Cast Echocasting Symposium by paying {4}{U}{U}, creating a token copy of Timestream Navigator and exiling Echocasting Symposium.
If you don't have the city's blessing, the Timestream Navigators will give you the city's blessing.
Activate the oldest Timestream Navigator by paying {2}{U}{U}, tapping it and putting it from the battlefield onto the bottom of your library, causing you to take an extra turn after this one.
Move to your next turn. At the beginning of your precombat main phase, Echocasting Symposium's paradigm ability triggers, causing you to cast a copy of it from exile. Resolve the copy, creating a token copy of Timestream Navigator.
Repeat from step 3.

Infinite turns

Lock

Timestream Navigator

Echocasting Symposium

Cast Time Warp by paying its mana cost, causing you to take an extra turn after this one.
Move to your next turn. At the beginning of your precombat main phase, Echocasting Symposium's paradigm ability triggers, causing you to cast a copy of it from exile. 
Resolve the copy, creating a token copy of Archaeomancer
When the Archaeomancer token enters, it triggers, returning Time Warp from your graveyard to your hand.
Repeat.

Archaeomancer

Time Warp

Cast Echocasting Symposium by paying {4}{U}{U}, causing an opponent to create a token copy of Phage and exiling Echocasting Symposium.
When the Phage token enters, it triggers, causing its controller to lose the game.
During your next turn, at the beginning of your precombat main phase, Echocasting Symposium's paradigm ability triggers, causing you to cast a copy of it from exile. Resolve the copy, causing an opponent to create a token copy of Phage.
Repeat from step 2.

Target player loses the game on each of your turns

Phage the Untouchable

Cast Echocasting Symposium by paying {4}{U}{U}, creating a token copy of Myr Battlesphere and exiling Echocasting Symposium.
When Myr Battlesphere enters, it triggers, creating four 1/1 Myr artifact creature tokens.
Activate Time Sieve by tapping it, sacrificing the Myr Battlesphere token and the four Myr tokens, causing you to take an extra turn after this one.
Move to your next turn. At the beginning of your precombat main phase, Echocasting Symposium's paradigm ability triggers, causing you to cast a copy of it from exile. Resolve the copy, creating a token copy of Myr Battlesphere.
Repeat from step 2.

Combos with "Echocasting Symposium"