We define the height of a motive over a number field. We show that if we assume the finiteness of motives of bounded height, Tate conjecture for the $p$-adic Tate module can be proved for motives with good reduction at $p$.

We give a complete classification of toroidal Seifert fibered surgeries on alternating knots. Precisely, we show that if an alternating knot $K$ admits a toroidal Seifert fibered surgery, then $K$ is either the trefoil knot and the surgery slope is zero, or the connected sum of a $(2,p)$-torus knot and a $(2,q)$-torus knot and the surgery slope is $2(p+q)$ with $|p|, |q| \ge 3$.

We prove the vanishing of the Futaki-type invariant defined by Tian and Zhu, which is an obstruction to the existence of Kähler-Ricci solitons.

It is shown that mass-parameter-dependent solutions of the imaginary-time magnetic relativistic Schrödinger equations converge as functionals of Lévy processes represented by stochastic integrals of stationary Poisson point processes if mass-parameter goes to zero.