Geometry of singular differential equations

Notes will appear here as we progress through the term.

Please discuss the problems, but avoid reading a written solution before you write your own, since these must be original. Also, do not share written solutions with anyone, even after the deadline.

Late assignments will not be accepted: please hand in whatever you have at the deadline.

Assignments are marked for correctness, but also clarity. Keep your solutions concise, and make sure the structure of your argument is clear.

All assignments must be submitted in LaTeX, I suggest using Overleaf if you need to get up to speed quickly.

• Perturbation theory, divergent series, and asymptotic expansions
• The Borel–Laplace method, Borel resummation, resurgence
• Stokes phenomenon
• Regular and Irregular singularities
• Riemann surfaces of infinite type and endless analytic continuation
• Groupoids for singular differential equations

• “The Stokes Groupoids”, by Gualtieri, Li and Pym
• “Asymptotics and Special Functions”, by Olver
• “Algebraic analysis of singular perturbation theory”, by Kawai and Takei
• “Spectral networks”, by Gaiotto, Moore and Neitzke
• “The resurgent structure of quantum knot invariants”, by Garoufalidis, Gu, and Marino
• “Resurgent methods in semi-classical asymptotics”, by Delabaere and Pham
• more to follow.