Ilia Gaiur (IHES) : Higher Bessel Product Formulas and multi-variable deformations of Landau-Ginzburg type potentials

Higher Bessel functions are the solutions to the quantum differential equations for $\mathbb{P}^{N-1}$. These functions are connected to the periods of the Dwork families via the Laplace transform, and the functions themselves are exponential integrals. In my talk, I will show how product formulas for these irregular special functions lead to other geometric differential equations associated with higher-dimensional families of algebraic varieties. I will discuss the geometric and algebraic properties of the periods for these families and later provide further perspectives on these correspondences. If time remains, I will discuss possible extensions of the formulas to the finite fields and to the q-commutative setting.