Add badges to README + links to Zulip

CONTRIBUTING.md

@@ -38,7 +38,7 @@ When filing an [issue](https://github.com/apache/polaris/issues), make sure to a
 4. What did you expect to see?
 5. What did you see instead?
 
-Troubleshooting questions should be posted on [dev mailing list](mailto:[email protected]) (you can [subscribe](mailto:[email protected])) instead of the issue tracker. Maintainers and community members will answer your questions there or ask you to file an issue if you’ve encountered a bug. 
+Troubleshooting questions should be posted on the [public chat](https://polaris-catalog.zulipchat.com/) (no invite needed) or on [dev mailing list](mailto:[email protected]) (you can [subscribe](mailto:[email protected])) instead of the issue tracker. Maintainers and community members will answer your questions there or ask you to file an issue if you’ve encountered a bug. 
 
 
 ### How to suggest a feature or enhancement

README.md

@@ -28,6 +28,13 @@ Documentation is available at https://polaris.apache.org, including
 [Polaris management API doc](https://polaris.apache.org/index.html#tag/polaris-management-service_other)
 and [Apache Iceberg REST API doc](https://polaris.apache.org/index.html#tag/Configuration-API).
 
+[![Zulip](https://img.shields.io/badge/Zulip-Chat-blue?color=3d4db3&logo=zulip&style=for-the-badge&logoColor=white)](https://polaris-catalog.zulipchat.com/)
+[![Build Status](https://img.shields.io/github/actions/workflow/status/apache/polaris/gradle.yml?branch=main&label=Main%20CI&logo=Github&style=for-the-badge)](https://github.com/apache/polaris/actions/workflows/gradle.yml?query=branch%3Amain)
+
+## Community
+
+Join us on the [Apache Polaris public chat](https://polaris-catalog.zulipchat.com/) (no invite needed).
+
 ## Development
 
 See [CONTRIBUTING](CONTRIBUTING.md) for contribution requirements.