Matrix is an open source project that publishes the Matrix open standard for secure, decentralised, real-time communication maintained by the non-profit Matrix.org Foundation.
In practice, this provides chat rooms where you can connect and talk with people and it also allows you to send direct messages (which is essentially a chat room with two people).
There is a lot of good things about this in its details such as the fact that the network is formed by many different servers connecting together so there is no single corporation or government that has control over all of the communications. In a way, this idea is very similar to how e-mail works. Though, we get much more than e-mail here. We can send messages, we can make video calls and we can create rooms for discussions on different topics. Moreover, all these can be done in an encrypted way (via double ratchet encryption).
Another good feature of it is that it supports bridging messages from different chat applications into Matrix rooms. These bridges are programs that run on the server and communicate with the non-Matrix servers. For example, I can send and receive messages to and from someone connected to Signal (free and open source alternative to the malicious software Whatsapp) within Matrix.
The official public server of matrix is at matrix.org but there are numerous other servers all around the world. I have set up a matrix server on the domain freemath.xyz following a tutorial by Matthew Hodgson.
In order to connect to the server you need a client. There are many clients to choose from here. You can just download the mobile ones as an app. There are also web based ones that you can use. The most popular one seems to be Element. I set up a web based Element client at element.freemath.xyz. If you use that you will connect to our matrix server. Otherwise, in order to connect to our server, you will need to enter matrix.freemath.xyz as the address of the server in your favourite client.
So, please come join to the Matrix. I believe this is the future of communication. I hope mathematicians and scientists will adapt this open and secure way of communication. Interestingly, French government has already adopted Matrix. In our humble Matrix server, we have recently been having conversations about Floer homotopy type. There are many more things to communicate about!