ReNewQuantum

Maxim Kontsevich (IHÉS) - Exponential integrals, Lefschetz thimbles and linear resurgence

June 30th 2020, 03:00 PM CEST 
ZOOM Seminar + YouTube Live Stream 

Lecture slides (pdf)

Very often in physics and mathematics we have an asymptotic expansion in small parameter which is divergent because the coefficients have factorial growth a_n ∼ n! exp(O(n)). The property of resurgence means that the Borel transform ∑_n a_nζⁿ/n! admits an analytic continuation, which allows to reconstruct the exact value of the original divergent series.

I will review the theory of resurgence and resummation for the asymptotic expansions of exponential integrals. I will illustrate the theory by finite-dimensional examples (Airy function, Stirling formula for Γ-function), and infinite-dimensional ones (heat kernel, quantum Chern-Simons theory).

Bertrand Eynard (IPhT)- Quantum curves and topological recursion.

July 28th 2020, 03:00 PM CEST 
ZOOM Seminar + YouTube Live Stream 
Abstract TBA

Marcos Mariño (UNIGE)- Topological strings, q-series, and a volume conjecture for toric Calabi-Yau manifolds

August 25th 2020, 03:00 PM CEST 
ZOOM Seminar + YouTube Live Stream 
We show that, as a consequence of the correspondence with spectral theory, topological string partition functions of toric Calabi-Yaus are encoded in quantum invariants similar to state integrals, which can be explicitly written in terms of q-series. The radial asymptotics of these q-series reconstructs the perturbative topological string. The volume conjecture, which relates the asymptotics of the quantum invariant to the hyperbolic volume, turns out to have a counterpart in this formulation of topological string theory: the asymptotic behavior of the quantum invariants is related to the "volume" of the Calabi-Yau at the conifold point. This is work done in collaboration with Jie Gu.