I am a beginner in mathematical physics and geometric Langlands, having very limited knowledge in both fields so far.
The proof of geometric Langlands conjecture is published a few months ago. What are the possible impacts of this proof on the future developments of geometric Langlands related research? Does this proof resolve the main questions in the geometric Langlands program, or are there new directions, generalizations, or open questions that it might inspire? Besides, I am curious if the techniques involved in the proof introduce new tools or perspectives that may influence research in other fields.
I am specifically interested in:
- The intersection between geometric Langlands and physics (conformal field theory, gauge theory, etc).
- The relations between geometric Langlands and higher category theory/derived algebraic geometry.
Possible impacts of the proof of geometric Langlands conjecture in other topics/fields are also welcomed.
Here is a nice thread on implications of geometric Langlands conjecture but it was asked and answered more than one decade before the proof was released.