You can find out if you need a visa for Ecuador at Ecuadorian Migration Agency web page Requirements for Visa Application. Here you can find what do you need do to obtain the visa.
If you need a visa to attend the conference, you can get the required invitation letter. Please note that you need to register to the conference before requesting an invitation letter. The invitation letter will be sent to the provided email address.
You can fill in the information required for the visa invitation letter at the following link.