5 problems

Let $J_m(n)$ denote the join of $m$ suitably balanced cycles on $n$ vertices, the proposed extremal flag odd-dimensional sphere. Adamaszek–Hladký pseudomanifold upper bound conject…

Generalized upper bound conjecture for sublevels. Then

Let $J_m^*(n)$ be the suspension of a join of $m$ balanced cycles as defined in the source, and let $\mathcal{J}_m^*(n)$ be the family of joins $S*C_2*\cdots*C_m$ with $S$ a flag 2…

Let $J_m(n)$ be the simplicial $(2m-1)$-sphere on $n$ vertices obtained as the join of $m$ cycles, each having either $\lfloor n/m\rfloor$ or $\lceil n/m\rceil$ vertices. Flag uppe…

Kühnel's conjecture. The inequality