# Seminars this semester

Series:

 Oct 9 Tue Angelo Rendina (Sheffield) 14:00 J11 Nearly holomorphic Siegel modular forms and applications Abstract: Nearly holomorphic modular forms were introduced by Shimura as a generalization of modular forms to study a more general class of Eisenstein series. I will introduce some of the tools that we use to work with them, such as the Shimura-Maass differential operator and holomorphic projection, and present some applications: some formulae for the sum of divisor $s_r$ and Ramanujan $\tau$ functions and then congruences of critical $L$-values attached to Siegel modular forms, the latter being part of my research project. Oct 23 Tue Kim Klinger-Logan (Minnesota) 14:00 J11 The Riemann Hypothesis and periods of Eisenstein series Abstract: This summer at Perspectives on the Riemann Hypothesis, Bombieri and Garrett discussed modifications to the invariant Laplacian $\Delta=y^2(\partial_x^2+\partial_y^2)$ on $SL_2(\mathbb{Z})\backslash\mathfrak{H}$ possibly relevant to RH. We will present a $GL(2)$ $L$-function as a period of Eisenstein series which can, in turn, be thought of as a linear functional on an Eisenstein series and we will discuss how such functionals may be use to analyze the zeros of the $L$-function. This idea is an extension of recent work of Bombieri and Garrett and uses techniques from functional analysis and spectral theory of automorphic forms. Oct 30 Tue Adel Betina (Sheffield) 14:00 J11 On the p-adic periods of semi-stable modular curves Abstract: I will present a joint work with E.Lecouturier in which we prove a variant of Oesterlé's conjecture about $p$-adic periods of the modular curve $X_0(p)$, with an additional $Γ(2)$-structure. We use de Shalit's techniques and $p$-adic uniformization of Mumford curves whose reduction is semi-stable. Nov 6 Tue Vlad Serban (Vienna) 14:00 J11 A finiteness result for families of Bianchi modular forms Abstract: We develop a p-adic "unlikely intersection” result and show how it can be used to examine which Hida families over imaginary quadratic fields interpolate a dense set of modular forms for GL2 over an imaginary quadratic field. In this way we arrive at the first proven examples where only finitely many classical automorphic forms are on a p-adic family. Nov 20 Tue Ciaran Schembri (Sheffield) 14:00 J11 TBA Nov 27 Tue Jack Shotton (Durham) 14:00 J11 TBA Dec 11 Tue TBA 14:00 J11 Dec 13 Thu Alice Pozzi (UCL) 14:00 J11 TBA