Hello Math Stack Exchange Community,
As I embark on the journey of selecting a PhD research topic in mathematics, my interests are gravitating towards model theory, with a specific focus on combinatorics in NIP theories, and exploring the notion of tameness, including aspects of Shelah's classification theory.
While I realize that seeking PhD topic suggestions here might be somewhat atypical, I believe this community's diverse expertise could offer invaluable perspectives. I have had preliminary discussions with a few professors on these topics, but I am eager to broaden my horizon by considering insights from a wider academic community.
I am particularly interested in any open problems or emerging research areas within model theory that intertwine with combinatorics in NIP theories, or that delve into the concept of tameness, especially in the context of Shelah's classification. Suggestions that are slightly adjacent to these specific interests are also welcome, as they might provide a fresh angle to my research.
Your thoughts and guidance on potential PhD topics in this realm would be greatly appreciated. Thank you for taking the time to read my query and for any suggestions you might offer!