My talk will focus on the brain mechanisms of addiction with a particular emphasis on the use of brain imaging [both PET and MRI]. I will discuss the latest research in relation to the neurotransmitter mechanisms of addiction and show how we can develop imaging techniques to explore the modes of actions of existing and novel treatments for addiction

Certain nontempered liftings from PGL (2) × PGL (2) to PGSp (4) are constructed using the theory of (local and global) theta lifts. The resulting representations on PGSp (4) are the SaitoKurokawa representations. The lifting is shown to be functorial under certain reasonable assumptions on the local Langlands correspondence for PGSp (4). Introduction. The classical Saito-Kurokawa lifting associ...

Let f ∈ S2κ−2(Γ0(M)) be a Hecke eigenform with κ ≥ 2 even and M ≥ 1 and odd and square-free. In this paper we survey the construction of the Saito-Kurokawa lifting from the classical and representation theoretic point of view. We also provide some arithmetic results on the Fourier coefficients of Saito-Kurokawa liftings. We then calculate the norm of the Saito-Kurokawa lift.

Masahiko Yokoi, Sho-ichi Yamagishi, Akari Saito, Yumiko Yoshida, Takanori Matsui, Wataru Saito, Shigeki Hirose, Kazuhiro Ohgami, Manabu Kase, Shigeaki Ohno . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

— We associate to any convenient nondegenerate Laurent polynomial f on the complex torus (C) a canonical Frobenius-Saito structure on the base space of its universal unfolding. According to the method of K. Saito (primitive forms) and of M. Saito (good basis of the Gauss-Manin system), the main problem, which is solved in this article, is the analysis of the Gauss-Manin system of f (or its univ...

— We associate to any convenient nondegenerate Laurent polynomial f on the complex torus (C∗ )n a canonical Frobenius-Saito structure on the base space of its universal unfolding. According to the method of K. Saito (primitive forms) and of M. Saito (good basis of the Gauss-Manin system), the main problem, which is solved in this article, is the analysis of the Gauss-Manin system of f (or its u...

The first part of the paper contains a detailed proof of M. Saito’s generalization of the Kodaira vanishing theorem, following the original argument and with ample background. The second part contains some recent applications, and a Kawamata-Viehweg-type statement in the setting of mixed Hodge modules.

There exist two different generalizations of the classical Saito–Kurokawa lifting to modular forms with (square-free) level; one lifting produces modular forms with respect to Γ0(m), the other one with respect to the paramodular group Γ(m). We shall give an alternative and unified construction of both liftings using group theoretic methods. The construction shows that a single elliptic modular ...