Lets provide useful examples of possible topics for a thesis or a research papers here:
Computer Science:
- Eclipse attacks on Ergo nodes and counter-measures (research on Bitcoin Core clients: https://www.usenix.org/conference/usenixsecurity15/technical-sessions/presentation/heilman etc)
- Looking for DoS attacks possibilities on Ergo nodes and counter-measures
- Improving blacklisting rules (introduce graylists maybe) for P2P layer
- Lazy loading of authenticated state (Load UTXO set's AVL+ tree lazily · Issue #1707 · ergoplatform/ergo · GitHub), finding most performant strategies and parameters for it
Economics / monetary:
- Implement LETS (local exchange trading system, collateralized or not), Local Exchange Trading Systems - ErgoDocs (do backend and UI, test within a group of people)
- Implement different monetary systems and applications on top of ChainCash GitHub - ChainCashLabs/chaincash: ChainCash - elastic peer-to-peer money collectively backed by blockchain assets and trust
Please feel free to add.