On the Arithmetic of Del Pezzo Surfaces of Degree 2

We study the arithmetic of certain del Pezzo surfaces of degree2. We produce examples of Brauer-Manin obstruction to the Hasseprinciple, coming from 2- and 4-torsion elements in the Brauergroup. 2000 Mathematics Subject Classification 14G05 (primary),12G05 (secondary).     

Effectivity of Brauer–Manin obstructions on surfaces

We study Brauer–Manin obstructions to the Hasse principle and to weak approximation on algebraic surfaces over number fields. A technique for constructing Azumaya algebra representatives of Brauer group elements is given, and this is applied to the computation of obstructions.     

Quantum Pieri rules for isotropic Grassmannians

We study the three point genus zero Gromov-Witten invariants on the Grassmannians which parametrize non-maximal isotropic subspaces in a vector space equipped with a nondegenerate symmetric or skew-symmetric form. We establish Pieri rules for the classical cohomology and the small quantum cohomology ring of these varieties, which give a combinatorial formula for the product of any Schubert class with certain special Schubert classes. We also give presentations of these rings, with integer coefficients, in terms of special Schubert class generators and relations.     

Effectivity of Brauer-Manin obstructions

We study Brauer-Manin obstructions to the Hasse principle and to weak approximation, with special regard to effectivity questions.     

Adiabatic electron-phonon interaction and high-temperature thermodynamics of A15 compounds

Inelastic neutron scattering was used to measure the phonon densities of states of the A15 compounds V3Si, V3Ge, and V3Co at temperatures from 10 to 1,273 K. It was found that phonons in V3Si and V3Ge, which are superconducting at low temperatures, exhibit an anomalous stiffening with increasing temperature, whereas phonons in V3Co have a normal softening behavior. First-principles calculations show that this anomalous increase in phonon frequencies at high temperatures originates with an adiabatic electron-phonon coupling mechanism. The anomaly is caused by the thermally induced broadening of sharp peaks in the electronic density of states of V3Si and V3Ge, which tends to decrease the electronic density at the Fermi level. These results show that the adiabatic electron-phonon coupling can influence the phonon thermodynamics at temperatures exceeding 1,000 K.     

Quantum Giambelli formulas for isotropic Grassmannians

Let X be a symplectic or odd orthogonal Grassmannian which parametrizes isotropic subspaces in a vector space equipped with a nondegenerate (skew) symmetric form. We prove quantum Giambelli formulas which express an arbitrary Schubert class in the small quantum cohomology ring of X as a polynomial in certain special Schubert classes, extending the authors?? cohomological Giambelli formulas.     

Phonons and thermodynamics of unmixed and disordered Li0.6FePO4

The lithium-storage material Li(0.6)FePO(4) was studied by inelastic neutron scattering and differential scanning calorimetry. Li(0.6)FePO(4) undergoes a transformation from a two-phase mixture (heterosite and triphylite) to a disordered solid-solution at 200 degrees C. Phonon densities of states (DOS) obtained from the inelastic neutron scattering were similar for the two-phase sample measured at 180 degrees C and the disordered sample measured at 220 degrees C. The vibrational entropy of transformation is 1.8 +/-0.9 J/(K mol), which is smaller than the configurational entropy difference of approximately 3.1 J/(K mol). The measured enthalpy of the disordering transition was estimated as 2.5 kJ/mol. The phonon data show a small change in lattice dynamics upon disordering.