5 problems

Let $G$ be a reductive algebraic group with involution $\theta$, let $K=G^{\theta}_0$ be the identity component of the fixed-point group, and let $B\supset H$ be a $\theta$-stable…

Equivariant signature conjecture. The signature of the invariant residue pairing satisfies

Strong positivity conjecture of Mather classes. The coefficients satisfy $a_v>0$, and $a_v(t)=a_v(\alpha_1,\ldots,\alpha_r)$ is a polynomial in the positive simple roots…

Let $X=G/P$ be a cominuscule space, and let $v,w\in W^P$. Write the Mather class of the Schubert variety $X_w^P$ as … The local Euler obstruction coefficients $e_{w,v}$ are non-neg…

Let $G$ be a complex algebraic group, let $p$ be a fixed odd prime, and consider the refined cycle class map … Assume that the complex cobordism ring of $\mathbf{B}G$ is concentrat…