10 problems

Let $G$ be an algebraic group whose classifying space $BG$ has cohomology concentrated in even degrees. Write $CH^*BG$ for its Chow ring and $MU^*BG/MU^{<0}(pt).MU^*BG$ for the ind…

The generalized quantum cohomology theory is defined by ${\bf MU}_{\Lambda}$, and the group of antiperiodic loops is the loop group appearing in the representation-theoretic constr…

The paper studies equivariant and nonabelian symplectic quotients in integral $K$-theory, where the results avoid torsion difficulties that obstruct analogous statements in integra…

Parity-vanishing surjectivity conjecture. If $\mathcal U^{\operatorname{ev}}(X)=0$ or $\mathcal U^{\mathrm{odd}}(X)=0$, then $\rho$ is a surjection.

Let $DMT(\mathbb Z)$ be the category of mixed Tate motives over $\mathbb Z$, let ${\rm Gal}_{\rm mot}(\overline{\mathbb Q}/\mathbb Q)$ be its motivic Galois groupscheme, and let…

Compatibility conjecture. In the context of Corollary, one can choose an $MU$-algebra structure on $MU/J$ compatible with any given structure of an $MU$-ring spectrum on $MU/J$.

Let $A$ be a finite abelian group, and let $\mathrm{MU}_A$ denote the equivariant complex cobordism spectrum. An equivariant formal group law is the equivariant analogue of a forma…

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…

Number-theoretic conjecture. There exists an integer

Toric polynomial generator conjecture. For each $n\geq 1$, there exists a smooth projective toric variety whose cobordism class can be chosen for the polynomial generator…