You have the following options to get to Cádiz, Spain:

Flight to Madrid

From Barajas Airport you can take a train to Atocha Rail Station, from 5.59 to 22.28 hours, each 30 minutes and the duration is 25 minutes.
In Atocha Rail Station you can take a train to Cádiz (Duration of the trains: 4 hours). Link to the Rail Station company.

Flight to Sevilla

From Sevilla Airport you can take a bus to Santa Justa Rail Station, from 5:20 to 00:45 hours, each 20 minutes aprox. and the duration is 30 minutes.  Special Airport Line Info.
In Santa Justa Rail Station you can take a train to Cádiz (Duration of the trains: 1h 40 min.) Link to the Rail Station company.

Flight to Jerez de la Frontera

From Jerez de la Frontera Airport you take a train o bus to Cádiz. You can see the current timetable in this link.

The conference will be held at 1,6 Km from the Cádiz Rail Station (last stop of the train).