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We construct biharmonic real hypersurfaces and La-grangian submanifolds of Clifford torus type in CP n via the Hopf fibration; and get new examples of biharmonic submanifolds in S 2n+1 as byproducts .
In this thesis we study special cycles on Shimura varieties of orthogonal type. We confirm a conjecture of Kudla in [K2] on the modularity of generating functions of special cycles of any codimension on Shimura varieties of orthogonal type, provided their convergence. This is a generalization of theorems of Hirzebruch-Zagier, Gross-Kohnen-Zagier and… (More)
The performance of perovskite solar cells has been progressing over the past few years and efficiency is likely to continue to increase. However, a negative aspect for the integration of perovskite solar cells in the built environment is that the color gamut available in these materials is very limited and does not cover the green-to-blue region of the… (More)
The goal of this series of talks is to study the Gross–Zagier (GZ) formula and related results. The main results we will cover this semester are: • the original GZ formula [GZ] (lectures 2-6), • the result of Kolyvagin [Gr, Ru] and Wei Zhang [Zh], • Waldspurger's period formula [Wa], • the GZ formula of Yuan-Zhang-Zhang [YZZ]. Lectures 2-5 are basic and… (More)
Contents 1. Introduction 2 1.1. p-adic Maass functions and p-adic torus periods 2 1.2. A p-adic Rankin–Selberg L-function 4 1.3. A p-adic Waldspurger formula 6 1.4. Notation and conventions 6 2. Arithmetic of quaternionic Shimura curves 8 2.1. Fourier theory on Lubin–Tate group 8 2.2. Kodaira–Spencer isomorphism 9 2.3. Universal convergent modular forms 12… (More)
Solution-processed metal halide perovskite semiconductors, such as CH3NH3PbI3, have exhibited remarkable performance in solar cells, despite having non-negligible density of defect states. A likely candidate is halide vacancies within the perovskite crystals, or the presence of metallic lead, both generated due to the imbalanced I/Pb stoichiometry which… (More)
The Generalized Minimal Residual method (GMRES) is often used to solve a nonsymmetric linear system Ax = b. But its convergence analysis is a rather difficult task in general. A commonly used approach is to diagonalize A = XΛX −1 and then separate the study of GMRES convergence behavior into optimizing the condition number of X and a polynomial minimization… (More)