I want to get server sockets working for HTTP/2 in Java, preferably TLS/https.
I\'ve got a TLS server socket working fine, but browsers will only talk HTTP/1.1 to it
Java won't get ALPN until at least JDK 9, which is slated for late 2016 or 2017.
Meanwhile, you can use Jetty's ALPN implementation, or better yet, use Jetty (or other servers as suggested) directly rather than doing your own HTTP/2 implementation using ServerSocket.
[Disclaimer, I am a Jetty committer] Jetty 9.3 has great support for HTTP/2, including HTTP/2 Push.