can I run askbot on tornado instead of django

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You can find simple tutorial for askbot/django + tornado there: Deploying Django Projects on Tornado

Also you need to patch tornado/wsgi.py in some places.

It is works for me.

Tornado is a webserver, django is not. I think if you really want it you can run askbot through tornado instead of some other webserver. It's unlikely that you will benefit from such configuration at this point because askbot does not yet heavily use asynchronous communication.

However running askbot without django is impossible, because it is written using Django framework. Just look at the askbot source code and see how many times there is a statement like from django... import xyz.