It is my first post here but I have come to ask a question that will, hopefully, clear the ambiguity I have regarding the subject.
A bit of a background about myself - I am a physics undergraduate student (with a VERY strong inclination towards math) in my final year of UG studies and am deciding on a path for grad studies in mathematics. This year I did a summer-long research project on non-linear sigma models and their reduction to Riemannian Symmetric Spaces. It was the case that during this project I also picked up an interest in stochastic processes and stochastic DE, and subsequently asked my adviser about the merging of the two - stochastics and differential geometry. Turns out it's quite the blooming field! My primary physics/math interest is quantum computation (irrelevant here). In addition to that, I have also become interested in game theory (still in the air, have read only a single book on it till now), and have been a long-time fan of chess and RTS games like SC1,2; WC3. As a final note, I have experience with Mathematica and Java; math-wise have done all UG analysis courses (Measure Theory included) and learned abstract and linear algebra through projects.
Now, what I would like to know is what type of research-level mathematics goes into devising an AI tailored towards solving problems like chess or developing opponents for games like SC2? Can I translate my knowledge of analysis and geometry into something like this? Apart from the game-solving AI, that would be a good suggestion to look into for someone with my background?
Thank you very much!