Are there any mathematical explanations for the following surprising facts?
$$\int_{Gr(2,8)} c_{\text{top}}(TX(-2)) = 6556 = \frac{1}{2} \deg(E_7/P(\alpha_7)) + 1,$$
and
$$\int_{Gr(2,6)} c_{\text{top}}(TX(-2)) = 143 = \frac{1}{2} \deg(\mathbb{S}_{12}).$$
where $\mathbb{S}_{12}$ is the spinor variety of type $D_6.$
The homogeneous varieties $E_7/P(\alpha_7)$ and $\mathbb{S}_{12}$ appear in Landsberg-Manivel's spaces subexceptional series.

Related surprises appear in supersymmetric gauge theories studied by Dimofte and Gaiotto.

Added (Dec 2018):
$$\int_{Gr(2,5)} c_{\text{top}}(TX(-2)) = 22 = \frac{1}{2} \deg(Gr(3,6)) + 1.$$

This post imported from StackExchange MathOverflow at 2019-03-15 09:55 (UTC), posted by SE-user Richard Eager