generic job title that sounds better and does more justice (that I am more senior than I appear: a project leader, supervising people, and do not assist someone).

Is there a synonym that I can use instead? The requirement is that a title isn't fake. I don't want to claim a title that does not belong to me. I just want to find a better way to introduce myself to those who are outside academia.
I was thinking about using titles such as senior scientist, research director, lecturer, but these are actual job titles. Principal investigator, while truthful, may not be understood.

Maybe I should also state that I am male, so it is not about gender. I can imagine that if I were female it would be even worse.
I think you should just introduce yourself as 


  I work as a professor at the University of X.


omitting the assistant rank that can cause misunderstandings. 

The following conversation line feels also very safe:


  – Where do you work?
  
  – I do research and teach at the University of X.


which might be a better fit since it explains your job in a short sentence. However, nothing wrong with the first line that does not require a question to feel natural.

The actual rank (assistant/associate/full) might matter in a formal (mostly, written and official) context and rarely means a lot outside of the academic system. And that seems to be exactly the situation you happen to encounter issues.

Related questions:


How an assistant professor is called in North America?
Can I call an assistant professor Professor?


Cultural and linguistic differences can play a role, so it might not be as appropriate in certain countries; though, I doubt that would matter at all in a circle that is not familiar with academic ranks at all. Moreover, it is likely that there is no confusion because the rank in the other language is very different.

You might also dig in the direction of "Head of XXX lab" (in case it applies) or "research group supervisor", but I don't think there is a good reason. An assistant professor is a professor and no elaboration is needed in a laid-back unofficial atmosphere.