A319
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Total 8280.22; Flight Crew Type 6842.40
Aircraft Equipment Problem Critical
Air Traffic Control Provided Assistance; Flight Crew Returned To Departure Airport; Flight Crew Landed in Emergency Condition; Flight Crew Overcame Equipment Problem; General Maintenance Action
Aircraft
Departing ZZZ after takeoff aircraft was stuck in SRS (Speed Reference System) mode; unable to make flight director select a heading or NAV mode. Shortly thereafter; received ECAM for Eng 1 Reverser fault followed by Anti-Ice Capt Pitot. My ADI displayed the side stick position indicator as if we were on the ground followed by an electrical disturbance in the number one radio. The aircraft cycled into and out of ground mode as indicated by the side stick position indicator cycling on and off inflight. Each time it cycled; I could hear a clicking sound; like an electrical short in my headset. Ran QRH procedures for the reverser and pitot heat. We then [advised ATC] and Dispatch of our plan to return to ZZZ due to Eng 1 Reverser fault. I spoke to the flight attendants and the passengers to advise them of the issue. I gave the flight attendants the TEST and advised not to prep the cabin for an evacuation. On approach; when gear was selected down we received a LGCIU (Landing Gear Control Interface Unit) 1 fault; following the ECAM we continued for an overweight landing at 138.0 lbs with a smooth touchdown and hardly any braking. We referenced the QRH for the LGCIU ECAM before landing. We also referenced the QRH for landing/go around performance numbers. We exited the runway; had the Fire Chief inspect the aircraft for any obvious issues. We then taxied to the gate. Taxiing to the gate; several other lights and ECAM's came up and were entered in to the logbook. At the gate; I phoned the Chief Pilot and  Maintenance Control.
[Report narrative contained no additional information.]
A319 flight crew reported returning to the departure airport due to multiple ECAM warnings accompanied with cycling between air-ground modes immediately after departure.