22 problems

Let $f:{\mathbb{C}}^n\to {\mathbb{C}}^m$ be a map, and let its Thom polynomials be expressed in the Chern classes of $f$. Rimányi's Chern positivity conjecture. These Thom polynomi…

Positivity conjecture. Expanding this rational function in the domain $|z_1|\ll\dots\ll|z_d|$ gives a Laurent series with nonnegative coefficients. This is a stronger positivity st…

A Thom–Boardman class is a singularity class indexed by a sequence of nonnegative integers, and its Thom polynomial is the universal cohomology class representing the locus of maps…

Let $r$ be an orbit of the equioriented type $A$ quiver representation space, with Thom polynomial $\operatorname{Tp}_r$, and let $x^i$ denote the Chern roots associated to the $i$…

Let $(e_0,e_1,\dots,e_n)$ be a dimension vector for equioriented quiver representations, let $r$ be an orbit characterized by rank conditions, and write its Thom polynomial as … He…

Assume $l\geq 1$. Let $\underline{\eta}$ be a Mather T- or S-multisingularity, let $M(l)$ be the Mather bound, and let $\mathcal{C}_l$ be the class of maps under consideration. Wri…

Assume $l\geq 1$. Let $\mathcal{C}_l$ be the class of maps under consideration, let $\underline{\eta}$ be a T- or S-multisingularity, and let…

Let $T^{\mathrm{SSM}}(\tau,\ell)$ denote an SSM-Thom polynomial of a singularity $\tau$ and relative dimension $\ell$. For $\ell=0$, the SSM-Thom polynomials have alternating signs…

Let $T(\tau,cell)$ denote the ordinary Thom polynomial of a singularity $\tau$ for relative dimension $cell$. A polynomial is monomial positive when its expansion in Chern monomial…

Let $tp(A_\mu)$ be the Thom polynomial of the singularity type $A_\mu$, expanded in the Chern monomial basis. Rimányi's positivity conjecture. The Chern monomial basis expansion of…

Let $f:M\to N$ be a proper locally stable map, let $\overline{\underline{\eta}}$ be a prescribed multi-singularity type, and let…

Cobordism conjecture. This cobordism is oriented if $M$ and $N$ are oriented, the codimension $k$ is odd, and $r$ is even.

Let $f:M\to N$ be a holomorphic map, and consider the multipoint problem in which the residual polynomial is the kernel of Kazarian's sieve formula. Let $A_k$ denote the correspond…

Bérczi's neighbouring-coefficient conjecture. The quotient

Thom-polynomial coefficient-ratio conjecture. One has

Rimányi's conjecture. For every such multiindex, the coefficient is nonnegative:

Let $\operatorname{tp}_{A_n}(l)$ be the Thom polynomial of the Morin singularity $A_n$, written as a linear combination of Chern monomials, and let the width of a Chern monomial be…

Localization-form conjecture. If part (a) of the generating-function conjecture holds, then

Let $Q$ be a $[?]$-dimensional, commutative, nilpotent algebra with $\deg(\operatorname{tp}_Q(l))=\mu\cdot l+\gamma$. Write … and let $\operatorname{RES}$ denote the iterated resid…

Thom–Boardman constant conjecture. The constant $k_\eta$ is $1$ for Thom–Boardman singularities with arbitrary relative dimension $m-n$.

Let $ta]$ and $[?]$ be singularities, let $[\eta]|_\xi$ denote the restriction to $\xi$ of the Thom polynomial of $\eta$, and let $\overline\eta$ be the orbit closure of $\eta$. Ri…

Positivity conjecture. The coefficients in the Schur function expansion of a Thom polynomial are nonnegative.