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In the first part of the talk I will discuss the Eynard-Orantin theory to the family of spectral curves of Hitchin fibrations over a smooth base curve C of genus at least 2. In the second part we generalize this construction to meromorphic Higgs fields with possibly singular spectral curve embedded in the compactified cotangent bundle. We identify the spectral curve of the Eynard-Orantin recursion with a divisor in a ruled surface over the curve C. We further apply recursion to quantize spectral curve. We present as simple examples of our theory meromorphic Higgs bundles over the rational curve, and we obtain well-known classical equations as Airy function and Catalan recursion. This talk is based on my joint work with Motohico Mulase.

For the fall quarter the seminar will usually be at 1pm, so this seminar is an hour later than usual.