there are two ways (atleast) to do this.
the expensive way: [sub-domain pointers]
get the website hosting company of mycompany.com to offer you and setup a sub-domain pointer for mycompany.com/eventname
e.g. sub-domain pointer www.eventname.com points to www.mycompany.com/eventname
some hosting companies do not offer this service, some offer it for a fee.
the free way 
: [url forwarding]
i had the same issue when i setup my site… and this is how i did it…
go to www.mydomain.com and sign up. no really, that’s the website address, not an example
transfer the hosting (not the registrar) of www.eventname.com to www.mydomain.com’s service. how this is done is explained on their site.
once the domain is transferred to mydomain.com (about 48 hrs) , login to the control panel and setup domain forwarding. www.eventname.com will now point to www.mycompany.com/eventname
this method is simple, efficient and free. i have used the service for over 2 years and therefore can vouch for their reliability and level of service.
so that you understand how it’s done, i shall link my site here:
my problem was i couldn’t afford hosting space… so i got some space on www.ideadutch.com/notcomguys
and i registered the domain name www.notcomguys.com
now i wanted www.notcomguys.com to resolve to www.ideadutch.com/notcomguys/index.htm
i also had an additional requirement… i needed this to be done without the reader seeing www.ideadutch.com/notcomguys in the url bar when s/he comes to my site. i needed the url bar to display www.notcomguys.com
this is done by using a feature called stealth forwarding in the control panel options of mydomain.com
so here’s my site… you can see the end result:
http://www.notcomguys.com
(note how it’s hosted on another site’s subdirectory)
if you have any further questions, lemme know…