My publications are also listed on INSPIRE and zbMATH.
Torus Knots in Lens Spaces & Topological Strings
Ann. Henri Poincaré 16(8), 1937-1967 (2015) [arXiv:1308.5509]
We study the invariant of knots in lens spaces defined from quantum Chern-Simons theory. By means of the knot operator formalism, we derive a generalization of the Rosso-Jones formula for torus knots in L(p,1). In the second part of the paper, we propose a B-model topological string theory description of torus knots in L(2,1).
The uses of the refined matrix model recursion (with A. Brini & M. Mariño)
J. Math. Phys. 52(5), 052305 (2011) [arXiv:1010.1210]
We study matrix models in the beta ensemble by building on the refined recursion relation proposed by Chekhov and Eynard. We present explicit results for the first beta-deformed corrections in the one-cut and the two-cut cases, as well as two applications to supersymmetric gauge theories: the calculation of superpotentials in N=1 gauge theories, and the calculation of vevs of surface operators in superconformal N=2 theories and their Liouville duals. Finally, we study the beta deformation of the Chern-Simons matrix model. Our results indicate that this model does not provide an appropriate description of the Omega-deformed topological string on the resolved conifold, and therefore that the beta-deformation might provide a different generalization of topological string theory in toric Calabi-Yau backgrounds.
Chern-Simons Invariants of Torus Links
Ann. Henri Poincaré 11(7), 1201-1224 (2010) [arXiv:1003.2861]
We compute the vacuum expectation values of torus knot operators in Chern-Simons theory, and we obtain explicit formulae for all classical gauge groups and for arbitrary representations. We reproduce a known formula for the HOMFLY invariants of torus links and we obtain an analogous formula for Kauffman invariants. We also derive a formula for cable knots. We use our results to test a recently proposed conjecture that relates HOMFLY and Kauffman invariants.
Knot Invariants, Chern-Simons Theory and the Topological Recursion, PhD Thesis, University of Geneva (2014)
Knot Operators in Chern-Simons Gauge Theory, Master's Thesis, University of Geneva (2009)