Olivia Dumitrescu

Quantum Curves for Hitchin Fibrations and the Eynard-Orantin Theory

We generalize the topological recursion of Eynard–Orantin (JHEP 0612:053, 2006; Commun Number Theory Phys 1:347–452, 2007) to the family of spectral curves of Hitchin fibrations. A spectral curve in the topological recursion, which is defined to be a complex plane curve, is replaced with a generic curve in the cotangent bundle T*C of an arbitrary smooth base curve C. We then prove that these spectral curves are quantizable, using the new formalism. More precisely, we construct the canonical generators of the formal

VANISHING THEOREMS FOR LINEARLY OBSTRUCTED DIVISORS

{\hbar}

On the effective cone of Pn blown-up at n+3 points

ħ-deformation family of D modules over an arbitrary projective algebraic curve C of genus greater than 1, from the geometry of a prescribed family of smooth Hitchin spectral curves associated with the

Emptiness of homogeneous linear systems with ten general base points

{SL(2,\mathbb{C})}

On linear systems of P^3 with nine base points

SL(2,C)-character variety of the fundamental group π1(C). We show that the semi-classical limit through the WKB approximation of these