Rational curves on smooth hypersurfaces of low degree

We study the family of rational curves on arbitrary smooth hypersurfaces of low degree using tools from analytic number theory

Cubic hypersurfaces and a version of the circle method for number fields

A version of the Hardy–Littlewood circle method is developed for number fields K/QK/Q and is used to show that nonsingular projective cubic hypersurfaces over KK always have a KK-rational point when they have dimension at least 88

A fast algorithm to compute L(1/2, f x X(q))

Let $f$ be a fixed (holomorphic or Maass) modular cusp form. Let \cq be a Dirichlet character mod $q$. We describe a fast algorithm that computes the value $L(1/2,f\times\chi_q)$ up to any specified precision. In the case when $q$ is smooth or highly composite integer, the time complexity of the algorithm is given by $O(1+|q|^{5/6+o(1)})$

Rational points on cubic hypersurfaces over F(q,t)

The Hasse principle and weak approximation is established for non-singular cubic hypersurfaces X over the function field Fq(t)Fq(t), provided that char (Fq)>3(Fq)>3 and X has dimension at least 6

Uniform Bounds for Period Integrals and Sparse Equidistribution

Let M=Γ∖PSL(2,R) be a compact manifold, and let f∈C∞(M) be a function of zero average. We use spectral methods to get uniform (i.e., independent of spectral gap) bounds for twisted averages of f along long horocycle orbit segments. We apply this to obtain an equidistribution result for sparse subsets of horocycles on M

Circularly Polarized Luminescence from Intramolecular Excimers

In this chapter, examples of circularly polarized luminescence (CPL) stemming from intramolecularly formed excimers will be reviewed. Emission from excimers has peculiar photophysical properties with respect to fluorescence of regular monomers. In addition, if the fluorophoric couple forming the excimer in the excited state is mounted on a chiral scaffold, a strong CPL can be usually observed. Examples of chiral scaffolds include oligopeptides, macrocycles, binaphthyl, and diaminocyclohexane derivatives. CPL from excimers has mainly been observed from pyrenes but other molecules are also able to give rise to such phenomenon, e.g., perylenes and 1,8-naphthalene monoimide. Excimer CPL can provide important information about the conformation of a molecule in the excited state and how it evolves depending on the environment (e.g., solvent and temperature) or external stimuli (e.g., light irradiation and cation addition). Moreover, thanks to the peculiar photophysical nature of excimers, the degree of circular polarization associated with excimer emission is usually much larger than the one associated with the absorption (electronic circular dichroism, ECD) for the same molecule. This allows to study chiroptical emission properties of molecules which are ECD-silent (ground state cryptochirality). As a whole, excimer CPL is an interesting and useful strategy to develop organic molecular systems endowed with bright and highly polarized luminescence