Dermot Mccarthy, Texas Tech University

Modular Forms and Cellular Integrals

Abstract: The Ap{\'e}ry numbers, which arise in the irrationality proofs for
$\zeta(2)$ and $\zeta(3)$, satisfy many intriguing arithmetic properties,
and are also related to the $p$-th Fourier coefficients of modular forms.
We describe sequences associated to Brown's cellular integrals, of which
the Ap{\'e}ry numbers are special cases, and discuss recent work on
proving that the connection to modular forms persists for these sequences
in general.